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jeffreypierce/scala_v83.json

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scala_v83.json
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[
{
"id": "05_19",
"desc": "5 out of 19-tET",
"stepCount": "5",
"steps": ["252.63158", "505.26316", "757.89474", "1010.52632", "2/1"]
},
{
"id": "05_22",
"desc": "Pentatonic \"generator\"of 09-22.scl",
"stepCount": "5",
"steps": ["272.72727", "545.45455", "709.09091", "981.81818", "2/1"]
},
{
"id": "05_24",
"desc": "5 out of 24-tET, symmetrical",
"stepCount": "5",
"steps": ["100.00000", "550.00000", "650.00000", "1100.00000", "2/1"]
},
{
"id": "06_41",
"desc": "Hexatonic scale in 41-tET, Magic-6",
"stepCount": "6",
"steps": [
"321.95122",
"380.48780",
"702.43902",
"760.97561",
"1141.46341",
"2/1"
]
},
{
"id": "07_19",
"desc": "Nineteen-tone equal major",
"stepCount": "7",
"steps": [
"189.47368",
"378.94737",
"505.26316",
"694.73684",
"884.21053",
"1073.68421",
"2/1"
]
},
{
"id": "07_31",
"desc": "Strange diatonic-like strictly proper scale",
"stepCount": "7",
"steps": [
"116.12903",
"387.09677",
"425.80645",
"696.77419",
"812.90323",
"1006.45161",
"2/1"
]
},
{
"id": "07_37",
"desc": "Miller's Porcupine-7",
"stepCount": "7",
"steps": [
"162.16216",
"324.32432",
"486.48649",
"648.64865",
"810.81081",
"972.97297",
"2/1"
]
},
{
"id": "08_11",
"desc": "8 out of 11-tET",
"stepCount": "8",
"steps": [
"218.18182",
"327.27273",
"436.36364",
"654.54545",
"763.63636",
"872.72727",
"1090.90909",
"2/1"
]
},
{
"id": "08_13",
"desc": "8 out of 13-tET",
"stepCount": "8",
"steps": [
"92.30769",
"276.92308",
"461.53846",
"553.84615",
"738.46154",
"830.76923",
"1015.38462",
"2/1"
]
},
{
"id": "08_19",
"desc": "8 out of 19-tET, Mandelbaum",
"stepCount": "8",
"steps": [
"126.31579",
"315.78947",
"442.10526",
"568.42105",
"757.89474",
"884.21053",
"1010.52632",
"2/1"
]
},
{
"id": "08_37",
"desc": "Miller's Porcupine-8",
"stepCount": "8",
"steps": [
"162.16216",
"324.32432",
"486.48649",
"648.64865",
"810.81081",
"972.97297",
"1135.13514",
"2/1"
]
},
{
"id": "09_15",
"desc": "Charyan scale of Andal, Boudewijn Rempt (1999), 1/1=A",
"stepCount": "9",
"steps": [
"160.00000",
"320.00000",
"400.00000",
"560.00000",
"720.00000",
"800.00000",
"960.00000",
"1120.00000",
"2/1"
]
},
{
"id": "09_19",
"desc": "9 out of 19-tET, Mandelbaum. Negri[9]",
"stepCount": "9",
"steps": [
"126.31579",
"252.63158",
"442.10526",
"568.42105",
"694.73684",
"821.05263",
"947.36842",
"1073.68421",
"2/1"
]
},
{
"id": "09_19_a",
"desc": "Second strictly proper 9 out of 19 scale",
"stepCount": "9",
"steps": [
"126.31579",
"315.78947",
"378.94737",
"568.42105",
"694.73684",
"821.05263",
"947.36842",
"1073.68421",
"2/1"
]
},
{
"id": "09_22",
"desc": "Trivalent scale in 22-tET, TL 05-12-2000",
"stepCount": "9",
"steps": [
"109.09091",
"272.72727",
"381.81818",
"545.45455",
"709.09091",
"818.18182",
"981.81818",
"1036.36364",
"2/1"
]
},
{
"id": "09_23",
"desc": "9 out of 23-tET, Dan Stearns",
"stepCount": "9",
"steps": [
"156.52174",
"260.86957",
"417.39130",
"521.73913",
"678.26087",
"782.60870",
"939.13043",
"1043.47826",
"2/1"
]
},
{
"id": "09_29",
"desc": "Cycle of g=124.138 in 29-tET (Negri temperament)",
"stepCount": "9",
"steps": [
"124.13793",
"248.27586",
"372.41379",
"496.55172",
"620.68966",
"744.82759",
"868.96552",
"993.10345",
"2/1"
]
},
{
"id": "09_31",
"desc": "Scott Thompson scale 724541125",
"stepCount": "9",
"steps": [
"270.96774",
"348.38710",
"503.22581",
"696.77419",
"851.61290",
"890.32258",
"929.03226",
"1006.45161",
"2/1"
]
},
{
"id": "10_13_58",
"desc": "Single chain pseudo-MOS of major and neutral thirds in 58-tET",
"stepCount": "10",
"steps": [
"186.20690",
"289.65517",
"393.10345",
"537.93103",
"641.37931",
"744.82759",
"931.03448",
"1034.48276",
"1096.55172",
"2/1"
]
},
{
"id": "10_13",
"desc": "10 out of 13-tET MOS, Carl Lumma, TL 21-12-1999",
"stepCount": "10",
"steps": [
"184.61538",
"276.92308",
"369.23077",
"553.84615",
"646.15385",
"738.46154",
"923.07692",
"1015.38462",
"1107.69231",
"2/1"
]
},
{
"id": "10_19",
"desc": "10 out of 19-tET, Mandelbaum. Negri[10]",
"stepCount": "10",
"steps": [
"126.31579",
"252.63158",
"315.78947",
"442.10526",
"568.42105",
"694.73684",
"821.05263",
"947.36842",
"1073.68421",
"2/1"
]
},
{
"id": "10_29",
"desc": "10 out of 29-tET, chain of 124.138 cents intervals, Keenan",
"stepCount": "10",
"steps": [
"124.13793",
"248.27586",
"372.41379",
"455.17241",
"579.31034",
"703.44828",
"827.58621",
"951.72414",
"1075.86207",
"2/1"
]
},
{
"id": "11_18",
"desc": "11 out of 18-tET, g=333.33, TL 27-09-2009",
"stepCount": "11",
"steps": [
"133.33333",
"200.00000",
"333.33333",
"466.66667",
"533.33333",
"666.66667",
"800.00000",
"866.66667",
"1000.00000",
"1133.33333",
"2/1"
]
},
{
"id": "11_19_gould",
"desc": "11 out of 19-tET, Mark Gould (2002)",
"stepCount": "11",
"steps": [
"126.31579",
"252.63158",
"315.78947",
"442.10526",
"568.42105",
"694.73684",
"757.89474",
"884.21053",
"1010.52632",
"1136.84211",
"2/1"
]
},
{
"id": "11_19_krantz",
"desc": "11 out of 19-tET, Richard Krantz",
"stepCount": "11",
"steps": [
"126.31579",
"252.63158",
"378.94737",
"505.26316",
"631.57895",
"694.73684",
"821.05263",
"884.21053",
"1010.52632",
"1136.84211",
"2/1"
]
},
{
"id": "11_19_mclaren",
"desc": "11 out of 19-tET, Brian McLaren. Asc: 311313313 Desc: 313131313",
"stepCount": "11",
"steps": [
"189.47368",
"252.63158",
"315.78947",
"505.26316",
"568.42105",
"631.57895",
"694.73684",
"757.89474",
"947.36842",
"1010.52632",
"2/1"
]
},
{
"id": "11_23",
"desc": "11 out of 23-tET, Dan Stearns",
"stepCount": "11",
"steps": [
"104.34783",
"208.69565",
"313.04348",
"417.39130",
"521.73913",
"678.26087",
"782.60870",
"886.95652",
"991.30435",
"1095.65217",
"2/1"
]
},
{
"id": "11_31",
"desc": "Jon Wild, 11 out of 31-tET, g=7/6, TL 9-9-1999",
"stepCount": "11",
"steps": [
"116.12903",
"232.25806",
"387.09677",
"503.22581",
"541.93548",
"658.06452",
"774.19355",
"929.03226",
"1045.16129",
"1161.29032",
"2/1"
]
},
{
"id": "11_34",
"desc": "Erv Wilson, 11 out of 34-tET, chain of minor thirds",
"stepCount": "11",
"steps": [
"70.58824",
"247.05882",
"317.64706",
"494.11765",
"564.70588",
"635.29412",
"811.76471",
"882.35294",
"952.94118",
"1129.41176",
"2/1"
]
},
{
"id": "11_37",
"desc": "Jake Freivald, 11 out of 37-tET, g=11/8, TL 22-08-2012",
"stepCount": "11",
"steps": [
"162.16216",
"259.45946",
"356.75676",
"454.05405",
"551.35135",
"713.51351",
"810.81081",
"908.10811",
"1005.40541",
"1102.70270",
"2/1"
]
},
{
"id": "11_limit_only",
"desc": "11-limit-only",
"stepCount": "11",
"steps": [
"12/11",
"11/10",
"11/9",
"14/11",
"11/8",
"16/11",
"11/7",
"18/11",
"20/11",
"11/6",
"2/1"
]
},
{
"id": "12_17",
"desc": "12 out of 17-tET, chain of fifths",
"stepCount": "12",
"steps": [
"70.58824",
"141.17647",
"282.35294",
"352.94118",
"494.11765",
"564.70588",
"635.29412",
"776.47059",
"847.05882",
"988.23529",
"1058.82353",
"2/1"
]
},
{
"id": "12_19",
"desc": "12 out of 19-tET scale from Mandelbaum's dissertation",
"stepCount": "12",
"steps": [
"63.15789",
"189.47368",
"252.63158",
"378.94737",
"505.26316",
"568.42105",
"694.73684",
"757.89474",
"884.21053",
"947.36842",
"1073.68421",
"2/1"
]
},
{
"id": "12_22",
"desc": "12 out of 22-tET, chain of fifths",
"stepCount": "12",
"steps": [
"163.63636",
"218.18182",
"381.81818",
"436.36364",
"490.90909",
"654.54545",
"709.09091",
"872.72727",
"927.27273",
"1090.90909",
"1145.45455",
"2/1"
]
},
{
"id": "12_22_h",
"desc": "Hexachordal 12-tone scale in 22-tET",
"stepCount": "12",
"steps": [
"109.09091",
"218.18182",
"327.27273",
"436.36364",
"490.90909",
"600.00000",
"709.09091",
"818.18182",
"927.27273",
"1036.36364",
"1145.45455",
"2/1"
]
},
{
"id": "12_27",
"desc": "12 out of 27, Herman Miller's Galticeran scale",
"stepCount": "12",
"steps": [
"133.33333",
"222.22222",
"311.11111",
"400.00000",
"533.33333",
"622.22222",
"711.11111",
"800.00000",
"933.33333",
"1022.22222",
"1111.11111",
"2/1"
]
},
{
"id": "12_31_11",
"desc": "11-limit 12 out of 31-tET, George Secor",
"stepCount": "12",
"steps": [
"38.70968",
"193.54839",
"270.96774",
"387.09677",
"464.51613",
"541.93548",
"696.77419",
"774.19355",
"890.32258",
"967.74194",
"1083.87097",
"2/1"
]
},
{
"id": "12_31",
"desc": "12 out of 31-tET, meantone Eb-G#",
"stepCount": "12",
"steps": [
"77.41935",
"193.54839",
"309.67742",
"387.09677",
"503.22581",
"580.64516",
"696.77419",
"774.19355",
"890.32258",
"1006.45161",
"1083.87097",
"2/1"
]
},
{
"id": "12_43",
"desc": "12 out of 43-tET (1/5-comma meantone)",
"stepCount": "12",
"steps": [
"83.72093",
"195.34884",
"306.97674",
"390.69767",
"502.32558",
"586.04651",
"697.67442",
"781.39535",
"893.02326",
"1004.65116",
"1088.37209",
"2/1"
]
},
{
"id": "12_46",
"desc": "12 out of 46-tET, diaschismic",
"stepCount": "12",
"steps": [
"104.34783",
"208.69565",
"286.95652",
"391.30435",
"495.65217",
"600.00000",
"704.34783",
"808.69565",
"886.95652",
"991.30435",
"1095.65217",
"2/1"
]
},
{
"id": "12_46_p",
"desc": "686/675 comma pump scale in 46-tET",
"stepCount": "12",
"steps": [
"130.43478",
"260.86957",
"391.30435",
"443.47826",
"521.73913",
"573.91304",
"704.34783",
"834.78261",
"965.21739",
"1069.56522",
"1095.65217",
"2/1"
]
},
{
"id": "12_50",
"desc": "12 out of 50-tET, meantone Eb-G#",
"stepCount": "12",
"steps": [
"72.00000",
"192.00000",
"312.00000",
"384.00000",
"504.00000",
"576.00000",
"696.00000",
"768.00000",
"888.00000",
"1008.00000",
"1080.00000",
"2/1"
]
},
{
"id": "12_79_mos_159_et",
"desc": "12-tones out of 79 MOS 159ET, Splendid Beat Rates Based on Simple Frequencies version, C=262hz",
"stepCount": "12",
"steps": [
"91.68918",
"197.53525",
"302.37506",
"392.90890",
"4/3",
"589.34246",
"3/2",
"792.07675",
"897.52405",
"1003.09655",
"1093.54687",
"2/1"
]
},
{
"id": "12_yarman_24_a",
"desc": "12-tones out of Yarman24a, circulating in the style of Rameau's Modified Meantone Temperament",
"stepCount": "12",
"steps": [
"84.36000",
"192.18000",
"292.18000",
"5/4",
"4/3",
"584.07906",
"696.09000",
"788.27000",
"888.27000",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "12_yarman_24_b",
"desc": "12-tones out of Yarman24b, circulating in the style of Rameau's Modified Meantone Temperament",
"stepCount": "12",
"steps": [
"84.36000",
"192.18000",
"292.18000",
"5/4",
"4/3",
"584.35871",
"696.09000",
"788.27000",
"888.27000",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "12_yarman_24_c",
"desc": "12-tones out of Yarman24c, circulating in the style of Rameau's Modified Meantone Temperament",
"stepCount": "12",
"steps": [
"85.05893",
"191.77076",
"292.41297",
"156/125",
"4/3",
"581.38190",
"695.88538",
"788.73595",
"887.65614",
"16/9",
"234/125",
"2/1"
]
},
{
"id": "12_yarman_24_d",
"desc": "12-tones out of Yarman24d, circulating in the style of Rameau's Modified Meantone Temperament",
"stepCount": "12",
"steps": [
"83.32982",
"190.84857",
"291.83661",
"381.69714",
"4/3",
"579.07643",
"695.42429",
"787.58321",
"886.27286",
"16/9",
"1083.65214",
"2/1"
]
},
{
"id": "13_19",
"desc": "13 out of 19-tET, Mandelbaum",
"stepCount": "13",
"steps": [
"126.31579",
"189.47368",
"315.78947",
"378.94737",
"505.26316",
"568.42105",
"694.73684",
"757.89474",
"884.21053",
"947.36842",
"1073.68421",
"1136.84211",
"2/1"
]
},
{
"id": "13_22",
"desc": "13 out of 22-tET, generator = 5",
"stepCount": "13",
"steps": [
"109.09091",
"218.18182",
"327.27273",
"381.81818",
"490.90909",
"600.00000",
"654.54545",
"763.63636",
"872.72727",
"927.27273",
"1036.36364",
"1145.45455",
"2/1"
]
},
{
"id": "13_30_t",
"desc": "Tritave with 13/10 generator, 91/90 tempered out",
"stepCount": "13",
"steps": [
"126.79700",
"253.59400",
"443.78950",
"570.58650",
"697.38350",
"887.57900",
"1014.37600",
"1141.17300",
"1331.36850",
"1458.16550",
"1584.96250",
"1775.15800",
"3/1"
]
},
{
"id": "13_31",
"desc": "13 out of 31-tET Hemiw�rschmidt[13]",
"stepCount": "13",
"steps": [
"154.83871",
"193.54839",
"348.38710",
"387.09677",
"541.93548",
"580.64516",
"735.48387",
"774.19355",
"929.03226",
"967.74194",
"1122.58065",
"1161.29032",
"2/1"
]
},
{
"id": "14_19",
"desc": "14 out of 19-tET, Mandelbaum",
"stepCount": "14",
"steps": [
"63.15789",
"189.47368",
"252.63158",
"315.78947",
"442.10526",
"505.26316",
"568.42105",
"694.73684",
"757.89474",
"821.05263",
"947.36842",
"1010.52632",
"1136.84211",
"2/1"
]
},
{
"id": "14_26",
"desc": "Two interlaced diatonic in 26-tET, tetrachordal. Paul Erlich (1996)",
"stepCount": "14",
"steps": [
"92.30769",
"184.61538",
"276.92308",
"369.23077",
"461.53846",
"507.69231",
"600.00000",
"692.30769",
"784.61538",
"876.92308",
"969.23077",
"1061.53846",
"1153.84615",
"2/1"
]
},
{
"id": "14_26_a",
"desc": "Two interlaced diatonic in 26-tET, maximally even. Paul Erlich (1996)",
"stepCount": "14",
"steps": [
"92.30769",
"184.61538",
"276.92308",
"369.23077",
"461.53846",
"553.84615",
"600.00000",
"692.30769",
"784.61538",
"876.92308",
"969.23077",
"1061.53846",
"1153.84615",
"2/1"
]
},
{
"id": "15_37",
"desc": "Miller's Porcupine-15",
"stepCount": "15",
"steps": [
"97.29730",
"162.16216",
"259.45946",
"324.32432",
"421.62162",
"486.48649",
"583.78378",
"648.64865",
"745.94595",
"810.81081",
"908.10811",
"972.97297",
"1070.27027",
"1135.13514",
"2/1"
]
},
{
"id": "15_46",
"desc": "Valentine[15] in 46-et tuning",
"stepCount": "15",
"steps": [
"78.260870",
"156.521739",
"234.782609",
"313.043478",
"391.304348",
"469.565217",
"547.826087",
"626.086957",
"704.347826",
"782.608696",
"886.956522",
"965.217391",
"1043.478261",
"1121.739130",
"2/1"
]
},
{
"id": "16_31",
"desc": "Armodue semi-equalizzato",
"stepCount": "16",
"steps": [
"77.41935",
"154.83871",
"232.25806",
"309.67742",
"387.09677",
"464.51613",
"541.93548",
"619.35484",
"696.77419",
"774.19355",
"851.61290",
"929.03226",
"967.74194",
"1045.16129",
"1122.58065",
"2/1"
]
},
{
"id": "16_139",
"desc": "g=9 steps of 139-tET. Gene Ward Smith \"Quartaminorthirds\"7-limit temperament",
"stepCount": "16",
"steps": [
"77.69784",
"155.39568",
"233.09353",
"310.79137",
"388.48921",
"466.18705",
"543.88489",
"621.58273",
"699.28058",
"776.97842",
"854.67626",
"932.37410",
"1010.07194",
"1087.76978",
"1165.46763",
"2/1"
]
},
{
"id": "16_145",
"desc": "Magic[16] in 145-tET",
"stepCount": "16",
"steps": [
"148.96552",
"206.89655",
"264.82759",
"322.75862",
"380.68966",
"438.62069",
"587.58621",
"645.51724",
"703.44828",
"761.37931",
"819.31034",
"968.27586",
"1026.20690",
"1084.13793",
"1142.06897",
"2/1"
]
},
{
"id": "17_31",
"desc": "17 out of 31, with split C#/Db, D#/Eb, F#/Gb, G#/Ab and A#/Bb",
"stepCount": "17",
"steps": [
"77.41935",
"116.12903",
"193.54839",
"270.96774",
"309.67742",
"387.09677",
"503.22581",
"580.64516",
"619.35484",
"696.77419",
"774.19355",
"812.90323",
"890.32258",
"967.74194",
"1006.45161",
"1083.87097",
"2/1"
]
},
{
"id": "17_53",
"desc": "17 out of 53-tET, Arabic Pythagorean scale, Safiyudd�n Al-Urmaw� (Safi al-Din)",
"stepCount": "17",
"steps": [
"90.56604",
"181.13208",
"203.77358",
"294.33962",
"384.90566",
"407.54717",
"498.11321",
"588.67925",
"679.24528",
"701.88679",
"792.45283",
"883.01887",
"905.66038",
"996.22642",
"1086.79245",
"1177.35849",
"2/1"
]
},
{
"id": "19_31",
"desc": "19 out of 31-tET, meantone Gb-B#",
"stepCount": "19",
"steps": [
"77.41935",
"116.12903",
"193.54839",
"270.96774",
"309.67742",
"387.09677",
"464.51613",
"503.22581",
"580.64516",
"619.35484",
"696.77419",
"774.19355",
"812.90323",
"890.32258",
"967.74194",
"1006.45161",
"1083.87097",
"1161.29032",
"2/1"
]
},
{
"id": "19_31_ji",
"desc": "A septimal interpretation of 19 out of 31 tones, after Wilson, XH7+8",
"stepCount": "19",
"steps": [
"25/24",
"16/15",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"16/9",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "19_36",
"desc": "19 out of 36-tET, Tomasz Liese, Tuning List, 1997",
"stepCount": "19",
"steps": [
"66.66667",
"133.33333",
"200.00000",
"266.66667",
"333.33333",
"400.00000",
"466.66667",
"500.00000",
"566.66667",
"633.33333",
"700.00000",
"766.66667",
"833.33333",
"900.00000",
"966.66667",
"1033.33333",
"1100.00000",
"1133.33333",
"2/1"
]
},
{
"id": "19_50",
"desc": "19 out of 50-tET, meantone Gb-B#",
"stepCount": "19",
"steps": [
"72.00000",
"120.00000",
"192.00000",
"264.00000",
"312.00000",
"384.00000",
"456.00000",
"504.00000",
"576.00000",
"624.00000",
"696.00000",
"768.00000",
"816.00000",
"888.00000",
"960.00000",
"1008.00000",
"1080.00000",
"1152.00000",
"2/1"
]
},
{
"id": "19_53",
"desc": "19 out of 53-tET, Larry H. Hanson (1978), key 8 is Mason Green's 1953 scale",
"stepCount": "19",
"steps": [
"67.92453",
"135.84906",
"203.77358",
"249.05660",
"316.98113",
"384.90566",
"452.83019",
"498.11321",
"566.03774",
"633.96226",
"701.88679",
"769.81132",
"815.09434",
"883.01887",
"950.94340",
"1018.86792",
"1086.79245",
"1132.07547",
"2/1"
]
},
{
"id": "19_55",
"desc": "19 out of 55-tET, meantone Gb-B#",
"stepCount": "19",
"steps": [
"87.27273",
"109.09091",
"196.36364",
"283.63636",
"305.45455",
"392.72727",
"480.00000",
"501.81818",
"589.09091",
"610.90909",
"698.18182",
"785.45455",
"807.27273",
"894.54545",
"981.81818",
"1003.63636",
"1090.90909",
"1178.18182",
"2/1"
]
},
{
"id": "19_any",
"desc": "Two out of 1/7 1/5 1/3 1 3 5 7 CPS",
"stepCount": "19",
"steps": [
"16/15",
"35/32",
"8/7",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"32/21",
"8/5",
"5/3",
"12/7",
"7/4",
"64/35",
"15/8",
"2/1"
]
},
{
"id": "20_31",
"desc": "20 out of 31-tET",
"stepCount": "20",
"steps": [
"77.41935",
"116.12903",
"193.54839",
"270.96774",
"309.67742",
"387.09677",
"425.80645",
"503.22581",
"580.64516",
"619.35484",
"696.77419",
"735.48387",
"774.19355",
"851.61290",
"890.32258",
"967.74194",
"1006.45161",
"1083.87097",
"1161.29032",
"2/1"
]
},
{
"id": "20_55",
"desc": "20 out of 55-tET, J. Chesnut: Mozart's teaching of intonation, JAMS 30/2 (1977)",
"stepCount": "20",
"steps": [
"87.27273",
"109.09091",
"196.36364",
"218.18182",
"283.63636",
"305.45455",
"392.72727",
"414.54545",
"501.81818",
"589.09091",
"610.90909",
"698.18182",
"785.45455",
"807.27273",
"894.54545",
"916.36364",
"981.81818",
"1003.63636",
"1090.90909",
"2/1"
]
},
{
"id": "21_any",
"desc": "2)7 1.3.5.7.9.11.13 21-any, 1.3 tonic",
"stepCount": "21",
"steps": [
"33/32",
"13/12",
"9/8",
"55/48",
"7/6",
"39/32",
"5/4",
"21/16",
"65/48",
"11/8",
"35/24",
"143/96",
"3/2",
"77/48",
"13/8",
"5/3",
"7/4",
"11/6",
"15/8",
"91/48",
"2/1"
]
},
{
"id": "22_41",
"desc": "22 out of 41 by Stephen Soderberg, TL 17-11-98",
"stepCount": "22",
"steps": [
"58.53659",
"117.07317",
"175.60976",
"234.14634",
"292.68293",
"351.21951",
"380.48780",
"439.02439",
"497.56098",
"556.09756",
"614.63415",
"673.17073",
"731.70732",
"760.97561",
"819.51220",
"878.04878",
"936.58537",
"995.12195",
"1053.65854",
"1112.19512",
"1170.73171",
"2/1"
]
},
{
"id": "22_46",
"desc": "22 shrutis out of 46-tET by Graham Breed",
"stepCount": "22",
"steps": [
"78.26087",
"104.34783",
"182.60870",
"208.69565",
"286.95652",
"313.04348",
"391.30435",
"417.39130",
"495.65217",
"521.73913",
"600.00000",
"626.08696",
"704.34783",
"782.60870",
"808.69565",
"886.95652",
"913.04348",
"991.30435",
"1017.39130",
"1095.65217",
"1121.73913",
"2/1"
]
},
{
"id": "22_53",
"desc": "22 shrutis out of 53-tET",
"stepCount": "22",
"steps": [
"90.56604",
"113.20755",
"181.13208",
"203.77358",
"294.33962",
"316.98113",
"384.90566",
"407.54717",
"498.11321",
"520.75472",
"588.67925",
"611.32075",
"701.88679",
"792.45283",
"815.09434",
"883.01887",
"905.66038",
"996.22642",
"1018.86792",
"1086.79245",
"1109.43396",
"2/1"
]
},
{
"id": "22_100",
"desc": "MODMOS with 10 and 12-note chains of fifths by Gene Ward Smith, similar to Pajara",
"stepCount": "22",
"steps": [
"60.00000",
"108.00000",
"168.00000",
"216.00000",
"276.00000",
"336.00000",
"384.00000",
"444.00000",
"492.00000",
"552.00000",
"600.00000",
"660.00000",
"708.00000",
"768.00000",
"828.00000",
"876.00000",
"936.00000",
"984.00000",
"1044.00000",
"1092.00000",
"1152.00000",
"2/1"
]
},
{
"id": "22_100_a",
"desc": "Alternative version with 600 cents period",
"stepCount": "22",
"steps": [
"60.00000",
"108.00000",
"168.00000",
"216.00000",
"276.00000",
"324.00000",
"384.00000",
"432.00000",
"492.00000",
"540.00000",
"600.00000",
"660.00000",
"708.00000",
"768.00000",
"816.00000",
"876.00000",
"924.00000",
"984.00000",
"1032.00000",
"1092.00000",
"1140.00000",
"2/1"
]
},
{
"id": "24_41",
"desc": "24 out of 41-tET, g=neutral third, 22 neutral triads, Op de Coul (2001), Hemififths-24",
"stepCount": "24",
"steps": [
"29.26829",
"87.80488",
"146.34146",
"175.60976",
"234.14634",
"292.68293",
"351.21951",
"380.48780",
"439.02439",
"497.56098",
"526.82927",
"585.36585",
"643.90244",
"702.43902",
"731.70732",
"790.24390",
"848.78049",
"878.04878",
"936.58537",
"995.12195",
"1053.65854",
"1082.92683",
"1141.46341",
"2/1"
]
},
{
"id": "24_60",
"desc": "12 and 15-tET mixed. Novaro (1951)",
"stepCount": "24",
"steps": [
"80.00000",
"100.00000",
"160.00000",
"200.00000",
"240.00000",
"300.00000",
"320.00000",
"400.00000",
"480.00000",
"500.00000",
"560.00000",
"600.00000",
"640.00000",
"700.00000",
"720.00000",
"800.00000",
"880.00000",
"900.00000",
"960.00000",
"1000.00000",
"1040.00000",
"1100.00000",
"1120.00000",
"2/1"
]
},
{
"id": "24_80",
"desc": "Regular 705-cent temperament, 24 of 80-tET",
"stepCount": "24",
"steps": [
"60.00000",
"135.00000",
"195.00000",
"210.00000",
"270.00000",
"285.00000",
"345.00000",
"420.00000",
"480.00000",
"495.00000",
"555.00000",
"630.00000",
"690.00000",
"705.00000",
"765.00000",
"840.00000",
"900.00000",
"915.00000",
"975.00000",
"990.00000",
"1050.00000",
"1125.00000",
"1185.00000",
"2/1"
]
},
{
"id": "24_94",
"desc": "24 tone schismic temperament in 94-tET, Gene Ward Smith (2002)",
"stepCount": "24",
"steps": [
"25.53191",
"89.36170",
"114.89362",
"178.72340",
"204.25532",
"293.61702",
"319.14894",
"382.97872",
"408.51064",
"497.87234",
"523.40426",
"587.23404",
"612.76596",
"676.59574",
"702.12766",
"791.48936",
"817.02128",
"880.85106",
"906.38298",
"995.74468",
"1021.27660",
"1085.10638",
"1110.63830",
"2/1"
]
},
{
"id": "28_any",
"desc": "6)8 1.3.5.7.9.11.13.15 28-any, only 26 tones",
"stepCount": "26",
"steps": [
"65/64",
"15/14",
"13/12",
"195/176",
"65/56",
"13/11",
"39/32",
"5/4",
"195/154",
"13/10",
"65/48",
"15/11",
"39/28",
"13/9",
"65/44",
"3/2",
"65/42",
"13/8",
"5/3",
"195/112",
"39/22",
"65/36",
"13/7",
"15/8",
"65/33",
"2/1"
]
},
{
"id": "30_29_min_3",
"desc": "30/29 x 29/28 x 28/27 plus 6/5",
"stepCount": "9",
"steps": [
"30/29",
"15/14",
"10/9",
"4/3",
"3/2",
"45/29",
"45/28",
"5/3",
"2/1"
]
},
{
"id": "31_171",
"desc": "Tertiaseptal-31 in 171-tET, g=11\\171",
"stepCount": "31",
"steps": [
"42.10526",
"77.19298",
"119.29825",
"154.38596",
"196.49123",
"231.57895",
"273.68421",
"308.77193",
"350.87719",
"385.96491",
"428.07018",
"463.15789",
"505.26316",
"540.35088",
"582.45614",
"617.54386",
"659.64912",
"701.75439",
"736.84211",
"778.94737",
"814.03509",
"856.14035",
"891.22807",
"933.33333",
"968.42105",
"1010.52632",
"1045.61404",
"1087.71930",
"1122.80702",
"1164.91228",
"2/1"
]
},
{
"id": "46_72",
"desc": "46 note subset of 72-tET containing the 17-limit otonalities and utonalities by Rick Tagawa",
"stepCount": "46",
"steps": [
"100.00000",
"116.66667",
"133.33333",
"150.00000",
"166.66667",
"183.33333",
"200.00000",
"216.66667",
"233.33333",
"250.00000",
"266.66667",
"283.33333",
"316.66667",
"350.00000",
"383.33333",
"416.66667",
"433.33333",
"500.00000",
"533.33333",
"550.00000",
"566.66667",
"583.33333",
"600.00000",
"616.66667",
"633.33333",
"650.00000",
"666.66667",
"700.00000",
"766.66667",
"783.33333",
"816.66667",
"850.00000",
"883.33333",
"916.66667",
"933.33333",
"950.00000",
"966.66667",
"983.33333",
"1000.00000",
"1016.66667",
"1033.33333",
"1050.00000",
"1066.66667",
"1083.33333",
"1100.00000",
"2/1"
]
},
{
"id": "53_commas",
"desc": "so-called 1/9 comma division of Turkish Music by equal division of 9/8 into 9 equal string lengths",
"stepCount": "53",
"steps": [
"73/72",
"37/36",
"25/24",
"19/18",
"77/72",
"13/12",
"79/72",
"10/9",
"9/8",
"73/64",
"37/32",
"75/64",
"19/16",
"77/64",
"39/32",
"79/64",
"5/4",
"81/64",
"985/768",
"499/384",
"337/256",
"4/3",
"73/54",
"37/27",
"25/18",
"38/27",
"77/54",
"13/9",
"79/54",
"40/27",
"3/2",
"73/48",
"37/24",
"25/16",
"19/12",
"77/48",
"13/8",
"79/48",
"5/3",
"27/16",
"219/128",
"111/64",
"225/128",
"57/32",
"231/128",
"117/64",
"237/128",
"15/8",
"243/128",
"985/512",
"499/256",
"1011/512",
"2/1"
]
},
{
"id": "56_any",
"desc": "3)8 1.3.5.7.9.11.13.15 56-any, 1.3.5 tonic, only 48 notes",
"stepCount": "48",
"steps": [
"65/64",
"33/32",
"1001/960",
"21/20",
"13/12",
"35/32",
"11/10",
"143/128",
"9/8",
"91/80",
"7/6",
"143/120",
"77/64",
"39/32",
"99/80",
"5/4",
"77/60",
"13/10",
"21/16",
"429/320",
"11/8",
"7/5",
"45/32",
"91/64",
"231/160",
"117/80",
"143/96",
"3/2",
"91/60",
"99/64",
"63/40",
"77/48",
"13/8",
"33/20",
"27/16",
"273/160",
"55/32",
"7/4",
"143/80",
"9/5",
"117/64",
"11/6",
"15/8",
"91/48",
"77/40",
"39/20",
"63/32",
"2/1"
]
},
{
"id": "67_135",
"desc": "67 out of 135-tET by Ozan Yarman, g=17.7777",
"stepCount": "67",
"steps": [
"17.77778",
"35.55556",
"53.33333",
"71.11111",
"88.88889",
"106.66667",
"124.44444",
"142.22222",
"160.00000",
"177.77778",
"195.55556",
"213.33333",
"231.11111",
"248.88889",
"266.66667",
"284.44444",
"302.22222",
"320.00000",
"337.77778",
"355.55556",
"373.33333",
"391.11111",
"408.88889",
"426.66667",
"444.44444",
"462.22222",
"480.00000",
"497.77778",
"515.55556",
"533.33333",
"551.11111",
"568.88889",
"586.66667",
"604.44444",
"622.22222",
"640.00000",
"657.77778",
"675.55556",
"702.22222",
"720.00000",
"737.77778",
"755.55556",
"773.33333",
"791.11111",
"808.88889",
"826.66667",
"844.44444",
"862.22222",
"880.00000",
"897.77778",
"915.55556",
"933.33333",
"951.11111",
"968.88889",
"986.66667",
"1004.44444",
"1022.22222",
"1040.00000",
"1057.77778",
"1075.55556",
"1093.33333",
"1111.11111",
"1128.88889",
"1146.66667",
"1164.44444",
"1182.22222",
"2/1"
]
},
{
"id": "70_any",
"desc": "4)8 1.3.5.7.11.13.17.19 70-any, tonic 1.3.5.7",
"stepCount": "70",
"steps": [
"323/320",
"2717/2688",
"143/140",
"247/240",
"3553/3360",
"17/16",
"13/12",
"2431/2240",
"209/192",
"4199/3840",
"11/10",
"247/224",
"187/168",
"221/192",
"323/280",
"187/160",
"19/16",
"143/120",
"2717/2240",
"17/14",
"209/168",
"4199/3360",
"2431/1920",
"143/112",
"247/192",
"13/10",
"209/160",
"221/168",
"3553/2688",
"187/140",
"323/240",
"19/14",
"11/8",
"221/160",
"2717/1920",
"17/12",
"323/224",
"2431/1680",
"247/168",
"143/96",
"209/140",
"247/160",
"187/120",
"4199/2688",
"11/7",
"221/140",
"19/12",
"3553/2240",
"2717/1680",
"13/8",
"187/112",
"323/192",
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"2/1"
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{
"id": "ad_dik",
"desc": "Amin Ad-Dik, 24-tone Egyptian tuning, d'Erlanger vol.5, p. 42",
"stepCount": "24",
"steps": [
"1053/1024",
"256/243",
"12/11",
"9/8",
"147/128",
"32/27",
"27/22",
"5/4",
"9/7",
"4/3",
"48/35",
"1024/729",
"81/56",
"3/2",
"49/32",
"128/81",
"18/11",
"27/16",
"26/15",
"9/5",
"11/6",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "aeolic",
"desc": "Ancient Greek Aeolic, also tritriadic scale of the 54:64:81 triad",
"stepCount": "7",
"steps": ["9/8", "32/27", "4/3", "3/2", "128/81", "16/9", "2/1"]
},
{
"id": "aeu_41_ratios",
"desc": "AEU extended to quasi-cyclic 41-tones in simple ratios",
"stepCount": "41",
"steps": [
"67/66",
"27/26",
"59/56",
"63/59",
"38/35",
"71/64",
"9/8",
"8/7",
"111/95",
"32/27",
"125/104",
"16/13",
"146/117",
"81/64",
"9/7",
"46/35",
"4/3",
"23/17",
"18/13",
"59/42",
"131/92",
"68/47",
"71/48",
"3/2",
"32/21",
"81/52",
"128/81",
"109/68",
"85/52",
"198/119",
"27/16",
"12/7",
"163/93",
"16/9",
"119/66",
"24/13",
"88/47",
"112/59",
"27/14",
"69/35",
"2/1"
]
},
{
"id": "aeu_41",
"desc": "AEU extended to 41-quasi equal tones by Ozan Yarman",
"stepCount": "41",
"steps": [
"531441/524288",
"27/26",
"256/243",
"2187/2048",
"1162261467/1073741824",
"65536/59049",
"9/8",
"4782969/4194304",
"243/208",
"32/27",
"19683/16384",
"16/13",
"8192/6561",
"81/64",
"43046721/33554432",
"2097152/1594323",
"4/3",
"177147/131072",
"18/13",
"1024/729",
"729/512",
"387420489/268435456",
"262144/177147",
"3/2",
"1594323/1048576",
"81/52",
"128/81",
"6561/4096",
"111/68",
"32768/19683",
"27/16",
"14348907/8388608",
"8388608/4782969",
"16/9",
"59049/32768",
"24/13",
"4096/2187",
"243/128",
"129140163/67108864",
"1048576/531441",
"2/1"
]
},
{
"id": "agricola_p",
"desc": "Agricola's Pythagorean-type Monochord, Musica instrumentalis deudsch (1545)",
"stepCount": "12",
"steps": [
"109.77500",
"9/8",
"313.68501",
"81/64",
"4/3",
"607.82000",
"3/2",
"811.73001",
"27/16",
"1015.64001",
"243/128",
"2/1"
]
},
{
"id": "agricola",
"desc": "Agricola's Monochord, Rudimenta musices (1539)",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"1215/1024",
"81/64",
"4/3",
"45/32",
"3/2",
"405/256",
"27/16",
"16/9",
"243/128",
"2/1"
]
},
{
"id": "akea_46_13",
"desc": "Tridecimal Akea[46] hobbit minimax tuning. Commas 325/324, 352/351, 385/384",
"stepCount": "46",
"steps": [
"26.52580",
"53.05160",
"67.35084",
"111.95263",
"138.47843",
"152.77767",
"179.30347",
"205.82927",
"232.35507",
"264.73030",
"291.25610",
"317.78190",
"344.30770",
"358.60694",
"385.13274",
"411.65854",
"438.18434",
"470.55956",
"497.08537",
"523.61117",
"550.13697",
"564.43621",
"590.96201",
"635.56379",
"649.86303",
"676.38883",
"702.91463",
"729.44044",
"755.96624",
"788.34146",
"814.86726",
"841.39306",
"855.69230",
"882.21810",
"908.74390",
"935.26970",
"967.64493",
"994.17073",
"1020.69653",
"1047.22233",
"1061.52157",
"1088.04737",
"1114.57317",
"1146.94840",
"1173.47420",
"2/1"
]
},
{
"id": "al_din_19",
"desc": "Pythagorean Arabic scale by Safi al-Din",
"stepCount": "19",
"steps": [
"256/243",
"65536/59049",
"9/8",
"32/27",
"8192/6561",
"81/64",
"2097152/1594323",
"4/3",
"1024/729",
"262144/177147",
"3/2",
"128/81",
"32768/19683",
"27/16",
"8388608/4782969",
"16/9",
"4096/2187",
"1048576/531441",
"2/1"
]
},
{
"id": "al_din",
"desc": "Safi al-Din's complete lute tuning on 5 strings 4/3 apart",
"stepCount": "35",
"steps": [
"256/243",
"65536/59049",
"9/8",
"32/27",
"8192/6561",
"81/64",
"4/3",
"1024/729",
"262144/177147",
"3/2",
"128/81",
"32768/19683",
"27/16",
"16/9",
"4096/2187",
"1048576/531441",
"2/1",
"512/243",
"131072/59049",
"9/4",
"64/27",
"16384/6561",
"4194304/1594323",
"8/3",
"2048/729",
"524288/177147",
"3/1",
"256/81",
"65536/19683",
"16777216/4782969",
"32/9",
"8192/2187",
"2097152/531441",
"4/1",
"1024/243"
]
},
{
"id": "al_farabi_9",
"desc": "Al-Farabi 9 note ud scale",
"stepCount": "9",
"steps": [
"9/8",
"27/22",
"81/64",
"4/3",
"3/2",
"18/11",
"27/16",
"16/9",
"2/1"
]
},
{
"id": "al_farabi_19",
"desc": "Arabic scale by Al Farabi",
"stepCount": "19",
"steps": [
"256/243",
"12/11",
"9/8",
"32/27",
"8192/6561",
"81/64",
"2816/2187",
"4/3",
"1024/729",
"16/11",
"3/2",
"128/81",
"32768/19683",
"27/16",
"891/512",
"16/9",
"4096/2187",
"64/33",
"2/1"
]
},
{
"id": "al_farabi_22",
"desc": "Al-Farabi 22 note ud scale",
"stepCount": "22",
"steps": [
"256/243",
"18/17",
"12/11",
"9/8",
"32/27",
"27/22",
"8192/6561",
"81/64",
"4/3",
"1024/729",
"24/17",
"16/11",
"3/2",
"128/81",
"18/11",
"32768/19683",
"27/16",
"16/9",
"4096/2187",
"32/17",
"64/33",
"2/1"
]
},
{
"id": "al_farabi_blue",
"desc": "Another tuning from Al Farabi, c700 AD",
"stepCount": "7",
"steps": ["9/8", "45/32", "131/90", "3/2", "15/8", "31/16", "2/1"]
},
{
"id": "al_farabi_chrom",
"desc": "Al Farabi's Chromatic c700 AD",
"stepCount": "7",
"steps": ["9/8", "27/20", "729/512", "3/2", "9/5", "19/10", "2/1"]
},
{
"id": "al_farabi_chrom_2",
"desc": "Al-Farabi's Chromatic permuted",
"stepCount": "7",
"steps": ["16/15", "56/45", "4/3", "3/2", "8/5", "28/15", "2/1"]
},
{
"id": "al_farabi_diat",
"desc": "Al-Farabi's Diatonic",
"stepCount": "7",
"steps": ["8/7", "64/49", "4/3", "3/2", "12/7", "96/49", "2/1"]
},
{
"id": "al_farabi_diat_2",
"desc": "Old Phrygian, permuted form of Al-Farabi's reduplicated 10/9 diatonic genus, same as ptolemy_diat.scl",
"stepCount": "7",
"steps": ["10/9", "6/5", "4/3", "3/2", "5/3", "9/5", "2/1"]
},
{
"id": "al_farabi_div",
"desc": "Al Farabi's 10 intervals for the division of the tetrachord",
"stepCount": "10",
"steps": [
"256/243",
"18/17",
"162/149",
"54/49",
"9/8",
"32/27",
"81/68",
"27/22",
"81/64",
"4/3"
]
},
{
"id": "al_farabi_div_2",
"desc": "Al-Farabi's tetrachord division, incl. extra 2187/2048 & 19683/16384",
"stepCount": "12",
"steps": [
"256/243",
"18/17",
"2187/2048",
"162/149",
"54/49",
"9/8",
"32/27",
"81/68",
"19683/16384",
"27/22",
"81/64",
"4/3"
]
},
{
"id": "al_farabi_divo",
"desc": "Al Farabi's theoretical octave division with identical tetrachords, 10th c.",
"stepCount": "24",
"steps": [
"256/243",
"18/17",
"162/149",
"54/49",
"9/8",
"32/27",
"81/68",
"27/22",
"81/64",
"4/3",
"1024/729",
"24/17",
"216/149",
"3/2",
"128/81",
"27/17",
"243/149",
"81/49",
"27/16",
"16/9",
"243/136",
"81/44",
"243/128",
"2/1"
]
},
{
"id": "al_farabi_dor",
"desc": "Dorian mode of Al-Farabi's 10/9 Diatonic",
"stepCount": "7",
"steps": ["27/25", "6/5", "4/3", "3/2", "81/50", "9/5", "2/1"]
},
{
"id": "al_farabi_dor_2",
"desc": "Dorian mode of Al-Farabi's Diatonic",
"stepCount": "7",
"steps": ["49/48", "7/6", "4/3", "3/2", "49/32", "7/4", "2/1"]
},
{
"id": "al_farabi_g_1",
"desc": "Al-Farabi's Greek genus conjunctum medium, Land",
"stepCount": "7",
"steps": ["9/8", "81/64", "45/32", "3/2", "27/16", "15/8", "2/1"]
},
{
"id": "al_farabi_g_3",
"desc": "Al-Farabi's Greek genus conjunctum primum",
"stepCount": "7",
"steps": ["9/8", "9/7", "81/56", "3/2", "12/7", "27/14", "2/1"]
},
{
"id": "al_farabi_g_4",
"desc": "Al-Farabi's Greek genus forte duplicatum primum",
"stepCount": "7",
"steps": ["9/8", "9/7", "72/49", "3/2", "12/7", "96/49", "2/1"]
},
{
"id": "al_farabi_g_5",
"desc": "Al-Farabi's Greek genus conjunctum tertium, or forte aequatum",
"stepCount": "7",
"steps": ["9/8", "5/4", "11/8", "3/2", "5/3", "11/6", "2/1"]
},
{
"id": "al_farabi_g_6",
"desc": "Al-Farabi's Greek genus forte disjunctum primum",
"stepCount": "7",
"steps": ["9/8", "9/7", "10/7", "3/2", "12/7", "40/21", "2/1"]
},
{
"id": "al_farabi_g_7",
"desc": "Al-Farabi's Greek genus non continuum acre",
"stepCount": "7",
"steps": ["9/8", "21/16", "63/44", "3/2", "7/4", "21/11", "2/1"]
},
{
"id": "al_farabi_g_8",
"desc": "Al-Farabi's Greek genus non continuum mediocre",
"stepCount": "7",
"steps": ["9/8", "27/20", "81/56", "3/2", "9/5", "27/14", "2/1"]
},
{
"id": "al_farabi_g_9",
"desc": "Al-Farabi's Greek genus non continuum laxum",
"stepCount": "7",
"steps": ["9/8", "45/32", "22/15", "3/2", "15/8", "88/45", "2/1"]
},
{
"id": "al_farabi_g_10",
"desc": "Al-Farabi's Greek genus chromaticum forte",
"stepCount": "7",
"steps": ["9/8", "21/16", "45/32", "3/2", "7/4", "15/8", "2/1"]
},
{
"id": "al_farabi_g_11",
"desc": "Al-Farabi's Greek genus chromaticum mollissimum",
"stepCount": "7",
"steps": ["9/8", "27/20", "729/512", "3/2", "9/5", "243/128", "2/1"]
},
{
"id": "al_farabi_g_12",
"desc": "Al-Farabi's Greek genus mollissimum ordinantium",
"stepCount": "7",
"steps": ["9/8", "45/32", "93/64", "3/2", "15/8", "31/16", "2/1"]
},
{
"id": "al_farabi",
"desc": "Al-Farabi Syn Chrom",
"stepCount": "7",
"steps": ["16/15", "8/7", "4/3", "3/2", "8/5", "12/7", "2/1"]
},
{
"id": "al_hwarizmi",
"desc": "Al-Hwarizmi's tetrachord division",
"stepCount": "6",
"steps": ["9/8", "81/70", "81/68", "27/22", "81/64", "4/3"]
},
{
"id": "al_kindi",
"desc": "Al-Kindi's tetrachord division",
"stepCount": "6",
"steps": ["256/243", "2187/2048", "9/8", "32/27", "81/64", "4/3"]
},
{
"id": "al_kindi_2",
"desc": "Arabic mode by al-Kindi",
"stepCount": "14",
"steps": [
"256/243",
"9/8",
"32/27",
"8192/6561",
"81/64",
"4/3",
"1024/729",
"3/2",
"128/81",
"32768/19683",
"27/16",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "al_mausili",
"desc": "Arabic mode by Ishaq al-Mausili (? - 850 AD)",
"stepCount": "11",
"steps": [
"256/243",
"9/8",
"32/27",
"81/64",
"4/3",
"1024/729",
"3/2",
"128/81",
"27/16",
"16/9",
"2/1"
]
},
{
"id": "alembert_rousseau",
"desc": "d'Alembert and Rousseau temp�rament ordinaire (1752/1767)",
"stepCount": "12",
"steps": [
"86.31371",
"193.15686",
"288.26871",
"5/4",
"496.08957",
"586.31371",
"696.57843",
"786.31371",
"889.73529",
"992.17914",
"1086.31371",
"2/1"
]
},
{
"id": "alembert_rousseau_2",
"desc": "d'Alembert and Rousseau (1752-1767) different interpretation",
"stepCount": "12",
"steps": [
"86.31371",
"193.57843",
"289.73625",
"5/4",
"496.57875",
"586.31371",
"697.00000",
"786.31371",
"890.15686",
"993.15750",
"1086.31371",
"2/1"
]
},
{
"id": "alembert",
"desc": "Jean-Le Rond d'Alembert modified meantone (1752)",
"stepCount": "12",
"steps": [
"78.14893",
"193.15686",
"281.57050",
"386.31372",
"493.85684",
"580.87053",
"696.57843",
"775.42734",
"889.73529",
"987.71367",
"1083.59212",
"2/1"
]
},
{
"id": "alves_12",
"desc": "Bill Alves, tuning for \"Metalloid\", TL 12-12-2007",
"stepCount": "12",
"steps": [
"49/48",
"9/8",
"7/6",
"9/7",
"21/16",
"49/36",
"3/2",
"49/32",
"12/7",
"7/4",
"27/14",
"2/1"
]
},
{
"id": "alves_22",
"desc": "Bill Alves, 11-limit rational interpretation of 22-tET, TL 9-1-98",
"stepCount": "22",
"steps": [
"33/32",
"16/15",
"11/10",
"25/22",
"7/6",
"40/33",
"5/4",
"9/7",
"4/3",
"11/8",
"99/70",
"16/11",
"3/2",
"14/9",
"8/5",
"33/20",
"12/7",
"44/25",
"20/11",
"15/8",
"64/33",
"2/1"
]
},
{
"id": "alves_pelog",
"desc": "Bill Alves JI Pelog, 1/1 vol.9 no.4, 1997. 1/1=293.33 Hz",
"stepCount": "7",
"steps": ["8/7", "6/5", "21/16", "3/2", "8/5", "7/4", "2/1"]
},
{
"id": "alves_slendro",
"desc": "Bill Alves, slendro for Gender Barung, 1/1 vol.9 no.4, 1997. 1/1=282.86 Hz",
"stepCount": "5",
"steps": ["8/7", "4/3", "14/9", "16/9", "2/1"]
},
{
"id": "alves",
"desc": "Bill Alves, tuning for \"Instantaneous Motion\", 1/1 vol.6 no.3",
"stepCount": "13",
"steps": [
"49/48",
"9/8",
"7/6",
"5/4",
"9/7",
"4/3",
"11/8",
"3/2",
"13/8",
"12/7",
"7/4",
"27/14",
"2/1"
]
},
{
"id": "amity",
"desc": "Amity temperament, g=339.508826, 5-limit",
"stepCount": "39",
"steps": [
"23.43822",
"87.72065",
"111.15887",
"134.59709",
"158.03530",
"181.47352",
"204.91174",
"269.19417",
"292.63239",
"316.07061",
"339.50883",
"362.94704",
"386.38526",
"450.66769",
"474.10591",
"497.54413",
"520.98235",
"544.42057",
"608.70300",
"632.14122",
"655.57943",
"679.01765",
"702.45587",
"725.89409",
"790.17652",
"813.61474",
"837.05296",
"860.49117",
"883.92939",
"948.21182",
"971.65004",
"995.08826",
"1018.52648",
"1041.96470",
"1065.40291",
"1129.68535",
"1153.12356",
"1176.56178",
"2/1"
]
},
{
"id": "amity_53_pure",
"desc": "Amity[53] in pure-fifths tuning",
"stepCount": "53",
"steps": [
"22.73700",
"45.47400",
"68.21100",
"256/243",
"112.96200",
"135.69900",
"158.43600",
"181.17300",
"9/8",
"226.64700",
"249.38400",
"271.39800",
"32/27",
"316.87200",
"339.60900",
"362.34600",
"385.08300",
"81/64",
"429.83400",
"452.57100",
"475.30800",
"4/3",
"520.78200",
"543.51900",
"566.25600",
"588.99300",
"611.00700",
"633.74400",
"656.48100",
"679.21800",
"3/2",
"724.69200",
"747.42900",
"770.16600",
"128/81",
"814.91700",
"837.65400",
"860.39100",
"883.12800",
"27/16",
"928.60200",
"950.61600",
"973.35300",
"16/9",
"1018.82700",
"1041.56400",
"1064.30100",
"1087.03800",
"243/128",
"1131.78900",
"1154.52600",
"1177.26300",
"2/1"
]
},
{
"id": "ammerbach",
"desc": "Elias Mikolaus Ammerbach (1571), from Ratte: Temperierungspraktiken im s�ddeutschen Orgelbau p. 412",
"stepCount": "12",
"steps": [
"86.31499",
"198.04500",
"302.93250",
"392.18000",
"4/3",
"590.22500",
"3/2",
"784.35999",
"894.13500",
"999.02250",
"1092.18000",
"2/1"
]
},
{
"id": "ammerbach_1",
"desc": "Elias Mikolaus Ammerbach (1571, 1583) interpretation 1, Ratte, 1991",
"stepCount": "12",
"steps": [
"89.68501",
"197.91000",
"300.13500",
"395.82000",
"4/3",
"593.73001",
"3/2",
"791.64001",
"893.86500",
"1002.09000",
"1097.77500",
"2/1"
]
},
{
"id": "ammerbach_2",
"desc": "Elias Mikolaus Ammerbach (1571, 1583) interpretation 2, Ratte, 1991",
"stepCount": "12",
"steps": [
"85.68501",
"197.91000",
"303.13500",
"391.82000",
"4/3",
"589.73001",
"3/2",
"783.64001",
"893.86500",
"999.09000",
"1091.77500",
"2/1"
]
},
{
"id": "angklung",
"desc": "Scale of an anklung set from Tasikmalaya. 1/1=174 Hz",
"stepCount": "8",
"steps": [
"206.12000",
"382.32900",
"610.00900",
"823.60700",
"1234.47800",
"1406.12000",
"1633.42500",
"1841.20400"
]
},
{
"id": "ankara",
"desc": "Ankara Turkish State Radio Tanbur Frets",
"stepCount": "34",
"steps": [
"1053/1000",
"533/500",
"1079/1000",
"273/250",
"111/100",
"281/250",
"589/500",
"239/200",
"1211/1000",
"123/100",
"156/125",
"158/125",
"1333/1000",
"677/500",
"1373/1000",
"1393/1000",
"7/5",
"1421/1000",
"721/500",
"3/2",
"317/200",
"201/125",
"407/250",
"1653/1000",
"167/100",
"211/125",
"1777/1000",
"1801/1000",
"1827/1000",
"1853/1000",
"47/25",
"951/500",
"1931/1000",
"2/1"
]
},
{
"id": "appunn",
"desc": "Probable tuning of A. Appunn's 36-tone harmonium w. 3 manuals 80/81 apart (1887)",
"stepCount": "36",
"steps": [
"25/24",
"135/128",
"2187/2048",
"800/729",
"10/9",
"9/8",
"204800/177147",
"2560/2187",
"32/27",
"100/81",
"5/4",
"81/64",
"25600/19683",
"320/243",
"4/3",
"25/18",
"45/32",
"729/512",
"3200/2187",
"40/27",
"3/2",
"25/16",
"405/256",
"6561/4096",
"400/243",
"5/3",
"27/16",
"102400/59049",
"1280/729",
"16/9",
"50/27",
"15/8",
"243/128",
"12800/6561",
"160/81",
"2/1"
]
},
{
"id": "arabic_bastanikar_on_b",
"desc": "Arabic Bastanikar with perde iraq on B by Dr. Ozan Yarman",
"stepCount": "12",
"steps": [
"825/784",
"55/49",
"40/33",
"49/40",
"147/110",
"45/32",
"3/2",
"165/98",
"19/11",
"25/14",
"147/80",
"441/220"
]
},
{
"id": "arabic_bayati_and_bayati_shuri_on_d",
"desc": "Arabic Bayati and Bayati-Shuri (Karjighar) with perde dugah on D by Dr. Oz.",
"stepCount": "11",
"steps": [
"55/49",
"11/9",
"49/40",
"147/110",
"77/48",
"3/2",
"25/14",
"165/98",
"11/6",
"90/49",
"441/220"
]
},
{
"id": "arabic_bayati_and_ushshaq_misri_on_d",
"desc": "Arabic Bayati and Ushshaq Misri with perde dugah on D by Dr. Oz.",
"stepCount": "11",
"steps": [
"11/9",
"55/49",
"49/40",
"63/50",
"147/110",
"3/2",
"25/14",
"165/98",
"11/6",
"90/49",
"441/220"
]
},
{
"id": "arabic_huzam_on_e",
"desc": "Arabic Huzam with perde segah on E by Dr. Oz.",
"stepCount": "12",
"steps": [
"63/55",
"55/49",
"25/21",
"49/40",
"147/110",
"25/18",
"3/2",
"49/30",
"165/98",
"98/55",
"121/64",
"441/220"
]
},
{
"id": "arabic_rast_on_c",
"desc": "Arabic Rast with perde rast on C by Dr. Ozan Yarman",
"stepCount": "8",
"steps": [
"55/49",
"27/22",
"147/110",
"3/2",
"165/98",
"25/14",
"81/44",
"441/220"
]
},
{
"id": "arabic_saba_on_d",
"desc": "Arabic Saba with perde dugah on D by Dr. Oz.",
"stepCount": "11",
"steps": [
"825/784",
"55/49",
"49/40",
"63/50",
"147/110",
"45/32",
"3/2",
"165/98",
"25/14",
"147/80",
"441/220"
]
},
{
"id": "arabic_saba_zamzama_on_d",
"desc": "Arabic Saba-Zamzama with perde dugah on D by Dr. Oz.",
"stepCount": "11",
"steps": [
"825/784",
"55/49",
"40/33",
"63/50",
"147/110",
"45/32",
"3/2",
"165/98",
"25/14",
"147/80",
"441/220"
]
},
{
"id": "arabic_segah_mustaar_on_e",
"desc": "Arabic Segah and Mustaar with perde segah on E by Dr. Oz.",
"stepCount": "12",
"steps": [
"63/55",
"55/49",
"25/21",
"49/40",
"147/110",
"25/18",
"3/2",
"49/30",
"165/98",
"98/55",
"147/80",
"441/220"
]
},
{
"id": "arabic_zanjaran_on_c",
"desc": "Arabic Zanjaran with perde rast on C by Dr. Oz.",
"stepCount": "7",
"steps": ["27/25", "63/50", "147/110", "3/2", "165/98", "25/14", "441/220"]
},
{
"id": "arch_chrom",
"desc": "Archytas' Chromatic",
"stepCount": "7",
"steps": ["28/27", "9/8", "4/3", "3/2", "14/9", "27/16", "2/1"]
},
{
"id": "arch_chro_mc_2",
"desc": "Product set of 2 of Archytas' Chromatic",
"stepCount": "14",
"steps": [
"28/27",
"9/8",
"7/6",
"81/64",
"21/16",
"4/3",
"112/81",
"3/2",
"14/9",
"392/243",
"27/16",
"7/4",
"243/128",
"2/1"
]
},
{
"id": "arch_dor",
"desc": "Dorian mode of Archytas' Chromatic with added 16/9",
"stepCount": "8",
"steps": ["28/27", "9/8", "4/3", "3/2", "14/9", "16/9", "27/16", "2/1"]
},
{
"id": "arch_enh",
"desc": "Archytas' Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "4/3", "3/2", "14/9", "8/5", "2/1"]
},
{
"id": "arch_enh_2",
"desc": "Archytas' Enharmonic with added 16/9",
"stepCount": "8",
"steps": ["28/27", "16/15", "4/3", "3/2", "14/9", "16/9", "8/5", "2/1"]
},
{
"id": "arch_enh_3",
"desc": "Complex 9 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "9/7", "4/3", "48/35", "12/7", "2/1"]
},
{
"id": "arch_enhp",
"desc": "Permutation of Archytas' Enharmonic with 36/35 first",
"stepCount": "7",
"steps": ["36/35", "16/15", "4/3", "3/2", "54/35", "8/5", "2/1"]
},
{
"id": "arch_enht",
"desc": "Complex 6 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["36/35", "28/27", "16/15", "9/7", "4/3", "27/14", "2/1"]
},
{
"id": "arch_en_ht_2",
"desc": "Complex 5 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "5/4", "4/3", "15/8", "35/18", "2/1"]
},
{
"id": "arch_enht_3",
"desc": "Complex 1 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "784/729", "448/405", "4/3", "112/81", "2/1"]
},
{
"id": "arch_enht_4",
"desc": "Complex 8 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "5/4", "35/27", "4/3", "5/3", "2/1"]
},
{
"id": "arch_enht_5",
"desc": "Complex 10 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["245/243", "28/27", "16/15", "35/27", "4/3", "35/18", "2/1"]
},
{
"id": "arch_enht_6",
"desc": "Complex 2 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["28/27", "16/15", "448/405", "256/225", "4/3", "64/45", "2/1"]
},
{
"id": "arch_enht_7",
"desc": "Complex 11 of p. 113 based on Archytas's Enharmonic",
"stepCount": "7",
"steps": ["36/35", "28/27", "16/15", "192/175", "4/3", "48/35", "2/1"]
},
{
"id": "arch_mult",
"desc": "Multiple Archytas",
"stepCount": "12",
"steps": [
"28/27",
"16/15",
"5/4",
"9/7",
"4/3",
"112/81",
"3/2",
"14/9",
"8/5",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "arch_ptol",
"desc": "Archytas/Ptolemy Hybrid 1",
"stepCount": "12",
"steps": [
"28/27",
"16/15",
"10/9",
"32/27",
"4/3",
"112/81",
"3/2",
"14/9",
"8/5",
"5/3",
"16/9",
"2/1"
]
},
{
"id": "arch_ptol_2",
"desc": "Archytas/Ptolemy Hybrid 2",
"stepCount": "12",
"steps": [
"28/27",
"16/15",
"9/8",
"6/5",
"4/3",
"112/81",
"3/2",
"14/9",
"8/5",
"27/16",
"9/5",
"2/1"
]
},
{
"id": "arch_sept",
"desc": "Archytas Septimal",
"stepCount": "12",
"steps": [
"28/27",
"16/15",
"9/8",
"32/27",
"4/3",
"112/81",
"3/2",
"14/9",
"8/5",
"27/16",
"16/9",
"2/1"
]
},
{
"id": "archchro",
"desc": "Archytas' Chromatic in hemif temperament, 58-tET tuning",
"stepCount": "7",
"steps": [
"62.06897",
"206.89655",
"496.55172",
"703.44828",
"765.51724",
"910.34483",
"2/1"
]
},
{
"id": "archytas_7",
"desc": "Archytas (64/63) hobbit in POTE tuning",
"stepCount": "7",
"steps": [
"218.64253",
"393.37465",
"490.67874",
"709.32126",
"806.62535",
"981.35747",
"2/1"
]
},
{
"id": "archytas_12",
"desc": "Archytas[12] (64/63) hobbit, 9-limit minimax",
"stepCount": "12",
"steps": [
"98.09924",
"217.54205",
"315.64129",
"393.12974",
"491.22898",
"610.67178",
"708.77102",
"806.87026",
"926.31307",
"982.45795",
"1101.90076",
"2/1"
]
},
{
"id": "archytas_12_sync",
"desc": "Archytas[12] (64/63) hobbit, sync beating",
"stepCount": "12",
"steps": [
"96.45889",
"222.99262",
"319.45150",
"392.04481",
"488.50369",
"615.03742",
"711.49631",
"807.95519",
"934.48892",
"977.00738",
"1103.54111",
"2/1"
]
},
{
"id": "ares_12",
"desc": "Ares[12] (64/63&100/99) hobbit, POTE tuning",
"stepCount": "12",
"steps": [
"98.86242",
"172.07703",
"318.23612",
"391.45073",
"490.31315",
"563.52776",
"709.68685",
"808.54927",
"881.76388",
"1027.92297",
"1101.13758",
"2/1"
]
},
{
"id": "ares_12_opt",
"desc": "Lesfip scale derived from Ares[12], 13 cents, 11-limit",
"stepCount": "12",
"steps": [
"98.47604",
"165.71169",
"321.40156",
"392.10465",
"485.69654",
"551.05641",
"711.71088",
"809.46455",
"871.65772",
"1030.05511",
"1099.72190",
"2/1"
]
},
{
"id": "ariel_19",
"desc": "Ariel's 19-tone scale",
"stepCount": "19",
"steps": [
"25/24",
"16/15",
"10/9",
"125/108",
"6/5",
"5/4",
"32/25",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"216/125",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "ariel_31",
"desc": "Ariel's 31-tone system",
"stepCount": "31",
"steps": [
"128/125",
"25/24",
"16/15",
"625/576",
"9/8",
"144/125",
"75/64",
"6/5",
"625/512",
"5/4",
"32/25",
"125/96",
"4/3",
"512/375",
"25/18",
"36/25",
"375/256",
"3/2",
"192/125",
"25/16",
"8/5",
"1024/625",
"5/3",
"128/75",
"125/72",
"16/9",
"1152/625",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "ariel_1",
"desc": "Ariel 1",
"stepCount": "12",
"steps": [
"27/25",
"9/8",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2"
]
},
{
"id": "ariel_2",
"desc": "Ariel 2",
"stepCount": "12",
"steps": [
"16/15",
"10/9",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2"
]
},
{
"id": "ariel_3",
"desc": "Ariel's 12-tone JI scale",
"stepCount": "12",
"steps": [
"16/15",
"10/9",
"32/27",
"100/81",
"4/3",
"25/18",
"3/2",
"8/5",
"5/3",
"16/9",
"50/27",
"2/1"
]
},
{
"id": "arist_archenh",
"desc": "PsAristo Arch. Enharmonic, 4 + 3 + 23 parts, similar to Archytas' enharmonic",
"stepCount": "7",
"steps": [
"66.66667",
"116.66667",
"500.00000",
"700.00000",
"766.66667",
"816.66667",
"2/1"
]
},
{
"id": "arist_chrom",
"desc": "Dorian, Neo-Chromatic,6+18+6 parts = Athanasopoulos' Byzant.liturg. 2nd chromatic",
"stepCount": "7",
"steps": [
"100.00000",
"400.00000",
"500.00000",
"700.00000",
"800.00000",
"1100.00000",
"2/1"
]
},
{
"id": "arist_chrom_2",
"desc": "Dorian Mode, a 1:2 Chromatic, 8 + 18 + 4 parts",
"stepCount": "7",
"steps": [
"133.33333",
"433.33333",
"500.00000",
"700.00000",
"833.33333",
"1133.33333",
"2/1"
]
},
{
"id": "arist_chrom_3",
"desc": "PsAristo 3 Chromatic, 7 + 7 + 16 parts",
"stepCount": "7",
"steps": [
"445/416",
"230/201",
"295/221",
"442/295",
"928/579",
"1159/676",
"2/1"
]
},
{
"id": "arist_chrom_4",
"desc": "PsAristo Chromatic, 5.5 + 5.5 + 19 parts",
"stepCount": "7",
"steps": [
"91.66667",
"183.33333",
"500.00000",
"700.00000",
"791.66667",
"883.33333",
"2/1"
]
},
{
"id": "arist_chromenh",
"desc": "Aristoxenos' Chromatic/Enharmonic, 3 + 9 + 18 parts",
"stepCount": "7",
"steps": [
"50.00000",
"200.00000",
"500.00000",
"700.00000",
"750.00000",
"900.00000",
"2/1"
]
},
{
"id": "arist_chrominv",
"desc": "Aristoxenos' Inverted Chromatic, Dorian mode, 18 + 6 + 6 parts",
"stepCount": "7",
"steps": [
"300.000 cents",
"400.000 cents",
"500.000 cents",
"700.000 cents",
"1000.000 cents",
"1100.000 cents",
"2/1"
]
},
{
"id": "arist_chromrej",
"desc": "Aristoxenos Rejected Chromatic, 6 + 3 + 21 parts",
"stepCount": "7",
"steps": [
"100.000 cents",
"150.000 cents",
"500.000 cents",
"700.000 cents",
"800.000 cents",
"850.000 cents",
"2/1"
]
},
{
"id": "arist_chromunm",
"desc": "Unmelodic Chromatic, genus of Aristoxenos, Dorian Mode, 4.5 + 3.5 + 22 parts",
"stepCount": "7",
"steps": [
"75.00000",
"133.33333",
"500.00000",
"700.00000",
"775.00000",
"833.33333",
"2/1"
]
},
{
"id": "arist_diat",
"desc": "Phrygian octave species on E, 12 + 6 + 12 parts",
"stepCount": "7",
"steps": [
"200.00000",
"300.00000",
"500.00000",
"700.00000",
"900.00000",
"1000.00000",
"2/1"
]
},
{
"id": "arist_diat_2",
"desc": "PsAristo 2 Diatonic, 7 + 11 + 12 parts",
"stepCount": "7",
"steps": [
"116.66667",
"300.00000",
"500.00000",
"700.00000",
"816.66667",
"1000.00000",
"2/1"
]
},
{
"id": "arist_diat_3",
"desc": "PsAristo Diat 3, 9.5 + 9.5 + 11 parts",
"stepCount": "7",
"steps": [
"158.33333",
"316.66667",
"500.00000",
"700.00000",
"858.33333",
"1016.66667",
"2/1"
]
},
{
"id": "arist_diat_4",
"desc": "PsAristo Diatonic, 8 + 8 + 14 parts",
"stepCount": "7",
"steps": [
"133.33333",
"266.66667",
"500.00000",
"700.00000",
"833.33333",
"966.66667",
"2/1"
]
},
{
"id": "arist_diatdor",
"desc": "PsAristo Redup. Diatonic, 14 + 2 + 14 parts",
"stepCount": "7",
"steps": [
"233.33333",
"266.66667",
"500.00000",
"700.00000",
"933.33333",
"966.66667",
"2/1"
]
},
{
"id": "arist_diatinv",
"desc": "Lydian octave species on E, major mode, 12 + 12 + 6 parts",
"stepCount": "7",
"steps": [
"200.000",
"400.000",
"500.000",
"700.000",
"900.000",
"1100.000",
"2/1"
]
},
{
"id": "arist_diatred",
"desc": "Aristo Redup. Diatonic, Dorian Mode, 14 + 14 + 2 parts",
"stepCount": "7",
"steps": [
"233.33333",
"466.66667",
"500.00000",
"700.00000",
"933.33333",
"1166.66667",
"2/1"
]
},
{
"id": "arist_diatred_2",
"desc": "PsAristo 2 Redup. Diatonic 2, 4 + 13 + 13 parts",
"stepCount": "7",
"steps": [
"66.66667",
"283.33333",
"500.00000",
"700.00000",
"766.66667",
"983.33333",
"2/1"
]
},
{
"id": "arist_diatred_3",
"desc": "PsAristo 3 Redup. Diatonic, 8 + 11 + 11 parts",
"stepCount": "7",
"steps": [
"133.33333",
"316.66667",
"500.00000",
"700.00000",
"833.33333",
"1016.66667",
"2/1"
]
},
{
"id": "arist_enh",
"desc": "Aristoxenos' Enharmonion, Dorian mode",
"stepCount": "7",
"steps": [
"50.00000",
"100.00000",
"500.00000",
"700.00000",
"750.00000",
"800.00000",
"2/1"
]
},
{
"id": "arist_enh_2",
"desc": "PsAristo 2 Enharmonic, 3.5 + 3.5 + 23 parts",
"stepCount": "7",
"steps": [
"58.33300",
"116.66700",
"500.00000",
"700.00000",
"758.33300",
"816.66700",
"2/1"
]
},
{
"id": "arist_enh_3",
"desc": "PsAristo Enharmonic, 2.5 + 2.5 + 25 parts",
"stepCount": "7",
"steps": [
"41.66700",
"83.33300",
"500.00000",
"700.00000",
"741.66700",
"783.33300",
"2/1"
]
},
{
"id": "arist_hemchrom",
"desc": "Aristoxenos's Chromatic Hemiolion, Dorian Mode",
"stepCount": "7",
"steps": [
"75.00000",
"150.00000",
"500.00000",
"700.00000",
"775.00000",
"850.00000",
"2/1"
]
},
{
"id": "arist_hemchrom_2",
"desc": "PsAristo C/H Chromatic, 4.5 + 7.5 + 18 parts",
"stepCount": "7",
"steps": [
"75.00000",
"200.00000",
"500.00000",
"700.00000",
"775.00000",
"900.00000",
"2/1"
]
},
{
"id": "arist_hemchrom_3",
"desc": "Dorian mode of Aristoxenos' Hemiolic Chromatic according to Ptolemy's interpretation",
"stepCount": "7",
"steps": ["80/77", "40/37", "4/3", "3/2", "120/77", "60/37", "2/1"]
},
{
"id": "arist_hypenh_2",
"desc": "PsAristo 2nd Hyperenharmonic, 37.5 + 37.5 + 425 cents",
"stepCount": "7",
"steps": [
"37.500 cents",
"75.000 cents",
"500.000 cents",
"700.000 cents",
"737.500 cents",
"775.000 cents",
"2/1"
]
},
{
"id": "arist_hypenh_3",
"desc": "PsAristo 3 Hyperenharmonic, 1.5 + 1.5 + 27 parts",
"stepCount": "7",
"steps": [
"25.000 cents",
"50.000 cents",
"500.000 cents",
"700.000 cents",
"725.000 cents",
"750.000 cents",
"2/1"
]
},
{
"id": "arist_hypenh_4",
"desc": "PsAristo 4 Hyperenharmonic, 2 + 2 + 26 parts",
"stepCount": "7",
"steps": [
"33.333 cents",
"66.667 cents",
"500.000 cents",
"700.000 cents",
"733.333 cents",
"766.667 cents",
"2/1"
]
},
{
"id": "arist_hypenh_5",
"desc": "PsAristo Hyperenharmonic, 23 + 23 + 454 cents",
"stepCount": "7",
"steps": [
"23.000 cents",
"46.000 cents",
"500.000 cents",
"700.000 cents",
"723.000 cents",
"746.000 cents",
"2/1"
]
},
{
"id": "arist_intdiat",
"desc": "Dorian mode of Aristoxenos's Intense Diatonic according to Ptolemy",
"stepCount": "7",
"steps": ["20/19", "20/17", "4/3", "3/2", "30/19", "30/17", "2/1"]
},
{
"id": "arist_penh_2",
"desc": "Permuted Aristoxenos's Enharmonion, 3 + 24 + 3 parts",
"stepCount": "7",
"steps": [
"50.00000",
"450.00000",
"500.00000",
"700.00000",
"750.00000",
"1150.00000",
"2/1"
]
},
{
"id": "arist_penh_3",
"desc": "Permuted Aristoxenos's Enharmonion, 24 + 3 + 3 parts",
"stepCount": "7",
"steps": [
"400.000 cents",
"450.000 cents",
"500.000 cents",
"700.000 cents",
"1100.000 cents",
"1150.000 cents",
"2/1"
]
},
{
"id": "arist_pschrom_2",
"desc": "PsAristo 2 Chromatic, 6.5 + 6.5 + 17 parts",
"stepCount": "7",
"steps": [
"108.33333",
"216.66667",
"500.00000",
"700.00000",
"808.33333",
"916.66667",
"2/1"
]
},
{
"id": "arist_softchrom",
"desc": "Aristoxenos's Chromatic Malakon, Dorian Mode",
"stepCount": "7",
"steps": [
"66.66667",
"133.33333",
"500.00000",
"700.00000",
"766.66667",
"833.33333",
"2/1"
]
},
{
"id": "arist_softchrom_2",
"desc": "Aristoxenos' Soft Chromatic, 6 + 16.5 + 9.5 parts",
"stepCount": "7",
"steps": [
"100.000 cents",
"375.000 cents",
"500.000 cents",
"700.000 cents",
"800.000 cents",
"1075.000 cents",
"2/1"
]
},
{
"id": "arist_softchrom_3",
"desc": "Aristoxenos's Chromatic Malakon, 9.5 + 16.5 + 6 parts",
"stepCount": "7",
"steps": [
"125.000 cents",
"400.000 cents",
"500.000 cents",
"700.000 cents",
"825.000 cents",
"1100.000 cents",
"2/1"
]
},
{
"id": "arist_softchrom_4",
"desc": "PsAristo S. Chromatic, 6 + 7.5 + 16.5 parts",
"stepCount": "7",
"steps": [
"100.000 cents",
"225.000 cents",
"500.000 cents",
"700.000 cents",
"800.000 cents",
"925.000 cents",
"2/1"
]
},
{
"id": "arist_softchrom_5",
"desc": "Dorian mode of Aristoxenos' Soft Chromatic according to Ptolemy's interpretation",
"stepCount": "7",
"steps": ["30/29", "15/14", "4/3", "3/2", "45/29", "45/28", "2/1"]
},
{
"id": "arist_softdiat",
"desc": "Aristoxenos's Diatonon Malakon, Dorian Mode",
"stepCount": "7",
"steps": [
"100.00000",
"250.00000",
"500.00000",
"700.00000",
"800.00000",
"950.00000",
"2/1"
]
},
{
"id": "arist_softdiat_2",
"desc": "Dorian Mode, 6 + 15 + 9 parts",
"stepCount": "7",
"steps": [
"100.00000",
"350.00000",
"500.00000",
"700.00000",
"800.00000",
"1050.00000",
"2/1"
]
},
{
"id": "arist_softdiat_3",
"desc": "Dorian Mode, 9 + 15 + 6 parts",
"stepCount": "7",
"steps": [
"150.00000",
"400.00000",
"500.00000",
"700.00000",
"850.00000",
"1000.00000",
"2/1"
]
},
{
"id": "arist_softdiat_4",
"desc": "Dorian Mode, 9 + 6 + 15 parts",
"stepCount": "7",
"steps": [
"150.00000",
"250.00000",
"500.00000",
"700.00000",
"850.00000",
"950.00000",
"2/1"
]
},
{
"id": "arist_softdiat_5",
"desc": "Dorian Mode, 15 + 6 + 9 parts",
"stepCount": "7",
"steps": [
"250.00000",
"350.00000",
"500.00000",
"700.00000",
"950.00000",
"1050.00000",
"2/1"
]
},
{
"id": "arist_softdiat_6",
"desc": "Dorian Mode, 15 + 9 + 6 parts",
"stepCount": "7",
"steps": [
"250.00000",
"400.00000",
"500.00000",
"700.00000",
"950.00000",
"1100.00000",
"2/1"
]
},
{
"id": "arist_softdiat_7",
"desc": "Dorian mode of Aristoxenos's Soft Diatonic according to Ptolemy",
"stepCount": "7",
"steps": ["20/19", "8/7", "4/3", "3/2", "30/19", "12/7", "2/1"]
},
{
"id": "arist_synchrom",
"desc": "Aristoxenos's Chromatic Syntonon, Dorian Mode",
"stepCount": "7",
"steps": [
"100.00000",
"200.00000",
"500.00000",
"700.00000",
"800.00000",
"900.00000",
"2/1"
]
},
{
"id": "arist_syndiat",
"desc": "Aristoxenos's Diatonon Syntonon, Dorian Mode",
"stepCount": "7",
"steps": [
"100.00000",
"300.00000",
"500.00000",
"700.00000",
"800.00000",
"1000.00000",
"2/1"
]
},
{
"id": "arist_unchrom",
"desc": "Aristoxenos's Unnamed Chromatic, Dorian Mode, 4 + 8 + 18 parts",
"stepCount": "7",
"steps": [
"66.66667",
"200.00000",
"500.00000",
"700.00000",
"766.66667",
"900.00000",
"2/1"
]
},
{
"id": "arist_unchrom_2",
"desc": "Dorian Mode, a 1:2 Chromatic, 8 + 4 + 18 parts",
"stepCount": "7",
"steps": [
"133.33333",
"200.00000",
"500.00000",
"700.00000",
"833.33333",
"900.00000",
"2/1"
]
},
{
"id": "arist_unchrom_3",
"desc": "Dorian Mode, a 1:2 Chromatic, 18 + 4 + 8 parts",
"stepCount": "7",
"steps": [
"300.00000",
"366.66667",
"500.00000",
"700.00000",
"1000.00000",
"1066.66667",
"2/1"
]
},
{
"id": "arist_unchrom_4",
"desc": "Dorian Mode, a 1:2 Chromatic, 18 + 8 + 4 parts",
"stepCount": "7",
"steps": [
"300.00000",
"433.33333",
"500.00000",
"700.00000",
"1000.00000",
"1133.33333",
"2/1"
]
},
{
"id": "arnautoff_21",
"desc": "Philip Arnautoff, transposed Archytas enharmonic (2005), 1/1 vol.12 no.1",
"stepCount": "21",
"steps": [
"28/27",
"16/15",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"112/81",
"45/32",
"64/45",
"81/56",
"3/2",
"14/9",
"8/5",
"5/3",
"12/7",
"16/9",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "aron_neidhardt",
"desc": "Aron-Neidhardt equal beating well temperament",
"stepCount": "12",
"steps": [
"256/243",
"193.32804",
"32/27",
"386.35659",
"4/3",
"1024/729",
"697.46266",
"128/81",
"889.89223",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "art_nam",
"desc": "Artificial Nam System",
"stepCount": "9",
"steps": [
"11/10",
"17/14",
"36/29",
"4/3",
"27/20",
"3/2",
"33/20",
"38/21",
"2/1"
]
},
{
"id": "artusi",
"desc": "Clavichord tuning of Giovanni Maria Artusi (1603). 1/4-comma with mean semitones",
"stepCount": "12",
"steps": [
"96.57800",
"193.15700",
"289.73500",
"5/4",
"503.42200",
"600.00000",
"696.57800",
"793.15700",
"889.73500",
"986.31400",
"1082.89200",
"2/1"
]
},
{
"id": "artusi_2",
"desc": "Artusi's tuning no. 2, 1/6-comma meantone with mean semitones",
"stepCount": "12",
"steps": [
"98.37050",
"196.74100",
"295.11150",
"393.48200",
"501.62900",
"600.00000",
"698.37100",
"796.74150",
"895.11200",
"993.48250",
"1091.85300",
"2/1"
]
},
{
"id": "artusi_3",
"desc": "Artusi's tuning no. 3",
"stepCount": "12",
"steps": [
"77.00770",
"10/9",
"298.00613",
"403.40214",
"508.79814",
"585.80585",
"691.20186",
"768.20956",
"873.60557",
"989.20799",
"1094.60399",
"2/1"
]
},
{
"id": "athan_chrom",
"desc": "Athanasopoulos's Byzantine Liturgical mode Chromatic",
"stepCount": "7",
"steps": [
"150.00000",
"400.00000",
"500.00000",
"700.00000",
"850.00000",
"1100.00000",
"2/1"
]
},
{
"id": "atomschis",
"desc": "Atom Schisma Scale",
"stepCount": "12",
"steps": [
"156348578434374084375/147573952589676412928",
"134217728/119574225",
"1307544150375/1099511627776",
"18014398509481984/14297995284350625",
"10935/8192",
"1709671705179880612640625/1208925819614629174706176",
"16384/10935",
"14297995284350625/9007199254740992",
"2199023255552/1307544150375",
"119574225/67108864",
"295147905179352825856/156348578434374084375",
"2/1"
]
},
{
"id": "augdimhextrug",
"desc": "Sister wakalix to Wilson class",
"stepCount": "12",
"steps": [
"15/14",
"35/32",
"6/5",
"5/4",
"75/56",
"7/5",
"3/2",
"25/16",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "augdommean",
"desc": "August-dominant-meantone Fokker block",
"stepCount": "12",
"steps": [
"28/27",
"9/8",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"14/9",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "augment_15_br_1",
"desc": "Augmented[15] with a brat of 1",
"stepCount": "15",
"steps": [
"93.47087",
"186.94174",
"213.05826",
"306.52913",
"400.00000",
"493.47087",
"586.94174",
"613.05826",
"706.52913",
"800.00000",
"893.47087",
"986.94174",
"1013.05826",
"1106.52913",
"2/1"
]
},
{
"id": "augteta",
"desc": "Linear Division of the 11/8, duplicated on the 16/11",
"stepCount": "8",
"steps": [
"44/41",
"22/19",
"44/35",
"11/8",
"16/11",
"64/41",
"32/19",
"64/35"
]
},
{
"id": "augteta_2",
"desc": "Linear Division of the 7/5, duplicated on the 10/7",
"stepCount": "8",
"steps": ["14/13", "7/6", "14/11", "7/5", "10/7", "20/13", "5/3", "20/11"]
},
{
"id": "augtetb",
"desc": "Harmonic mean division of 11/8",
"stepCount": "8",
"steps": [
"88/85",
"44/41",
"22/19",
"11/8",
"16/11",
"128/85",
"64/41",
"32/19"
]
},
{
"id": "augtetc",
"desc": "11/10 C.I.",
"stepCount": "8",
"steps": [
"15/14",
"15/13",
"5/4",
"11/8",
"16/11",
"120/77",
"240/143",
"20/11"
]
},
{
"id": "augtetd",
"desc": "11/9 C.I.",
"stepCount": "8",
"steps": [
"27/26",
"27/25",
"9/8",
"11/8",
"16/11",
"216/143",
"432/275",
"18/11"
]
},
{
"id": "augtete",
"desc": "5/4 C.I.",
"stepCount": "8",
"steps": ["33/32", "33/31", "11/10", "11/8", "16/11", "3/2", "48/31", "8/5"]
},
{
"id": "augtetf",
"desc": "5/4 C.I. again",
"stepCount": "8",
"steps": ["99/98", "33/32", "11/10", "11/8", "16/11", "72/49", "3/2", "8/5"]
},
{
"id": "augtetg",
"desc": "9/8 C.I.",
"stepCount": "8",
"steps": [
"33/31",
"33/29",
"11/9",
"11/8",
"16/11",
"48/31",
"48/29",
"16/9"
]
},
{
"id": "augteth",
"desc": "9/8 C.I. A gapped version of this scale is called AugTetI",
"stepCount": "8",
"steps": ["33/31", "11/10", "11/9", "11/8", "16/11", "48/31", "8/5", "16/9"]
},
{
"id": "augtetj",
"desc": "9/8 C.I. comprised of 11:10:9:8 subharmonic series on 1 and 8:9:10:11 on 16/11",
"stepCount": "6",
"steps": ["11/10", "11/9", "11/8", "16/11", "18/11", "20/11"]
},
{
"id": "augtetk",
"desc": "9/8 C.I. This is the converse form of AugTetJ",
"stepCount": "6",
"steps": ["9/8", "5/4", "11/8", "16/11", "8/5", "16/9"]
},
{
"id": "augtetl",
"desc": "9/8 C.I. This is the harmonic form of AugTetI",
"stepCount": "6",
"steps": ["9/8", "5/4", "11/8", "16/11", "18/11", "20/11"]
},
{
"id": "avg_bac",
"desc": "Average Bac System",
"stepCount": "7",
"steps": ["10/9", "20/17", "4/3", "3/2", "5/3", "30/17", "2/1"]
},
{
"id": "avicenna_17",
"desc": "Tuning by Avicenna (Ibn Sina), Ahmed Mahmud Hifni, Cairo, 1977",
"stepCount": "17",
"steps": [
"273/256",
"13/12",
"9/8",
"32/27",
"39/32",
"81/64",
"4/3",
"91/64",
"13/9",
"3/2",
"128/81",
"13/8",
"27/16",
"16/9",
"91/48",
"52/27",
"2/1"
]
},
{
"id": "avicenna_19",
"desc": "Arabic scale by Ibn Sina",
"stepCount": "19",
"steps": [
"256/243",
"1024/945",
"9/8",
"32/27",
"8192/6561",
"81/64",
"4/3",
"48/35",
"729/512",
"4096/2835",
"3/2",
"128/81",
"512/315",
"27/16",
"16/9",
"64/35",
"243/128",
"129140163/67108864",
"2/1"
]
},
{
"id": "avicenna_chrom",
"desc": "Dorian mode a chromatic genus of Avicenna",
"stepCount": "7",
"steps": ["36/35", "8/7", "4/3", "3/2", "54/35", "12/7", "2/1"]
},
{
"id": "avicenna_chrom_2",
"desc": "Dorian Mode, a 1:2 Chromatic, 4 + 18 + 8 parts",
"stepCount": "7",
"steps": [
"66.66667",
"366.66667",
"500.00000",
"700.00000",
"766.66667",
"1066.66667",
"2/1"
]
},
{
"id": "avicenna_chrom_3",
"desc": "Avicenna's Chromatic permuted",
"stepCount": "7",
"steps": ["10/9", "35/27", "4/3", "3/2", "5/3", "35/18", "2/1"]
},
{
"id": "avicenna_diat",
"desc": "Dorian mode a soft diatonic genus of Avicenna",
"stepCount": "7",
"steps": ["14/13", "7/6", "4/3", "3/2", "21/13", "7/4", "2/1"]
},
{
"id": "avicenna_diff",
"desc": "Difference tones of Avicenna's Soft diatonic reduced by 2/1",
"stepCount": "12",
"steps": [
"33/32",
"35/32",
"9/8",
"19/16",
"21/16",
"45/32",
"3/2",
"49/32",
"27/16",
"7/4",
"63/32",
"2/1"
]
},
{
"id": "avicenna_enh",
"desc": "Dorian mode of Avicenna's (Ibn Sina) Enharmonic genus",
"stepCount": "7",
"steps": ["40/39", "16/15", "4/3", "3/2", "20/13", "8/5", "2/1"]
},
{
"id": "avicenna",
"desc": "Soft diatonic of Avicenna (Ibn Sina)",
"stepCount": "7",
"steps": ["10/9", "8/7", "4/3", "3/2", "5/3", "12/7", "2/1"]
},
{
"id": "awad",
"desc": "d'Erlanger vol.5, p. 37, after Mans.ur 'Awad",
"stepCount": "24",
"steps": [
"40/39",
"20/19",
"40/37",
"10/9",
"8/7",
"20/17",
"40/33",
"5/4",
"40/31",
"4/3",
"48/35",
"24/17",
"16/11",
"3/2",
"20/13",
"30/19",
"60/37",
"5/3",
"12/7",
"30/17",
"20/11",
"15/8",
"60/31",
"2/1"
]
},
{
"id": "awraamoff",
"desc": "Awraamoff Septimal Just (1920)",
"stepCount": "12",
"steps": [
"9/8",
"8/7",
"6/5",
"5/4",
"21/16",
"4/3",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "ayers_19",
"desc": "Lydia Ayers, NINETEEN, for 19 for the 90's CD. Repeats at 37/19 (or 2/1)",
"stepCount": "19",
"steps": [
"37/36",
"37/35",
"37/34",
"37/33",
"37/32",
"37/31",
"37/30",
"37/29",
"37/28",
"37/27",
"37/26",
"37/25",
"37/24",
"37/23",
"37/22",
"37/21",
"37/20",
"37/19",
"2/1"
]
},
{
"id": "ayers_37",
"desc": "Lydia Ayers, algorithmic composition, subharmonics 1-37",
"stepCount": "36",
"steps": [
"37/36",
"37/35",
"37/34",
"37/33",
"37/32",
"37/31",
"37/30",
"37/29",
"37/28",
"37/27",
"37/26",
"37/25",
"37/24",
"37/23",
"37/22",
"37/21",
"37/20",
"37/19",
"37/18",
"37/17",
"37/16",
"37/15",
"37/14",
"37/13",
"37/12",
"37/11",
"37/10",
"37/9",
"37/8",
"37/7",
"37/6",
"37/5",
"37/4",
"37/3",
"37/2",
"37/1"
]
},
{
"id": "ayers_me",
"desc": "Lydia Ayers, Merapi (1996), Slendro 0 2 4 5 7 9, Pelog 0 1 3 6 8 9",
"stepCount": "9",
"steps": [
"15/14",
"8/7",
"33/28",
"9/7",
"3/2",
"45/28",
"12/7",
"27/14",
"2/1"
]
},
{
"id": "b_8_11",
"desc": "8-tET approximation with minimal order 11 beats",
"stepCount": "8",
"steps": ["12/11", "6/5", "13/10", "7/5", "17/11", "5/3", "11/6", "2/1"]
},
{
"id": "b_10_13",
"desc": "10-tET approximation with minimal order 13 beats",
"stepCount": "10",
"steps": [
"14/13",
"8/7",
"16/13",
"4/3",
"17/12",
"3/2",
"13/8",
"7/4",
"13/7",
"2/1"
]
},
{
"id": "b_12_17",
"desc": "12-tET approximation with minimal order 17 beats",
"stepCount": "12",
"steps": [
"18/17",
"9/8",
"19/16",
"5/4",
"4/3",
"17/12",
"3/2",
"27/17",
"5/3",
"16/9",
"17/9",
"2/1"
]
},
{
"id": "b_14_19",
"desc": "14-tET approximation with minimal order 19 beats",
"stepCount": "14",
"steps": [
"20/19",
"21/19",
"7/6",
"11/9",
"9/7",
"4/3",
"17/12",
"3/2",
"25/16",
"23/14",
"31/18",
"29/16",
"19/10",
"2/1"
]
},
{
"id": "b_15_21",
"desc": "15-tET approximation with minimal order 21 beats",
"stepCount": "15",
"steps": [
"22/21",
"11/10",
"23/20",
"6/5",
"5/4",
"4/3",
"29/21",
"13/9",
"3/2",
"27/17",
"5/3",
"7/4",
"31/17",
"21/11",
"2/1"
]
},
{
"id": "badings_1",
"desc": "Henk Badings, harmonic scale, Lydomixolydisch",
"stepCount": "9",
"steps": ["9/8", "5/4", "11/8", "3/2", "13/8", "7/4", "2/1", "9/4", "5/2"]
},
{
"id": "badings_2",
"desc": "Henk Badings, subharmonic scale, Dorophrygisch",
"stepCount": "9",
"steps": [
"10/9",
"5/4",
"10/7",
"20/13",
"5/3",
"20/11",
"2/1",
"20/9",
"5/2"
]
},
{
"id": "bagpipe_1",
"desc": "Bulgarian bagpipe tuning",
"stepCount": "12",
"steps": [
"66.00000",
"202.00000",
"316.00000",
"399.00000",
"509.00000",
"640.00000",
"706.00000",
"803.00000",
"910.00000",
"1011.00000",
"1092.00000",
"2/1"
]
},
{
"id": "bagpipe_2",
"desc": "Highland Bagpipe, from Acustica4: 231 (1954) J.M.A Lenihan and S. McNeill",
"stepCount": "9",
"steps": ["8/9", "1/1", "9/8", "5/4", "27/20", "3/2", "5/3", "9/5", "2/1"]
},
{
"id": "bagpipe_3",
"desc": "Highland Bagpipe, Allan Chatto, 1991. From Australian Pipe Band College",
"stepCount": "9",
"steps": ["9/10", "1/1", "9/8", "5/4", "4/3", "3/2", "5/3", "9/5", "2/1"]
},
{
"id": "bagpipe_4",
"desc": "Highland Bagpipe, Ewan Macpherson in 'NZ Pipeband', Winter 1998",
"stepCount": "9",
"steps": [
"7/8",
"1/1",
"9/8",
"5/4",
"4/3",
"3/2",
"5/3",
"7/4",
"1190.00000"
]
},
{
"id": "bailey_well",
"desc": "Paul Bailey's proportional beating modern temperament (1993)",
"stepCount": "12",
"steps": [
"92.16501",
"195.19000",
"296.05501",
"391.68000",
"499.94501",
"590.17001",
"698.69500",
"794.06001",
"893.78500",
"997.95001",
"1093.67500",
"2/1"
]
},
{
"id": "bailey_well_2",
"desc": "Paul Bailey's modern well temperament (2002)",
"stepCount": "12",
"steps": [
"92.51501",
"195.69000",
"296.45501",
"392.18000",
"500.44501",
"590.57001",
"699.99500",
"794.46001",
"894.28500",
"998.45001",
"1094.17500",
"2/1"
]
},
{
"id": "bailey_well_3",
"desc": "Paul Bailey's equal beating well temperament",
"stepCount": "12",
"steps": [
"256/243",
"12224/10935",
"32/27",
"13696/10935",
"4/3",
"1024/729",
"16348/10935",
"128/81",
"18304/10935",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "balafon",
"desc": "Observed balafon tuning from Patna, Helmholtz/Ellis p. 518, nr.81",
"stepCount": "7",
"steps": [
"187.00000",
"356.00000",
"526.00000",
"672.00000",
"856.00000",
"985.00000",
"1222.00000"
]
},
{
"id": "balafon_2",
"desc": "Observed balafon tuning from West-Africa, Helmholtz/Ellis p. 518, nr.86",
"stepCount": "7",
"steps": [
"152.00000",
"287.00000",
"533.00000",
"724.00000",
"890.00000",
"1039.00000",
"2/1"
]
},
{
"id": "balafon_3",
"desc": "Pitt-River's balafon tuning from West-Africa, Helmholtz/Ellis p. 518, nr.87",
"stepCount": "7",
"steps": [
"195.00000",
"289.00000",
"513.00000",
"686.00000",
"796.00000",
"1008.00000",
"1209.00000"
]
},
{
"id": "balafon_4",
"desc": "Mandinka balafon scale from Gambia",
"stepCount": "7",
"steps": [
"151.00000",
"345.00000",
"526.00000",
"660.00000",
"861.00000",
"1025.00000",
"1141.00000"
]
},
{
"id": "balafon_5",
"desc": "An observed balafon tuning from Singapore, Helmholtz/Ellis p. 518, nr.82",
"stepCount": "7",
"steps": [
"169.00000",
"350.00000",
"543.00000",
"709.00000",
"894.00000",
"1040.00000",
"1205.00000"
]
},
{
"id": "balafon_6",
"desc": "Observed balafon tuning from Burma, Helmholtz/Ellis p. 518, nr.84",
"stepCount": "7",
"steps": [
"114.00000",
"350.00000",
"550.00000",
"687.00000",
"838.00000",
"1032.00000",
"1196.00000"
]
},
{
"id": "balafon_7",
"desc": "Observed South Pacific pentatonic balafon tuning, Helmholtz/Ellis p. 518, nr.93",
"stepCount": "5",
"steps": ["202.00000", "370.00000", "685.00000", "903.00000", "2/1"]
},
{
"id": "baldy_17",
"desc": "Baldy[17] 2.9.5.7.13 subgroup scale in 147-tET tuning",
"stepCount": "17",
"steps": [
"24.48980",
"179.59184",
"204.08163",
"228.57143",
"383.67347",
"408.16327",
"432.65306",
"587.75510",
"612.24490",
"636.73469",
"791.83673",
"816.32653",
"971.42857",
"995.91837",
"1020.40816",
"1175.51020",
"2/1"
]
},
{
"id": "bamboo",
"desc": "Pythagorean scale with fifth average from Chinese bamboo tubes",
"stepCount": "23",
"steps": [
"48.00000",
"102.00000",
"156.00000",
"204.00000",
"258.00000",
"312.00000",
"366.00000",
"414.00000",
"468.00000",
"522.00000",
"570.00000",
"624.00000",
"678.00000",
"726.00000",
"780.00000",
"834.00000",
"882.00000",
"936.00000",
"990.00000",
"1044.00000",
"1092.00000",
"1146.00000",
"2/1"
]
},
{
"id": "banchieri",
"desc": "Adriano Banchieri, in L'Organo suonarino (1605)",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"6/5",
"81/64",
"4/3",
"45/32",
"3/2",
"405/256",
"27/16",
"9/5",
"243/128",
"2/1"
]
},
{
"id": "bapere",
"desc": "African, Bapere Horns Aerophone, made of reed, one note each",
"stepCount": "5",
"steps": [
"599.00000",
"813.00000",
"1011.00000",
"1217.00000",
"1510.00000"
]
},
{
"id": "barbour_chrom_1",
"desc": "Barbour's #1 Chromatic",
"stepCount": "7",
"steps": ["55/54", "10/9", "4/3", "3/2", "55/36", "5/3", "2/1"]
},
{
"id": "barbour_chrom_2",
"desc": "Barbour's #2 Chromatic",
"stepCount": "7",
"steps": ["40/39", "10/9", "4/3", "3/2", "20/13", "5/3", "2/1"]
},
{
"id": "barbour_chrom_3",
"desc": "Barbour's #3 Chromatic",
"stepCount": "7",
"steps": ["64/63", "8/7", "4/3", "3/2", "32/21", "12/7", "2/1"]
},
{
"id": "barbour_chrom_3_p",
"desc": "permuted Barbour's #3 Chromatic",
"stepCount": "7",
"steps": ["9/8", "8/7", "4/3", "3/2", "27/16", "12/7", "2/1"]
},
{
"id": "barbour_chrom_3_p_2",
"desc": "permuted Barbour's #3 Chromatic",
"stepCount": "7",
"steps": ["7/6", "32/27", "4/3", "3/2", "7/4", "16/9", "2/1"]
},
{
"id": "barbour_chrom_4",
"desc": "Barbour's #4 Chromatic",
"stepCount": "7",
"steps": ["81/80", "9/8", "4/3", "3/2", "243/160", "27/16", "2/1"]
},
{
"id": "barbour_chrom_4_p",
"desc": "permuted Barbour's #4 Chromatic",
"stepCount": "7",
"steps": ["10/9", "9/8", "4/3", "3/2", "5/3", "27/16", "2/1"]
},
{
"id": "barbour_chrom_4_p_2",
"desc": "permuted Barbour's #4 Chromatic",
"stepCount": "7",
"steps": ["32/27", "6/5", "4/3", "3/2", "16/9", "9/5", "2/1"]
},
{
"id": "barca_a",
"desc": "Barca A",
"stepCount": "12",
"steps": [
"92.18000",
"200.00000",
"296.09000",
"397.39333",
"4/3",
"593.48333",
"3/2",
"794.13500",
"899.34833",
"998.04500",
"1095.43833",
"2/1"
]
},
{
"id": "barca",
"desc": "Barca",
"stepCount": "12",
"steps": [
"92.18000",
"197.39333",
"296.09000",
"393.48333",
"4/3",
"590.22500",
"698.04500",
"794.13500",
"895.43833",
"16/9",
"1091.52833",
"2/1"
]
},
{
"id": "barkechli",
"desc": "Mehdi Barkechli, 27-tone pyth. Arabic scale",
"stepCount": "27",
"steps": [
"531441/524288",
"256/243",
"2187/2048",
"65536/59049",
"9/8",
"4782969/4194304",
"32/27",
"19683/16384",
"8192/6561",
"81/64",
"4/3",
"177147/131072",
"1024/729",
"729/512",
"262144/177147",
"3/2",
"1594323/1048576",
"128/81",
"6561/4096",
"32768/19683",
"27/16",
"16/9",
"59049/32768",
"4096/2187",
"243/128",
"1048576/531441",
"2/1"
]
},
{
"id": "barlow_13",
"desc": "7-limit rational 13-equal, Barlow, On the Quantification of Harmony and Metre",
"stepCount": "13",
"steps": [
"135/128",
"9/8",
"7/6",
"5/4",
"21/16",
"48/35",
"81/56",
"243/160",
"8/5",
"12/7",
"9/5",
"243/128",
"2/1"
]
},
{
"id": "barlow_17",
"desc": "11-limit rational 17-equal, Barlow, On the Quantification of Harmony and Metre",
"stepCount": "17",
"steps": [
"25/24",
"27/25",
"9/8",
"32/27",
"11/9",
"32/25",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"18/11",
"27/16",
"16/9",
"50/27",
"48/25",
"2/1"
]
},
{
"id": "barnes",
"desc": "John Barnes' temperament (1977) made after analysis of Wohltemperierte Klavier, 1/6 P",
"stepCount": "12",
"steps": [
"94.13500",
"196.09000",
"298.04500",
"392.18000",
"501.95500",
"592.18000",
"698.04500",
"796.09000",
"894.13500",
"1000.00000",
"1094.13500",
"2/1"
]
},
{
"id": "barnes_2",
"desc": "John Barnes' temperament (1971), 1/8 P",
"stepCount": "12",
"steps": [
"96.09000",
"198.04500",
"297.06750",
"396.09000",
"500.97750",
"594.13500",
"699.02250",
"798.04500",
"897.06750",
"999.02250",
"1095.11250",
"2/1"
]
},
{
"id": "barton",
"desc": "Jacob Barton, tetratetradic scale on 6:7:9:11",
"stepCount": "12",
"steps": [
"77/72",
"12/11",
"9/8",
"7/6",
"14/11",
"11/8",
"3/2",
"18/11",
"121/72",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "barton_2",
"desc": "Jacob Barton, mode of 88CET, TL 17-01-2007",
"stepCount": "11",
"steps": [
"176.00000",
"264.00000",
"440.00000",
"528.00000",
"616.00000",
"792.00000",
"880.00000",
"1056.00000",
"1144.00000",
"1320.00000",
"1408.00000"
]
},
{
"id": "battaglia_16",
"desc": "Mike Battaglia 5-limit 16-tone scale",
"stepCount": "16",
"steps": [
"16/15",
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "beardsley_8",
"desc": "David Beardsley's scale used in \"Sonic Bloom\"(1999)",
"stepCount": "8",
"steps": ["9/8", "7/6", "9/7", "11/8", "3/2", "13/8", "7/4", "2/1"]
},
{
"id": "bedos",
"desc": "Temperament of Dom Fran�ois B�dos de Celles (1770), after M. Tessmer",
"stepCount": "12",
"steps": [
"74.97368",
"191.00623",
"311.34003",
"5/4",
"502.34626",
"577.31994",
"697.65374",
"25/16",
"888.65997",
"1008.99377",
"1083.96746",
"2/1"
]
},
{
"id": "belet",
"desc": "Belet, Brian 1992 Proceedings of the ICMC pp.158-161.",
"stepCount": "13",
"steps": [
"16/15",
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"11/8",
"3/2",
"8/5",
"13/8",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "bell_mt_partials",
"desc": "Partials of major third bell. 1/1=523.5677 Hz, hum note=-1200.42 c. Andr� Lehr, 2006.",
"stepCount": "8",
"steps": [
"398.84731",
"698.85161",
"961.92407",
"1198.84247",
"1321.95084",
"1653.88234",
"1898.84245",
"2470.16884"
]
},
{
"id": "bellingwolde_org",
"desc": "Original tuning of the Freytag organ in Bellingwolde",
"stepCount": "12",
"steps": [
"256/243",
"196.09000",
"301.95500",
"392.18000",
"501.95500",
"1024/729",
"3/2",
"796.09000",
"894.13500",
"1000.00000",
"1094.13500",
"2/1"
]
},
{
"id": "bellingwolde",
"desc": "Current 1/6-P. comma mod.mean of Freytag organ in Bellingwolde. Ortgies,2002",
"stepCount": "12",
"steps": [
"256/243",
"196.09000",
"301.95500",
"392.18000",
"501.95500",
"1024/729",
"698.04500",
"796.09000",
"894.13500",
"1000.00000",
"1090.22500",
"2/1"
]
},
{
"id": "belobog_31",
"desc": "Belobog[31] hobbit in 626-tET, commas 3136/3125, 441/440",
"stepCount": "31",
"steps": [
"38.33866",
"82.42812",
"111.18211",
"164.85623",
"193.61022",
"231.94888",
"276.03834",
"304.79233",
"343.13099",
"387.22045",
"425.55911",
"469.64856",
"498.40256",
"536.74121",
"580.83067",
"619.16933",
"663.25879",
"701.59744",
"730.35144",
"774.44089",
"812.77955",
"856.86901",
"895.20767",
"923.96166",
"968.05112",
"1006.38978",
"1035.14377",
"1088.81789",
"1117.57188",
"1161.66134",
"2/1"
]
},
{
"id": "bemetzrieder_2",
"desc": "Anton Bemetzrieder temperament nr. 2 (1808), is Vallotti in F#",
"stepCount": "12",
"steps": [
"105.86500",
"9/8",
"301.95500",
"81/64",
"4/3",
"607.82000",
"3/2",
"803.91000",
"27/16",
"1000.00000",
"243/128",
"2/1"
]
},
{
"id": "bendeler_b",
"desc": "Die Br�che nach Bendeler, Jerzy Erdmann: Ein Rechenmodell f�r historische Mensurationsmethoden, p. 342",
"stepCount": "12",
"steps": [
"256/243",
"32768/29403",
"32/27",
"4096/3267",
"4/3",
"1024/729",
"65536/43923",
"128/81",
"16384/9801",
"16/9",
"2048/1089",
"2/1"
]
},
{
"id": "bendeler",
"desc": "J. Ph. Bendeler well temperament",
"stepCount": "12",
"steps": [
"256/243",
"194.63000",
"32/27",
"392.45000",
"4/3",
"1024/729",
"3/2",
"128/81",
"890.49500",
"16/9",
"1094.40500",
"2/1"
]
},
{
"id": "bendeler_1",
"desc": "Bendeler I temperament (c.1690), three 1/3P comma tempered fifths",
"stepCount": "12",
"steps": [
"256/243",
"188.26999",
"32/27",
"392.18000",
"4/3",
"1024/729",
"694.13500",
"128/81",
"890.22500",
"16/9",
"1094.13500",
"2/1"
]
},
{
"id": "bendeler_2",
"desc": "Bendeler II temperament (c.1690), three 1/3P comma tempered fifths",
"stepCount": "12",
"steps": [
"256/243",
"196.09000",
"32/27",
"392.18000",
"4/3",
"596.09000",
"694.13500",
"128/81",
"890.22500",
"16/9",
"1094.13500",
"2/1"
]
},
{
"id": "bendeler_3",
"desc": "Bendeler III temperament (c.1690), four 1/4P tempered fifths",
"stepCount": "12",
"steps": [
"96.09000",
"192.18000",
"32/27",
"396.09000",
"4/3",
"594.13500",
"696.09000",
"798.04500",
"894.13500",
"16/9",
"1092.18000",
"2/1"
]
},
{
"id": "bermudo_v",
"desc": "Bermudo's vihuela temperament, 3 1/6P, 1 1/2P comma",
"stepCount": "12",
"steps": [
"492075/463684",
"540/481",
"32/27",
"1215/964",
"4/3",
"164025/115921",
"3/2",
"1476225/927368",
"810/481",
"16/9",
"3645/1928",
"2/1"
]
},
{
"id": "bermudo",
"desc": "Temperament of Fr. Juan Bermudo (1555)",
"stepCount": "12",
"steps": [
"100.10289",
"200.20579",
"32/27",
"400.41158",
"4/3",
"598.14789",
"3/2",
"802.05790",
"902.16079",
"16/9",
"1102.36658",
"2/1"
]
},
{
"id": "bermudo_2",
"desc": "Temperament of Fr. Juan Bermudo, interpr. of Franz Josef Ratte: Die Temperatur der Clavierinstrumente, p. 227",
"stepCount": "12",
"steps": [
"100.00000",
"200.00000",
"32/27",
"400.00000",
"4/3",
"598.04500",
"3/2",
"801.95500",
"901.95500",
"16/9",
"1101.95500",
"2/1"
]
},
{
"id": "betacub",
"desc": "inverted 3x3x3 9-limit quintad cube beta (5120/5103) synch tempered",
"stepCount": "46",
"steps": [
"49.729878",
"85.285706",
"110.150645",
"120.600012",
"135.015584",
"170.329890",
"181.020779",
"205.885718",
"230.750657",
"255.615596",
"266.306484",
"316.036363",
"351.350669",
"386.906496",
"436.636374",
"472.192202",
"497.057141",
"521.922080",
"546.787019",
"582.342847",
"617.657153",
"632.072725",
"667.387031",
"702.942859",
"727.807798",
"752.672737",
"763.363626",
"788.228565",
"813.093504",
"823.542871",
"883.963637",
"898.379209",
"908.828577",
"933.693516",
"969.249343",
"994.114282",
"1004.563649",
"1018.979221",
"1043.844161",
"1079.399988",
"1089.849355",
"1114.714294",
"1129.129866",
"1139.579233",
"1164.444172",
"2/1"
]
},
{
"id": "bethisy",
"desc": "Bethisy temperament ordinaire, see Pierre-Yves Asselin: Musique et temperament",
"stepCount": "12",
"steps": [
"86.80400",
"193.15700",
"288.75800",
"5/4",
"496.25300",
"586.80400",
"696.57800",
"786.80300",
"889.73500",
"992.50600",
"1086.31400",
"2/1"
]
},
{
"id": "biezen_chaumont",
"desc": "Jan van Biezen, after Chaumont, 1/8 Pyth. comma. Lochem, Hervormde Gudulakerk (1978)",
"stepCount": "12",
"steps": [
"99.02250",
"198.04500",
"302.93250",
"396.09000",
"500.97750",
"600.00000",
"699.02250",
"798.04500",
"897.06750",
"1001.95500",
"1095.11250",
"2/1"
]
},
{
"id": "biezen",
"desc": "Jan van Biezen modified meantone (1974)",
"stepCount": "12",
"steps": [
"86.80214",
"193.15686",
"299.51157",
"5/4",
"503.42157",
"584.84714",
"696.57843",
"788.75714",
"889.73529",
"1001.46657",
"15/8",
"2/1"
]
},
{
"id": "biezen_2",
"desc": "Jan van Biezen 2, also Siracusa (early 17th cent.), modified 1/4 comma MT",
"stepCount": "12",
"steps": [
"86.80374",
"193.15750",
"32/27",
"386.31499",
"4/3",
"584.84874",
"696.57875",
"788.75875",
"889.73625",
"16/9",
"1082.89374",
"2/1"
]
},
{
"id": "biezen_3",
"desc": "Jan van Biezen 3 (2004) (also called Van Biezen I)",
"stepCount": "12",
"steps": [
"256/243",
"196.09000",
"298.04500",
"392.18000",
"501.95500",
"1024/729",
"698.04500",
"128/81",
"894.13500",
"1000.00000",
"1090.22500",
"2/1"
]
},
{
"id": "biggulp_bunya",
"desc": "Biggulp tempered in POTE-tuned 13-limit bunya",
"stepCount": "12",
"steps": [
"62.40123",
"207.08642",
"269.48764",
"382.97222",
"476.57406",
"558.85802",
"703.54321",
"765.94444",
"910.62962",
"973.03085",
"1086.51543",
"2/1"
]
},
{
"id": "biggulp",
"desc": "Big Gulp",
"stepCount": "12",
"steps": [
"33/32",
"9/8",
"7/6",
"5/4",
"21/16",
"11/8",
"3/2",
"99/64",
"27/16",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "bigler_12",
"desc": "Kurt Bigler, JI organ tuning, TL 28-3-2004",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"7/6",
"5/4",
"4/3",
"11/8",
"3/2",
"25/16",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "bihex_top",
"desc": "Bihexany in octoid TOP tuning",
"stepCount": "12",
"steps": [
"101.318325",
"267.590529",
"385.147324",
"417.624264",
"535.181059",
"701.453263",
"802.771588",
"883.963938",
"969.043793",
"1033.997672",
"1119.077527",
"1200.269877"
]
},
{
"id": "bihex_540",
"desc": "Bihexany in 540/539 tempering",
"stepCount": "12",
"steps": [
"101.621102",
"267.824229",
"386.256798",
"417.215888",
"535.648458",
"701.851584",
"803.472686",
"884.228421",
"969.675813",
"1033.620081",
"1119.067472",
"1199.823207"
]
},
{
"id": "bihexany_octoid",
"desc": "Octoid tempering of bihexany, 600-equal",
"stepCount": "12",
"steps": [
"102.000000",
"268.000000",
"386.000000",
"418.000000",
"536.000000",
"702.000000",
"804.000000",
"884.000000",
"970.000000",
"1034.000000",
"1120.000000",
"2/1"
]
},
{
"id": "bihexany",
"desc": "Hole around [0, 1/2, 1/2, 1/2]",
"stepCount": "12",
"steps": [
"35/33",
"7/6",
"5/4",
"14/11",
"15/11",
"3/2",
"35/22",
"5/3",
"7/4",
"20/11",
"21/11",
"2"
]
},
{
"id": "bihexanymyna",
"desc": "Myna tempered bihexany, 89-tET",
"stepCount": "12",
"steps": [
"107.86517",
"269.66292",
"391.01124",
"417.97753",
"539.32584",
"701.12360",
"808.98876",
"889.88764",
"970.78652",
"1038.20225",
"1119.10112",
"2/1"
]
},
{
"id": "billeter",
"desc": "Organ well temperament of Otto Bernhard Billeter",
"stepCount": "12",
"steps": [
"93.15750",
"198.04500",
"297.06750",
"392.18000",
"500.97750",
"591.20250",
"699.02250",
"795.11250",
"895.11250",
"999.02250",
"1092.18000",
"2/1"
]
},
{
"id": "billeter_2",
"desc": "Bernhard Billeter's Bach temperament (1977/79), 1/12 and 7/24 Pyth. comma",
"stepCount": "12",
"steps": [
"92.18000",
"200.00000",
"296.09000",
"390.22500",
"500.00000",
"590.22500",
"700.00000",
"794.13500",
"895.11250",
"998.04500",
"1090.22500",
"2/1"
]
},
{
"id": "bimarveldenewoo",
"desc": "bimarveldene = genus(27*25*11) in [10/3 7/2 11] marvel tuning",
"stepCount": "24",
"steps": [
"66.81488",
"116.23027",
"151.28207",
"232.46054",
"267.51234",
"316.92773",
"383.74261",
"433.15800",
"450.55749",
"499.97288",
"584.44007",
"616.20315",
"651.25495",
"700.67034",
"767.48522",
"816.90061",
"883.71549",
"933.13088",
"968.18268",
"999.94576",
"1084.41295",
"1133.82835",
"1151.22783",
"1200.64322"
]
},
{
"id": "blackbeat_15",
"desc": "Blackwood[15] with brats of -1",
"stepCount": "15",
"steps": [
"82.836732",
"157.163268",
"240.000000",
"322.836732",
"397.163268",
"480.000000",
"562.836732",
"637.163268",
"720.000000",
"802.836732",
"877.163268",
"960.000000",
"1042.836732",
"1117.163268",
"2/1"
]
},
{
"id": "blackchrome_2",
"desc": "Second 25/24&256/245 scale",
"stepCount": "10",
"steps": [
"16/15",
"9/8",
"6/5",
"4/3",
"27/20",
"3/2",
"8/5",
"16/9",
"9/5",
"2/1"
]
},
{
"id": "blackj_gws",
"desc": "Detempered Blackjack in 1/4 kleismic marvel tuning",
"stepCount": "21",
"steps": [
"37.62469",
"115.58705",
"153.21174",
"8/7",
"268.79879",
"346.76114",
"384.38583",
"468.85303",
"499.97288",
"584.44007",
"615.55993",
"700.02712",
"731.14697",
"815.61417",
"853.23886",
"931.20121",
"7/4",
"1046.78826",
"1084.41295",
"1162.37531",
"2/1"
]
},
{
"id": "blackjack_r",
"desc": "Rational \"Wilson/Grady\"-style version, Paul Erlich, TL 28-11-2001",
"stepCount": "21",
"steps": [
"21/20",
"15/14",
"9/8",
"8/7",
"6/5",
"11/9",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"32/21",
"8/5",
"18/11",
"12/7",
"7/4",
"11/6",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "blackjack_r_2",
"desc": "Another rational Blackjack maximising 1:3:7:9:11, Paul Erlich, TL 5-12-2001",
"stepCount": "21",
"steps": [
"49/48",
"77/72",
"12/11",
"8/7",
"7/6",
"27/22",
"96/77",
"21/16",
"4/3",
"108/77",
"63/44",
"3/2",
"49/32",
"77/48",
"18/11",
"12/7",
"7/4",
"11/6",
"144/77",
"21/11",
"2/1"
]
},
{
"id": "blackjack_r_3",
"desc": "7-Limit rational Blackjack, Dave Keenan, TL 5-12-2001",
"stepCount": "21",
"steps": [
"21/20",
"16/15",
"28/25",
"8/7",
"6/5",
"49/40",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"32/21",
"8/5",
"49/30",
"12/7",
"7/4",
"147/80",
"28/15",
"49/25",
"2/1"
]
},
{
"id": "blackjack",
"desc": "21 note MOS of \"MIRACLE\"temperament, Erlich & Keenan, miracle1.scl,TL 2-5-2001",
"stepCount": "21",
"steps": [
"83.33333 ! G#v",
"116.66667 ! Ab^",
"200.00000 ! A",
"233.33333 ! A>",
"316.66667 ! Bb^",
"350.00000 ! B[",
"383.33333 ! Bv",
"466.66667 ! C<",
"500.00000 ! C",
"583.33333 ! C#v",
"616.66667 ! Db^",
"700.00000 ! D",
"733.33333 ! D>",
"816.66667 ! Eb^",
"850.00000 ! E[",
"933.33333 ! E>",
"966.66667 ! F<",
"1050.00000 ! F]",
"1083.33333 ! F#v",
"1166.66667 ! G<",
"2/1 ! G"
]
},
{
"id": "blackjackg",
"desc": "Blackjack on G-D",
"stepCount": "21",
"steps": [
"83.33300",
"116.66700",
"200.00000",
"233.33300",
"316.66700",
"350.00000",
"433.33300",
"466.66700",
"550.00000",
"583.33300",
"666.66700",
"700.00000",
"783.33300",
"816.66700",
"900.00000",
"933.33300",
"1016.66700",
"1050.00000",
"1083.33300",
"1166.66700",
"2/1"
]
},
{
"id": "blackjb",
"desc": "Marvel (1,1) tuning of pipedum_21b",
"stepCount": "21",
"steps": [
"34.14257",
"116.51971",
"150.66228",
"233.03942",
"267.18199",
"349.55913",
"383.70170",
"466.73918",
"500.22141",
"583.25888",
"616.74112",
"699.77859",
"733.26082",
"816.29830",
"850.44087",
"932.81801",
"966.96058",
"1049.33772",
"1083.48029",
"1116.96252",
"2/1"
]
},
{
"id": "blackopkeegil_1",
"desc": "Blacksmith-Opossum-Keemun-Gilead Wakalix 1",
"stepCount": "15",
"steps": [
"21/20",
"15/14",
"7/6",
"6/5",
"5/4",
"9/7",
"7/5",
"10/7",
"3/2",
"49/30",
"5/3",
"7/4",
"9/5",
"35/18",
"2/1"
]
},
{
"id": "blackopkeegil_2",
"desc": "Blacksmith-Opossum-Keemun-Gilead Wakalix 2",
"stepCount": "15",
"steps": [
"36/35",
"10/9",
"8/7",
"6/5",
"35/27",
"4/3",
"7/5",
"10/7",
"14/9",
"8/5",
"5/3",
"12/7",
"28/15",
"40/21",
"2/1"
]
},
{
"id": "blackwoo",
"desc": "Irregular Blackjack from marvel woo tempering of Cartesian scale below",
"stepCount": "21",
"steps": [
"35.05180",
"116.23027",
"151.28207",
"232.46054",
"267.51234",
"348.69081",
"383.74261",
"468.20980",
"499.97288",
"584.44007",
"616.20315",
"700.67034",
"732.43342",
"816.90061",
"851.95241",
"933.13088",
"968.18268",
"1049.36115",
"1084.41295",
"1165.59142",
"1200.64322"
]
},
{
"id": "blackwood_6",
"desc": "Easley Blackwood, whole tone scale, arrangement of 4:5:7:9:11:13, 1/1=G, p.114",
"stepCount": "6",
"steps": ["9/8", "5/4", "11/8", "13/8", "7/4", "2/1"]
},
{
"id": "blackwood_9",
"desc": "Blackwood, scale with pure triads on I II III IV VI and dom.7th on V. page 83",
"stepCount": "9",
"steps": ["10/9", "9/8", "5/4", "21/16", "4/3", "3/2", "5/3", "15/8", "2/1"]
},
{
"id": "blackwood",
"desc": "Blackwood temperament, g=84.663787, p=240, 5-limit",
"stepCount": "25",
"steps": [
"70.67243",
"141.34485",
"155.33621",
"226.00864",
"240.00000",
"310.67243",
"381.34485",
"395.33621",
"466.00864",
"480.00000",
"550.67243",
"621.34485",
"635.33621",
"706.00864",
"720.00000",
"790.67243",
"861.34485",
"875.33621",
"946.00864",
"960.00000",
"1030.67243",
"1101.34485",
"1115.33621",
"1186.00864",
"1200.00000"
]
},
{
"id": "blasquinten",
"desc": "Blasquintenzirkel. 23 fifths in 2 oct. C. Sachs, Vergleichende Musikwiss. p. 28",
"stepCount": "23",
"steps": [
"156.00000",
"312.00000",
"468.00000",
"624.00000",
"678.00000",
"780.00000",
"834.00000",
"936.00000",
"990.00000",
"1092.00000",
"1146.00000",
"1248.00000",
"1302.00000",
"1404.00000",
"1458.00000",
"1560.00000",
"1614.00000",
"1716.00000",
"1770.00000",
"1926.00000",
"2082.00000",
"2238.00000",
"2394.00000"
]
},
{
"id": "blueji_cataclysmic",
"desc": "John O'Sullivan's Blueji tempered in 13-limit POTE-tuned cataclysmic",
"stepCount": "12",
"steps": [
"112.60347",
"204.43258",
"317.03605",
"385.18024",
"497.78371",
"589.61282",
"702.21629",
"814.81976",
"882.96395",
"1019.25234",
"1087.39653",
"2/1"
]
},
{
"id": "bluesmarvwoo",
"desc": "Marvel woo version of Graham Breed's Blues scale",
"stepCount": "12",
"steps": [
"133.88259",
"183.04515",
"383.74261",
"450.55749",
"499.97288",
"651.25495",
"683.01803",
"834.55293",
"883.71549",
"950.53037",
"1151.22783",
"1200.64322"
]
},
{
"id": "bluesrag",
"desc": "Ragismic tempered bluesji in 8419-tET",
"stepCount": "12",
"steps": [
"133.41252",
"182.30194",
"386.26915",
"449.12697",
"498.01639",
"653.09419",
"680.31833",
"835.39613",
"884.28554",
"947.14337",
"1151.11058",
"2/1"
]
},
{
"id": "bobro_phi",
"desc": "Cameron Bobro's phi scale, TL 06-05-2009",
"stepCount": "8",
"steps": [
"366.90970",
"466.18100",
"560.06656",
"733.81941",
"833.09030",
"982.55396",
"1068.86470",
"2/1"
]
},
{
"id": "bobro_phi_2",
"desc": "Cameron Bobro, first 5 golden cuts of Phi, TL 09-05-2009",
"stepCount": "6",
"steps": [
"93.88597",
"149.46366",
"235.77441",
"366.90970",
"560.06656",
"833.09030"
]
},
{
"id": "bobrova",
"desc": "Bobrova Cheerful 12 WT based on *19 EDL",
"stepCount": "12",
"steps": [
"19/18",
"19/17",
"19/16",
"361/288",
"4/3",
"361/256",
"323/216",
"19/12",
"57/34",
"57/32",
"361/192",
"2/1"
]
},
{
"id": "boeth_chrom",
"desc": "Boethius's Chromatic. The CI is 19/16",
"stepCount": "7",
"steps": ["256/243", "64/57", "4/3", "3/2", "128/81", "32/19", "2/1"]
},
{
"id": "boeth_enh",
"desc": "Boethius's Enharmonic, with a CI of 81/64 and added 16/9",
"stepCount": "8",
"steps": [
"512/499",
"256/243",
"4/3",
"3/2",
"768/499",
"16/9",
"128/81",
"2/1"
]
},
{
"id": "bohlen_8",
"desc": "See Bohlen, H. 13-Tonstufen in der Duodezime, Acustica 39: 76-86 (1978)",
"stepCount": "8",
"steps": ["10/9", "6/5", "9/7", "7/5", "14/9", "5/3", "9/5", "2/1"]
},
{
"id": "bohlen_11",
"desc": "11-tone scale by Bohlen, generated from the 1/1 3/2 5/2 triad",
"stepCount": "11",
"steps": [
"10/9",
"6/5",
"4/3",
"3/2",
"5/3",
"9/5",
"2/1",
"9/4",
"5/2",
"27/10",
"3/1"
]
},
{
"id": "bohlen_12",
"desc": "12-tone scale by Bohlen generated from the 4:7:10 triad, Acustica 39/2, 1978",
"stepCount": "12",
"steps": [
"11/10",
"6/5",
"30/23",
"10/7",
"11/7",
"7/4",
"21/11",
"21/10",
"23/10",
"5/2",
"11/4",
"3/1"
]
},
{
"id": "bohlen_arcturus",
"desc": "Paul Erlich, Arcturus-7, TOP tuning (15625/15309 tempered)",
"stepCount": "7",
"steps": [
"145.18162",
"734.21217",
"879.39379",
"1024.57540",
"1169.75702",
"1758.78757",
"1903.96919"
]
},
{
"id": "bohlen_canopus",
"desc": "Paul Erlich, Canopus-7, TOP tuning (16875/16807 tempered)",
"stepCount": "7",
"steps": [
"150.19306",
"583.78912",
"733.98218",
"1167.57824",
"1317.77131",
"1751.36736",
"1901.56043"
]
},
{
"id": "bohlen_coh",
"desc": "Differentially coherent Bohlen-Pierce, interval=2",
"stepCount": "13",
"steps": [
"140.70435",
"293.44906",
"434.26326",
"586.82503",
"727.82007",
"879.96401",
"1021.37276",
"1172.94424",
"1314.91823",
"1464.79932",
"1608.44866",
"1756.91884",
"3/1"
]
},
{
"id": "bohlen_coh_2",
"desc": "Differentially coherent Bohlen-Pierce, interval=1,2, subharmonic=25",
"stepCount": "13",
"steps": [
"27/25",
"6/5",
"32/25",
"36/25",
"38/25",
"42/25",
"9/5",
"49/25",
"54/25",
"59/25",
"63/25",
"69/25",
"3/1"
]
},
{
"id": "bohlen_coh_3",
"desc": "Differentially coherent Bohlen-Pierce, interval=1, subharmonic=75",
"stepCount": "13",
"steps": [
"27/25",
"6/5",
"97/75",
"104/75",
"39/25",
"42/25",
"9/5",
"148/75",
"54/25",
"7/3",
"63/25",
"69/25",
"3/1"
]
},
{
"id": "bohlen_d_ji",
"desc": "Bohlen's delta scale, just version. \"Dur\"form, \"moll\"is inversion.",
"stepCount": "9",
"steps": [
"25/21",
"9/7",
"75/49",
"5/3",
"9/5",
"15/7",
"7/3",
"25/9",
"3/1"
]
},
{
"id": "bohlen_delta",
"desc": "Bohlen's delta scale, a mode B-P, see Acustica 39: 76-86 (1978)",
"stepCount": "9",
"steps": [
"292.60846",
"438.91269",
"731.52115",
"877.82539",
"1024.12962",
"1316.73808",
"1463.04231",
"1755.65077",
"3/1"
]
},
{
"id": "bohlen_diat_top",
"desc": "BP Diatonic, TOP tuning (245/243 tempered)",
"stepCount": "9",
"steps": [
"141.64621",
"440.43170",
"582.07790",
"880.86339",
"1022.50960",
"1321.29509",
"1462.94130",
"1761.72679",
"1903.37300"
]
},
{
"id": "bohlen_enh",
"desc": "Bohlen-Pierce scale, all enharmonic tones",
"stepCount": "49",
"steps": [
"27/25",
"49/45",
"375/343",
"625/567",
"729/625",
"147/125",
"405/343",
"25/21",
"3969/3125",
"2401/1875",
"9/7",
"35/27",
"243/175",
"7/5",
"3375/2401",
"625/441",
"189/125",
"343/225",
"75/49",
"125/81",
"5103/3125",
"1029/625",
"81/49",
"5/3",
"9/5",
"49/27",
"625/343",
"3125/1701",
"243/125",
"49/25",
"675/343",
"125/63",
"1323/625",
"2401/1125",
"15/7",
"175/81",
"81/35",
"7/3",
"5625/2401",
"3125/1323",
"63/25",
"343/135",
"125/49",
"625/243",
"1701/625",
"343/125",
"135/49",
"25/9",
"3/1"
]
},
{
"id": "bohlen_eq",
"desc": "Most equal selection from all enharmonic Bohlen-Pierce tones",
"stepCount": "13",
"steps": [
"49/45",
"405/343",
"9/7",
"7/5",
"343/225",
"5/3",
"9/5",
"675/343",
"15/7",
"7/3",
"343/135",
"135/49",
"3/1"
]
},
{
"id": "bohlen_g_ji",
"desc": "Bohlen's gamma scale, just version",
"stepCount": "9",
"steps": [
"27/25",
"9/7",
"7/5",
"5/3",
"9/5",
"49/25",
"7/3",
"25/9",
"3/1"
]
},
{
"id": "bohlen_gamma",
"desc": "Bohlen's gamma scale, a mode of the Bohlen-Pierce scale",
"stepCount": "9",
"steps": [
"146.30423",
"438.91269",
"585.21692",
"877.82539",
"1024.12962",
"1170.43385",
"1463.04231",
"1755.65077",
"3/1"
]
},
{
"id": "bohlen_h_ji",
"desc": "Bohlen's harmonic scale, just version",
"stepCount": "9",
"steps": [
"27/25",
"9/7",
"7/5",
"5/3",
"9/5",
"15/7",
"7/3",
"63/25",
"3/1"
]
},
{
"id": "bohlen_harm",
"desc": "Bohlen's harmonic scale, inverse of lambda",
"stepCount": "9",
"steps": [
"146.30423",
"438.91269",
"585.21692",
"877.82539",
"1024.12962",
"1316.73808",
"1463.04231",
"1609.34654",
"3/1"
]
},
{
"id": "bohlen_l_ji",
"desc": "Bohlen's lambda scale, just version",
"stepCount": "9",
"steps": ["25/21", "9/7", "7/5", "5/3", "9/5", "15/7", "7/3", "25/9", "3/1"]
},
{
"id": "bohlen_lambda_pyth",
"desc": "Dave Benson's BP-Pythagorean scale, lambda mode of bohlen_pyth.scl",
"stepCount": "9",
"steps": [
"19683/16807",
"9/7",
"343/243",
"81/49",
"49/27",
"729/343",
"7/3",
"6561/2401",
"3/1"
]
},
{
"id": "bohlen_lambda",
"desc": "Bohlen's lambda scale, a mode of the Bohlen-Pierce scale",
"stepCount": "9",
"steps": [
"292.60846",
"438.91269",
"585.21692",
"877.82539",
"1024.12962",
"1316.73808",
"1463.04231",
"1755.65077",
"3/1"
]
},
{
"id": "bohlen_mean",
"desc": "1/3 minor BP diesis (245/243) tempered 7/3 meantone scale",
"stepCount": "13",
"steps": [
"142.69792",
"41553/35000",
"439.81427",
"7/5",
"75/49",
"879.62854",
"1022.32646",
"49/25",
"15/7",
"1462.14073",
"1604.83865",
"1759.25708",
"3/1"
]
},
{
"id": "bohlen_pent_top",
"desc": "BP Pentatonic, TOP tuning (245/243 tempered)",
"stepCount": "5",
"steps": [
"440.43170",
"880.86339",
"1321.29509",
"1761.72679",
"1903.37300"
]
},
{
"id": "bohlen_pyth",
"desc": "Cycle of 13 7/3 BP tenths",
"stepCount": "13",
"steps": [
"2401/2187",
"19683/16807",
"9/7",
"343/243",
"177147/117649",
"81/49",
"49/27",
"117649/59049",
"729/343",
"7/3",
"16807/6561",
"6561/2401",
"3/1"
]
},
{
"id": "bohlen_quintuple_j",
"desc": "Bohlen-Pierce quintuple scale (just version of 65ED3). Georg Hajdu (2017)",
"stepCount": "65",
"steps": [
"891/875",
"65/63",
"81/77",
"125/117",
"49/45",
"21/19",
"91/81",
"63/55",
"729/625",
"13/11",
"729/605",
"11/9",
"81/65",
"19/15",
"9/7",
"17/13",
"539/405",
"441/325",
"29/21",
"7/5",
"891/625",
"13/9",
"81/55",
"175/117",
"75/49",
"45/29",
"11/7",
"441/275",
"57/35",
"5/3",
"225/133",
"325/189",
"425/243",
"625/351",
"9/5",
"35/19",
"455/243",
"21/11",
"29/15",
"49/25",
"351/175",
"55/27",
"27/13",
"625/297",
"15/7",
"85/39",
"325/147",
"169/75",
"39/17",
"7/3",
"45/19",
"65/27",
"27/11",
"605/243",
"33/13",
"625/243",
"55/21",
"243/91",
"19/7",
"135/49",
"351/125",
"77/27",
"189/65",
"875/297",
"3/1"
]
},
{
"id": "bohlen_quintuple_t",
"desc": "Bohlen-Pierce quintuple scale, 65th root of 3. Georg Hajdu (2017)",
"stepCount": "65",
"steps": [
"29.26085",
"58.52169",
"87.78254",
"117.04338",
"146.30423",
"175.56508",
"204.82592",
"234.08677",
"263.34762",
"292.60846",
"321.86931",
"351.13015",
"380.39100",
"409.65185",
"438.91269",
"468.17354",
"497.43438",
"526.69523",
"555.95608",
"585.21692",
"614.47777",
"643.73862",
"672.99946",
"702.26031",
"731.52115",
"760.78200",
"790.04285",
"819.30369",
"848.56454",
"877.82539",
"907.08623",
"936.34708",
"965.60792",
"994.86877",
"1024.12962",
"1053.39046",
"1082.65131",
"1111.91215",
"1141.17300",
"1170.43385",
"1199.69469",
"1228.95554",
"1258.21639",
"1287.47723",
"1316.73808",
"1345.99892",
"1375.25977",
"1404.52062",
"1433.78146",
"1463.04231",
"1492.30315",
"1521.56400",
"1550.82485",
"1580.08569",
"1609.34654",
"1638.60739",
"1667.86823",
"1697.12908",
"1726.38992",
"1755.65077",
"1784.91162",
"1814.17246",
"1843.43331",
"1872.69415",
"3/1"
]
},
{
"id": "bohlen_sirius",
"desc": "Paul Erlich, Sirius-7, TOP tuning (3125/3087 tempered)",
"stepCount": "7",
"steps": [
"293.59737",
"587.19473",
"880.79210",
"1022.60982",
"1316.20719",
"1609.80455",
"1903.40192"
]
},
{
"id": "bohlen_t_ji",
"desc": "Bohlen, scale based on twelfth, just version",
"stepCount": "8",
"steps": ["6/5", "4/3", "3/2", "5/3", "2/1", "9/4", "5/2", "3/1"]
},
{
"id": "bohlen_t",
"desc": "Bohlen, scale based on the twelfth",
"stepCount": "8",
"steps": [
"300.00000",
"500.00000",
"700.00000",
"900.00000",
"1200.00000",
"1400.00000",
"1600.00000",
"1900.00000"
]
},
{
"id": "bohlen_eg",
"desc": "Bohlen-Pierce with two tones altered by minor BP diesis, slightly more equal",
"stepCount": "13",
"steps": [
"49/45",
"25/21",
"9/7",
"7/5",
"75/49",
"5/3",
"9/5",
"49/25",
"15/7",
"7/3",
"63/25",
"135/49",
"3/1"
]
},
{
"id": "bohlen_p_9",
"desc": "Bohlen-Pierce subscale by J.R. Pierce with 3:5:7 triads",
"stepCount": "9",
"steps": [
"146.30423",
"438.91269",
"585.21692",
"877.82539",
"1024.12962",
"1316.73808",
"1463.04231",
"1755.65077",
"3/1"
]
},
{
"id": "bohlen_p_9_a",
"desc": "Pierce's 9 of 3\\13, see Mathews et al., J. Acoust. Soc. Am. 84, 1214-1222",
"stepCount": "9",
"steps": [
"49/45",
"9/7",
"7/5",
"81/49",
"9/5",
"15/7",
"7/3",
"135/49",
"3/1"
]
},
{
"id": "bohlen_p_eb",
"desc": "Bohlen-Pierce scale with equal beating 5/3 and 7/3",
"stepCount": "13",
"steps": [
"152.07683",
"296.64928",
"441.22173",
"585.79418",
"737.87101",
"882.44346",
"1027.01591",
"1171.58837",
"1323.66519",
"1468.23765",
"1612.81010",
"1757.38255",
"3/1"
]
},
{
"id": "bohlen_p_ebt",
"desc": "Bohlen-Pierce scale with equal beating 7/3 tenth",
"stepCount": "13",
"steps": [
"145.30508",
"291.92921",
"439.77583",
"584.70367",
"730.97784",
"878.50029",
"1023.13607",
"1169.13919",
"1316.41049",
"1460.81993",
"1606.61294",
"1753.68948",
"3/1"
]
},
{
"id": "bohlen_p_ebt_2",
"desc": "Bohlen-Pierce scale with equal beating 7/5 tritone",
"stepCount": "13",
"steps": [
"145.69063",
"292.08731",
"439.13583",
"586.78567",
"732.13177",
"878.21021",
"1024.96498",
"1172.34389",
"1317.44491",
"1463.29687",
"1609.84255",
"1757.02855",
"3/1"
]
},
{
"id": "bohlen_p_et",
"desc": "13-tone equal division of 3/1. Bohlen-Pierce equal approximation",
"stepCount": "13",
"steps": [
"146.30423",
"292.60846",
"438.91269",
"585.21692",
"731.52115",
"877.82539",
"1024.12962",
"1170.43385",
"1316.73808",
"1463.04231",
"1609.34654",
"1755.65077",
"3/1"
]
},
{
"id": "bohlen_p_ring",
"desc": "Todd Harrop, symmetrical ring of Bohlen-Pierce enharmonics using 4 major and 8 minor dieses (2012)",
"stepCount": "13",
"steps": [
"49/45",
"147/125",
"35/27",
"243/175",
"189/125",
"81/49",
"49/27",
"125/63",
"175/81",
"81/35",
"125/49",
"135/49",
"3/1"
]
},
{
"id": "bohlen_p_sup",
"desc": "Superparticular Bohlen-Pierce scale",
"stepCount": "13",
"steps": [
"10/9",
"25/21",
"325/252",
"325/231",
"4225/2772",
"4225/2541",
"16900/9317",
"2600/1331",
"260/121",
"280/121",
"28/11",
"30/11",
"3/1"
]
},
{
"id": "bohlen_p",
"desc": "See Bohlen, H. 13-Tonstufen in der Duodezime, Acustica 39: 76-86 (1978)",
"stepCount": "13",
"steps": [
"27/25",
"25/21",
"9/7",
"7/5",
"75/49",
"5/3",
"9/5",
"49/25",
"15/7",
"7/3",
"63/25",
"25/9",
"3/1"
]
},
{
"id": "bohlen_5",
"desc": "5-limit version of Bohlen-Pierce",
"stepCount": "13",
"steps": [
"27/25",
"6/5",
"162/125",
"25/18",
"972/625",
"5/3",
"9/5",
"625/324",
"54/25",
"125/54",
"5/2",
"25/9",
"3/1"
]
},
{
"id": "bohlen_47",
"desc": "Heinz Bohlen, mode of 4\\47 (1998), www.huygens-fokker.org/bpsite/pythagorean.html",
"stepCount": "21",
"steps": [
"102.12766",
"255.31915",
"357.44681",
"459.57447",
"510.63830",
"612.76596",
"714.89362",
"817.02128",
"970.21277",
"1072.34043",
"1327.65957",
"1429.78723",
"1582.97872",
"1685.10638",
"1787.23404",
"1889.36170",
"1940.42553",
"2042.55319",
"2144.68085",
"2297.87234",
"4/1"
]
},
{
"id": "bohlen_47_r",
"desc": "Rational version, with alt.9 64/49 and alt.38 40/13",
"stepCount": "23",
"steps": [
"52/49",
"196/169",
"16/13",
"13/10",
"64/49",
"35/26",
"10/7",
"98/65",
"8/5",
"7/4",
"13/7",
"28/13",
"16/7",
"5/2",
"130/49",
"14/5",
"104/35",
"49/16",
"40/13",
"13/4",
"169/49",
"49/13",
"4/1"
]
},
{
"id": "bolivia",
"desc": "Observed scale from pan-pipe from La Paz. 1/1=171 Hz",
"stepCount": "7",
"steps": [
"326.00000",
"742.00000",
"1046.00000",
"1382.00000",
"1739.00000",
"2108.00000",
"2394.00000"
]
},
{
"id": "boomsliter",
"desc": "Boomsliter & Creel basic set of their referential tuning. [1 3 5 7 9] x u[1 3 5] cross set",
"stepCount": "12",
"steps": [
"9/8",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "boop_19",
"desc": "19 note detempered sensi MOS boop (245/243) scale, rms tuning",
"stepCount": "19",
"steps": [
"54.196169",
"122.781755",
"176.977924",
"263.949327",
"318.145497",
"386.731082",
"440.927252",
"495.123421",
"582.094824",
"617.905176",
"704.876579",
"759.072748",
"813.268918",
"881.854503",
"936.050673",
"1023.022076",
"1077.218245",
"1145.803831",
"2/1"
]
},
{
"id": "bossart_muri",
"desc": "Victor Ferdinand Bossart's Modified meantone (1743/44), organ in Klosterkirche Muri",
"stepCount": "12",
"steps": [
"80.44999",
"195.11250",
"305.86500",
"388.26999",
"501.95500",
"582.40499",
"699.02250",
"779.47249",
"891.20250",
"1000.97750",
"1085.33749",
"2/1"
]
},
{
"id": "bossart_1",
"desc": "Victor Ferdinand Bossart (erste Anweisung) organ temperament (1740?)",
"stepCount": "12",
"steps": [
"256/243",
"198.04500",
"308.79750",
"390.22500",
"503.91000",
"1024/729",
"699.02250",
"794.13500",
"894.13500",
"1007.82000",
"1089.24750",
"2/1"
]
},
{
"id": "bossart_2",
"desc": "Victor Ferdinand Bossart (zweite Anweisung) organ temperament (1740?)",
"stepCount": "12",
"steps": [
"94.13500",
"195.11250",
"308.79750",
"394.13500",
"503.91000",
"592.18000",
"699.02250",
"796.09000",
"894.13500",
"1004.88750",
"1096.09000",
"2/1"
]
},
{
"id": "bossart_3",
"desc": "Victor Ferdinand Bossart (dritte Anweisung) organ temperament (1740?)",
"stepCount": "12",
"steps": [
"93.15750",
"198.04500",
"305.86500",
"390.22500",
"503.91000",
"591.20250",
"699.02250",
"797.06750",
"894.13500",
"1004.88750",
"1089.24750",
"2/1"
]
},
{
"id": "boulliau",
"desc": "Monsieur Boulliau's irregular temp. (1373), reported by Mersenne in 1636",
"stepCount": "12",
"steps": [
"18/17",
"9/8",
"81/68",
"81/64",
"4/3",
"24/17",
"3/2",
"27/17",
"27/16",
"16/9",
"32/17",
"2/1"
]
},
{
"id": "bourdelle_1",
"desc": "Compromis Cordier, piano tuning by Jean-Pierre Chainais",
"stepCount": "88",
"steps": [
"100.1046295",
"200.209",
"300.314",
"400.419",
"500.523",
"600.628",
"700.732",
"800.837",
"900.942",
"1001.046",
"1101.151",
"1201.256",
"1301.360",
"1401.465",
"1501.569",
"1601.674",
"1701.779",
"1801.883",
"1901.988",
"2002.093",
"2102.197",
"2202.302",
"2302.406",
"2402.511",
"2502.616",
"2602.720",
"2702.825",
"2802.930",
"2903.034",
"3003.139",
"3103.244",
"3203.348",
"3303.453",
"3403.557",
"3503.662",
"3603.767",
"3703.871",
"3803.976",
"3904.081",
"4004.185",
"4104.290",
"4204.394",
"4304.499",
"4404.604",
"4504.708",
"4604.813",
"4704.918",
"4805.022",
"4905.127",
"5005.239",
"5105.358",
"5205.484",
"5305.618",
"5405.759",
"5505.907",
"5606.063",
"5706.226",
"5806.396",
"5906.573",
"6006.758",
"6106.950",
"6207.149",
"6307.356",
"6407.570",
"6507.791",
"6608.019",
"6708.255",
"6808.498",
"6908.748",
"7009.005",
"7109.270",
"7209.542",
"7309.821",
"7410.108",
"7510.402",
"7610.703",
"7711.011",
"7811.327",
"7911.650",
"8011.980",
"8112.318",
"8212.662",
"8313.014",
"8413.374",
"8513.740",
"8614.114",
"8714.495",
"8814.884"
]
},
{
"id": "bpg_55557777",
"desc": "Bohlen-Pierce extended to [55557777]",
"stepCount": "25",
"steps": [
"245/243",
"27/25",
"49/45",
"25/21",
"9/7",
"35/27",
"243/175",
"7/5",
"75/49",
"81/49",
"5/3",
"1225/729",
"2187/1225",
"9/5",
"49/27",
"49/25",
"15/7",
"175/81",
"81/35",
"7/3",
"63/25",
"135/49",
"25/9",
"729/245",
"3/1"
]
},
{
"id": "bps_temp_17",
"desc": "Bohlen-Pierce-Stearn temperament. Highest 7-limit error 8.4 cents, 2001",
"stepCount": "17",
"steps": [
"47.93500",
"179.49000",
"311.04500",
"442.60000",
"490.53500",
"622.09000",
"753.64500",
"885.20000",
"933.13500",
"1064.69000",
"1196.24500",
"1327.80000",
"1375.73500",
"1507.29000",
"1638.84500",
"1770.40000",
"3/1"
]
},
{
"id": "brac",
"desc": "Circulating temperament with simple beat ratios: 4 3/2 4 3/2 2 2 177/176 4 3/2 2 3/2 2",
"stepCount": "12",
"steps": [
"56640/53701",
"60008/53701",
"63720/53701",
"67264/53701",
"71685/53701",
"75056/53701",
"80276/53701",
"84960/53701",
"89920/53701",
"95580/53701",
"100544/53701",
"2/1"
]
},
{
"id": "breed_blues_1",
"desc": "Graham Breed's blues scale in 22-tET",
"stepCount": "7",
"steps": [
"218.18182",
"381.81818",
"436.36364",
"709.09091",
"872.72727",
"927.27273",
"2/1"
]
},
{
"id": "breed_blues_2",
"desc": "Graham Breed's blues scale in 29-tET",
"stepCount": "8",
"steps": [
"206.89655",
"248.27586",
"372.41379",
"455.17241",
"703.44828",
"868.96552",
"951.72414",
"2/1"
]
},
{
"id": "breed_bluesji",
"desc": "7-limit JI version of Graham Breed's Blues scale",
"stepCount": "12",
"steps": [
"27/25",
"10/9",
"5/4",
"35/27",
"4/3",
"35/24",
"40/27",
"81/50",
"5/3",
"140/81",
"35/18",
"2/1"
]
},
{
"id": "breed_dias_13",
"desc": "13-limit Diaschismic temperament, g=103.897, oct=1/2, 13-limit",
"stepCount": "46",
"steps": [
"23.38056",
"46.76112",
"70.14168",
"103.89676",
"127.27732",
"150.65788",
"174.03844",
"207.79352",
"8/7",
"254.55464",
"277.93520",
"311.69028",
"335.07084",
"358.45140",
"381.83196",
"415.58704",
"438.96760",
"64/49",
"485.72872",
"519.48380",
"542.86436",
"566.24492",
"600.00000",
"623.38056",
"646.76112",
"670.14168",
"703.89676",
"727.27732",
"750.65788",
"774.03844",
"807.79352",
"831.17408",
"854.55464",
"877.93520",
"911.69028",
"935.07084",
"958.45140",
"981.83196",
"1015.58704",
"1038.96760",
"1062.34816",
"1085.72872",
"1119.48380",
"1142.86436",
"1166.24492",
"2/1"
]
},
{
"id": "breed_ht",
"desc": "Hemithird temperament, g=193.202, 5-limit",
"stepCount": "19",
"steps": [
"111.62852",
"152.41536",
"193.20219",
"304.83072",
"345.61755",
"386.40439",
"498.03291",
"538.81975",
"579.60658",
"691.23510",
"732.02194",
"772.80878",
"884.43730",
"925.22413",
"966.01097",
"1077.63949",
"1118.42633",
"1159.21316",
"2/1"
]
},
{
"id": "breed_kleismic",
"desc": "Kleismic temperament, g=317.080, 5-limit",
"stepCount": "7",
"steps": [
"68.31870",
"317.07968",
"385.39838",
"634.15935",
"702.47805",
"951.23903",
"2/1"
]
},
{
"id": "breed_magic",
"desc": "Graham Breed's Magic temperament, g=380.384, 9-limit, close to 41-tET",
"stepCount": "13",
"steps": [
"203.83722",
"262.68605",
"321.53489",
"380.38372",
"584.22094",
"643.06978",
"701.91861",
"760.76744",
"964.60466",
"1023.45350",
"1082.30233",
"1141.15117",
"2/1"
]
},
{
"id": "breed_magic_5",
"desc": "Magic temperament, g=379.967949, 5-limit",
"stepCount": "19",
"steps": [
"79.48718",
"139.58334",
"199.67949",
"259.77564",
"319.87180",
"379.96795",
"459.45513",
"519.55129",
"579.64744",
"639.74359",
"699.83975",
"759.93590",
"839.42308",
"899.51924",
"959.61539",
"1019.71154",
"1079.80769",
"1139.90385",
"2/1"
]
},
{
"id": "breed_mystery",
"desc": "Mystery temperament, g=15.563, oct=1/29, 15-limit",
"stepCount": "58",
"steps": [
"15.56278",
"41.37931",
"56.94209",
"82.75862",
"98.32140",
"124.13793",
"139.70071",
"165.51724",
"181.08002",
"206.89655",
"222.45933",
"248.27586",
"263.83864",
"289.65517",
"305.21795",
"331.03448",
"346.59726",
"372.41379",
"387.97657",
"413.79310",
"429.35588",
"455.17241",
"470.73519",
"496.55172",
"512.11450",
"537.93103",
"553.49381",
"579.31034",
"594.87312",
"620.68966",
"636.25243",
"662.06897",
"677.63174",
"703.44828",
"719.01105",
"744.82759",
"760.39036",
"786.20690",
"801.76967",
"827.58621",
"843.14898",
"868.96552",
"884.52829",
"910.34483",
"925.90760",
"951.72414",
"967.28692",
"993.10345",
"1008.66623",
"1034.48276",
"1050.04554",
"1075.86207",
"1091.42485",
"1117.24138",
"1132.80416",
"1158.62069",
"1174.18347",
"2/1"
]
},
{
"id": "breed",
"desc": "Graham Breed's fourth based 12-tone keyboard scale. Tuning List 23-10-97",
"stepCount": "12",
"steps": [
"531441/524288",
"46.92002",
"2187/2048",
"1162261467/1073741824",
"9/8",
"4782969/4194304",
"32/27",
"19683/16384",
"341.05502",
"81/64",
"43046721/33554432",
"4/3"
]
},
{
"id": "breed_7_3",
"desc": "Graham Breed's 7 + 3 scale in 24-tET",
"stepCount": "10",
"steps": [
"150.00000",
"200.00000",
"350.00000",
"500.00000",
"650.00000",
"700.00000",
"850.00000",
"1000.00000",
"1050.00000",
"2/1"
]
},
{
"id": "breed_11",
"desc": "Breed[11] hobbit in 2749-tET",
"stepCount": "11",
"steps": [
"119.60713",
"231.35686",
"350.96399",
"386.32230",
"582.32084",
"617.67916",
"813.67770",
"849.03601",
"968.64314",
"1080.39287",
"2/1"
]
},
{
"id": "breedball_3",
"desc": "Third Breed ball around 49/40-7/4",
"stepCount": "12",
"steps": [
"49/48",
"21/20",
"15/14",
"49/40",
"5/4",
"7/5",
"10/7",
"3/2",
"49/32",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "breedball_4",
"desc": "Fourth Breed ball around 49/40-7/4",
"stepCount": "14",
"steps": [
"49/48",
"21/20",
"15/14",
"6/5",
"49/40",
"5/4",
"7/5",
"10/7",
"3/2",
"49/32",
"12/7",
"7/4",
"25/14",
"2/1"
]
},
{
"id": "breedpump",
"desc": "Comma pump in breed (2401/2400 planar) [[1, 1, -2]->[1, 1, -1]->[0, 1, -1]->[0, 0, -1]->[0, 0, 0]->[0, -1, 0],[0, -1, 1]->[0, -2, 1]->[-1, -2, 1]",
"stepCount": "16",
"steps": [
"50/49",
"16807/16000",
"343/320",
"400/343",
"20000/16807",
"49/40",
"5/4",
"7/5",
"10/7",
"2401/1600",
"49/32",
"80/49",
"4000/2401",
"7/4",
"25/14",
"2/1"
]
},
{
"id": "breedt_2",
"desc": "Graham Breed's 1/5 P temperament, TL 10-06-99",
"stepCount": "12",
"steps": [
"94.91700",
"199.21800",
"298.82700",
"393.74400",
"502.73700",
"592.96200",
"3/2",
"796.87200",
"896.48100",
"1000.78200",
"1095.69900",
"2/1"
]
},
{
"id": "breedt_3",
"desc": "Graham Breed's other 1/4 P temperament, TL 10-06-99",
"stepCount": "12",
"steps": [
"96.09000",
"198.04500",
"300.00000",
"396.09000",
"503.91000",
"594.13500",
"3/2",
"798.04500",
"894.13500",
"1001.95500",
"1092.18000",
"2/1"
]
},
{
"id": "breetet_2",
"desc": "doubled Breed tetrad",
"stepCount": "13",
"steps": [
"49/48",
"25/24",
"7/6",
"49/40",
"5/4",
"4/3",
"10/7",
"35/24",
"3/2",
"49/30",
"5/3",
"7/4",
"2/1"
]
},
{
"id": "breetet_3",
"desc": "tripled Breed tetrad",
"stepCount": "25",
"steps": [
"49/48",
"25/24",
"15/14",
"35/32",
"9/8",
"7/6",
"49/40",
"5/4",
"245/192",
"125/96",
"21/16",
"4/3",
"10/7",
"35/24",
"3/2",
"49/32",
"25/16",
"49/30",
"5/3",
"7/4",
"25/14",
"175/96",
"90/49",
"15/8",
"2/1"
]
},
{
"id": "breeza",
"desc": "A 40353607/40000000 & 40960000/40353607 Fokker block with 11 otonal and 10 utonal tetrads",
"stepCount": "27",
"steps": [
"50/49",
"16807/16000",
"128000/117649",
"6400000/5764801",
"8/7",
"400/343",
"2401/2000",
"49/40",
"5/4",
"64/49",
"3200/2401",
"160000/117649",
"7/5",
"10/7",
"117649/80000",
"2401/1600",
"1280000/823543",
"8/5",
"80/49",
"4000/2401",
"343/200",
"7/4",
"5764801/3200000",
"640/343",
"32000/16807",
"49/25",
"2/1"
]
},
{
"id": "breezb",
"desc": "Alternative block to breeza 40353607/40000000 & 40960000/40353607",
"stepCount": "27",
"steps": [
"50/49",
"16807/16000",
"128000/117649",
"28/25",
"8/7",
"400/343",
"2401/2000",
"49/40",
"5/4",
"64/49",
"3200/2401",
"160000/117649",
"7/5",
"10/7",
"117649/80000",
"2401/1600",
"1280000/823543",
"8/5",
"80/49",
"4000/2401",
"343/200",
"7/4",
"5764801/3200000",
"640/343",
"32000/16807",
"49/25",
"2/1"
]
},
{
"id": "bremmer_ebvt_1",
"desc": "Bill Bremmer EBVT I temperament (2011)",
"stepCount": "12",
"steps": [
"94.87252",
"197.05899",
"297.80000",
"394.21889",
"4/3",
"592.91752",
"699.31190",
"796.82704",
"896.20299",
"999.10000",
"1096.17389",
"2/1"
]
},
{
"id": "bremmer_ebvt_2",
"desc": "Bill Bremmer EBVT II temperament (2011)",
"stepCount": "12",
"steps": [
"94.87252",
"197.05899",
"297.80000",
"395.79561",
"4/3",
"592.91752",
"699.31190",
"796.82704",
"896.20299",
"999.10000",
"1096.17389",
"2/1"
]
},
{
"id": "bremmer_ebvt_3",
"desc": "Bill Bremmer EBVT III temperament (2011)",
"stepCount": "12",
"steps": [
"94.87252",
"197.05899",
"297.80000",
"395.79561",
"4/3",
"595.89736",
"699.31190",
"796.82704",
"896.20299",
"999.10000",
"1096.17389",
"2/1"
]
},
{
"id": "bremmer",
"desc": "Bill Bremmer's Shining Brow (1998)",
"stepCount": "12",
"steps": [
"95.52500",
"197.49000",
"299.01500",
"395.03999",
"500.00500",
"595.02999",
"699.49500",
"798.52000",
"897.48500",
"998.51000",
"1095.53499",
"2/1"
]
},
{
"id": "broadwood",
"desc": "Broadwood's Best (Ellis tuner number 4), Victorian (1885)",
"stepCount": "12",
"steps": [
"95.96501",
"197.99000",
"297.95501",
"392.98000",
"498.94501",
"594.97001",
"699.99500",
"796.96001",
"894.98500",
"998.95001",
"1093.97500",
"2/1"
]
},
{
"id": "broadwood_2",
"desc": "Broadwood's Usual (Ellis tuner number 2), Victorian (1885)",
"stepCount": "12",
"steps": [
"94.96501",
"196.99000",
"296.95501",
"391.98000",
"498.94501",
"593.97001",
"699.99500",
"795.96001",
"893.98500",
"997.95001",
"1092.97500",
"2/1"
]
},
{
"id": "broadwood_3",
"desc": "John Broadwood�s 1832 unequal temperament compiled by A.Sparschuh, a=403.0443",
"stepCount": "12",
"steps": [
"633527/600000",
"2691301/2400000",
"1429123/1200000",
"75449/60000",
"1068389/800000",
"1692133/1200000",
"898549/600000",
"3795083/2400000",
"1343481/800000",
"535057/300000",
"1506547/800000",
"2/1"
]
},
{
"id": "broeckaert_pbp",
"desc": "Johan Broeckaert-Devriendt, PBP temperament (2007). Equal PBP for C-E and G-B",
"stepCount": "12",
"steps": [
"256/243",
"195.25271",
"32/27",
"386.87185",
"4/3",
"1024/729",
"699.44315",
"128/81",
"891.06228",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "brown",
"desc": "Tuning of Colin Brown's Voice Harmonium, Glasgow. Helmholtz/Ellis p. 470-473, genus [3333333333333355]",
"stepCount": "45",
"steps": [
"25/24",
"256/243",
"135/128",
"2187/2048",
"800/729",
"10/9",
"18225/16384",
"9/8",
"2560/2187",
"75/64",
"32/27",
"1215/1024",
"100/81",
"5/4",
"81/64",
"320/243",
"675/512",
"4/3",
"10935/8192",
"25/18",
"1024/729",
"45/32",
"729/512",
"3200/2187",
"40/27",
"6075/4096",
"3/2",
"25/16",
"128/81",
"405/256",
"400/243",
"5/3",
"54675/32768",
"27/16",
"1280/729",
"225/128",
"16/9",
"3645/2048",
"50/27",
"4096/2187",
"15/8",
"243/128",
"160/81",
"2025/1024",
"2/1"
]
},
{
"id": "bruder_vier",
"desc": "Ignaz Bruder organ temperament (1829) according to P. Vier",
"stepCount": "12",
"steps": [
"95.00000",
"200.00000",
"295.00000",
"389.00000",
"499.00000",
"593.50000",
"698.50000",
"796.00000",
"897.00000",
"998.00000",
"1092.00000",
"2/1"
]
},
{
"id": "bruder",
"desc": "Ignaz Bruder organ temperament (1829), systematised by Ratte, p. 406",
"stepCount": "12",
"steps": [
"95.11250",
"202.93250",
"297.06750",
"391.20250",
"499.02250",
"593.64625",
"701.46625",
"796.09000",
"897.06750",
"998.04500",
"1092.18000",
"2/1"
]
},
{
"id": "bug_pelog",
"desc": "Pelog-like subset of bug[9] and superpelog[9], g=260.256797",
"stepCount": "7",
"steps": [
"101.28399",
"260.25680",
"520.51359",
"679.48641",
"780.77039",
"939.74320",
"2/1"
]
},
{
"id": "bugblock_19",
"desc": "Bug (<<2 3 0||) and <<5 2 -15|| <19 30 45| weak Fokker block: generators -9 to 9",
"stepCount": "19",
"steps": [
"128/125",
"25/24",
"16/15",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"45/32",
"64/45",
"3/2",
"25/16",
"8/5",
"5/3",
"128/75",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "burma_3",
"desc": "Burmese scale, von Hornbostel: �ber ein akustisches Kriterium.., 1911, p.613. 1/1=336 Hz",
"stepCount": "7",
"steps": [
"164.53576",
"336.12950",
"505.75652",
"688.16023",
"859.44844",
"1036.66952",
"2/1"
]
},
{
"id": "burt_fibo",
"desc": "Warren Burt, 3/2+5/3+8/5+etc. \"Recurrent Sequences\", 2002",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"305/256",
"5/4",
"21/16",
"89/64",
"377/256",
"3/2",
"13/8",
"55/32",
"233/128",
"2/1"
]
},
{
"id": "burt_fibo_23",
"desc": "Warren Burt, 23-tone Fibonacci scale. \"Recurrent Sequences\", 2002",
"stepCount": "23",
"steps": [
"4181/4096",
"17/16",
"17711/16384",
"9/8",
"75025/65536",
"305/256",
"5/4",
"323/256",
"21/16",
"5473/4096",
"89/64",
"1449/1024",
"377/256",
"3/2",
"1597/1024",
"13/8",
"6765/4096",
"55/32",
"28657/16384",
"233/128",
"121393/65536",
"987/512",
"2/1"
]
},
{
"id": "burt_forks",
"desc": "Warren Burt, 19-tone Forks. Interval 5(3): pp. 13+23, Winter 1986-87",
"stepCount": "19",
"steps": [
"28/27",
"16/15",
"10/9",
"9/8",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"16/9",
"9/5",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "burt_primes",
"desc": "Warren Burt, primes until 251. \"Some Numbers\", Dec. 2002",
"stepCount": "54",
"steps": [
"131/128",
"67/64",
"17/16",
"137/128",
"139/128",
"71/64",
"73/64",
"37/32",
"149/128",
"151/128",
"19/16",
"157/128",
"79/64",
"5/4",
"163/128",
"41/32",
"83/64",
"167/128",
"43/32",
"173/128",
"11/8",
"89/64",
"179/128",
"181/128",
"23/16",
"47/32",
"191/128",
"3/2",
"193/128",
"97/64",
"197/128",
"199/128",
"101/64",
"103/64",
"13/8",
"211/128",
"53/32",
"107/64",
"109/64",
"223/128",
"7/4",
"113/64",
"227/128",
"229/128",
"29/16",
"233/128",
"59/32",
"239/128",
"241/128",
"61/32",
"31/16",
"251/128",
"127/64",
"2/1"
]
},
{
"id": "burt_1",
"desc": "W. Burt's 13diatsub #1",
"stepCount": "12",
"steps": [
"26/25",
"13/12",
"26/23",
"13/11",
"13/10",
"26/19",
"13/9",
"27/17",
"13/8",
"26/15",
"13/7",
"2/1"
]
},
{
"id": "burt_2",
"desc": "W. Burt's 13enhsub #2",
"stepCount": "12",
"steps": [
"104/103",
"52/51",
"104/101",
"26/25",
"13/10",
"104/79",
"4/3",
"104/77",
"26/19",
"52/33",
"13/7",
"2/1"
]
},
{
"id": "burt_3",
"desc": "W. Burt's 13enhharm #3",
"stepCount": "12",
"steps": [
"14/13",
"33/26",
"19/13",
"77/52",
"3/2",
"79/52",
"20/13",
"25/13",
"101/52",
"51/26",
"103/52",
"2/1"
]
},
{
"id": "burt_4",
"desc": "W. Burt's 13diatharm #4, see his post 3/30/94 in Tuning Digest #57",
"stepCount": "12",
"steps": [
"14/13",
"15/13",
"16/13",
"17/13",
"18/13",
"19/13",
"20/13",
"22/13",
"23/13",
"24/13",
"25/13",
"2/1"
]
},
{
"id": "burt_5",
"desc": "W. Burt's 17diatsub #5",
"stepCount": "12",
"steps": [
"17/16",
"17/15",
"17/14",
"17/13",
"17/12",
"34/23",
"17/11",
"34/21",
"17/10",
"34/19",
"17/9",
"2/1"
]
},
{
"id": "burt_6",
"desc": "W. Burt's 17enhsub #6",
"stepCount": "12",
"steps": [
"68/67",
"34/33",
"68/65",
"17/16",
"17/12",
"34/23",
"17/11",
"136/87",
"68/43",
"8/5",
"34/21",
"2/1"
]
},
{
"id": "burt_7",
"desc": "W. Burt's 17enhharm #7",
"stepCount": "12",
"steps": [
"21/17",
"5/4",
"43/34",
"87/68",
"22/17",
"23/17",
"24/17",
"32/17",
"65/34",
"33/17",
"67/34",
"2/1"
]
},
{
"id": "burt_8",
"desc": "W. Burt's 17diatharm #8, harmonics 16 to 32",
"stepCount": "12",
"steps": [
"18/17",
"19/17",
"20/17",
"21/17",
"22/17",
"23/17",
"24/17",
"26/17",
"28/17",
"30/17",
"32/17",
"2/1"
]
},
{
"id": "burt_9",
"desc": "W. Burt's 19diatsub #9",
"stepCount": "12",
"steps": [
"38/37",
"19/18",
"19/17",
"19/16",
"19/14",
"38/27",
"19/13",
"38/25",
"19/12",
"38/23",
"19/11",
"2/1"
]
},
{
"id": "burt_10",
"desc": "W. Burt's 19enhsub #10",
"stepCount": "12",
"steps": [
"76/75",
"38/37",
"76/73",
"19/18",
"19/14",
"38/27",
"19/13",
"152/103",
"76/51",
"152/101",
"38/25",
"2/1"
]
},
{
"id": "burt_11",
"desc": "W. Burt's 19enhharm #11",
"stepCount": "12",
"steps": [
"25/19",
"101/76",
"51/38",
"103/76",
"26/19",
"27/19",
"28/19",
"36/19",
"73/38",
"37/19",
"75/38",
"2/1"
]
},
{
"id": "burt_12",
"desc": "W. Burt's 19diatharm #12",
"stepCount": "12",
"steps": [
"22/19",
"23/19",
"24/19",
"25/19",
"26/19",
"27/19",
"28/19",
"32/19",
"34/19",
"36/19",
"37/19",
"2/1"
]
},
{
"id": "burt_13",
"desc": "W. Burt's 23diatsub #13",
"stepCount": "12",
"steps": [
"23/22",
"23/21",
"46/41",
"23/20",
"23/18",
"23/17",
"23/16",
"23/15",
"23/14",
"46/27",
"23/13",
"2/1"
]
},
{
"id": "burt_14",
"desc": "W. Burt's 23enhsub #14",
"stepCount": "12",
"steps": [
"92/91",
"46/45",
"92/89",
"23/22",
"23/18",
"23/17",
"23/16",
"92/63",
"46/31",
"92/61",
"23/15",
"2/1"
]
},
{
"id": "burt_15",
"desc": "W. Burt's 23enhharm #15",
"stepCount": "12",
"steps": [
"30/23",
"61/46",
"31/23",
"63/46",
"32/23",
"34/23",
"36/23",
"44/23",
"89/46",
"45/23",
"91/46",
"2/1"
]
},
{
"id": "burt_16",
"desc": "W. Burt's 23diatharm #16",
"stepCount": "12",
"steps": [
"26/23",
"27/23",
"28/23",
"30/23",
"32/23",
"34/23",
"36/23",
"40/23",
"41/23",
"42/23",
"44/23",
"2/1"
]
},
{
"id": "burt_17",
"desc": "W. Burt's \"2 out of 3,5,11,17,31 dekany\"CPS with 1/1=3/1. 1/1 vol. 10(1) '98",
"stepCount": "36",
"steps": [
"98549/98304",
"2057/2048",
"13175/12288",
"275/256",
"52855/49152",
"8959/8192",
"561/512",
"4805/4096",
"28985/24576",
"605/512",
"2635/2048",
"165/128",
"10571/8192",
"15895/12288",
"63767/49152",
"8525/6144",
"1445/1024",
"5797/4096",
"775/512",
"4675/3072",
"18755/12288",
"1581/1024",
"3179/2048",
"425/256",
"81685/49152",
"1705/1024",
"10285/6144",
"465/256",
"44795/24576",
"935/512",
"179707/98304",
"3751/2048",
"255/128",
"16337/8192",
"1023/512",
"2/1"
]
},
{
"id": "burt_18",
"desc": "W. Burt's \"2 out of 1,3,5,7,11 dekany\"CPS with 1/1=1/1. 1/1 vol. 10(1) '98",
"stepCount": "36",
"steps": [
"525/512",
"33/32",
"4235/4096",
"539/512",
"275/256",
"35/32",
"1155/1024",
"147/128",
"75/64",
"605/512",
"77/64",
"315/256",
"2541/2048",
"165/128",
"21/16",
"2695/2048",
"693/512",
"175/128",
"45/32",
"363/256",
"735/512",
"385/256",
"99/64",
"1617/1024",
"825/512",
"105/64",
"847/512",
"55/32",
"1815/1024",
"231/128",
"15/8",
"1925/1024",
"245/128",
"495/256",
"63/32",
"2/1"
]
},
{
"id": "burt_19",
"desc": "W. Burt's \"2 out of 2,3,4,5,7 dekany\"CPS with 1/1=1/1. 1/1 vol. 10(1) '98",
"stepCount": "20",
"steps": [
"525/512",
"35/32",
"9/8",
"147/128",
"75/64",
"315/256",
"5/4",
"21/16",
"175/128",
"45/32",
"735/512",
"3/2",
"49/32",
"25/16",
"105/64",
"7/4",
"15/8",
"245/128",
"63/32",
"2/1"
]
},
{
"id": "burt_20",
"desc": "Warren Burt tuning for \"Commas\"(1993). 1/1=263 Hz, XH 16",
"stepCount": "12",
"steps": [
"36/35",
"16/15",
"2187/2048",
"9/8",
"729/640",
"512/405",
"6561/5120",
"45/32",
"36/25",
"63/40",
"8/5",
"2/1"
]
},
{
"id": "buselik_pentachord_13_limit",
"desc": "Buselik pentachord 132:147:156:176:198",
"stepCount": "4",
"steps": ["49/44", "13/11", "4/3", "3/2"]
},
{
"id": "buselik_pentachord_19_limit",
"desc": "Buselik pentachord 48:54:57:64:72",
"stepCount": "4",
"steps": ["9/8", "19/16", "4/3", "3/2"]
},
{
"id": "buselik_tetrachord_13_limit",
"desc": "Buselik tetrachord 132:147:156:176",
"stepCount": "3",
"steps": ["49/44", "13/11", "4/3"]
},
{
"id": "buselik_tetrachord_19_limit",
"desc": "Buselik tetrachord 48:54:57:64",
"stepCount": "3",
"steps": ["9/8", "19/16", "4/3"]
},
{
"id": "bushmen",
"desc": "Observed scale of South-African bushmen, almost (4 notes) equal pentatonic",
"stepCount": "4",
"steps": ["489.00000", "710.00000", "954.00000", "2/1"]
},
{
"id": "buurman",
"desc": "Buurman temperament, 1/8-Pyth. comma, organ Doetinchem Gereformeerde Gemeentekerk",
"stepCount": "12",
"steps": [
"93.15750",
"198.04500",
"297.06750",
"396.09000",
"500.97750",
"594.13500",
"699.02250",
"795.11250",
"897.06750",
"999.02250",
"1095.11250",
"2/1"
]
},
{
"id": "buzurg_al_erin_10",
"desc": "Decatonic with septimal Buzurg, Rastlike modes (cf. Secor, blarney.txt)",
"stepCount": "10",
"steps": [
"14/13",
"8/7",
"16/13",
"4/3",
"56/39",
"3/2",
"21/13",
"12/7",
"24/13",
"2/1"
]
},
{
"id": "buzurg_10_decoid",
"desc": "buzurg_al-erin10 in decoid temperament, POTE tuning",
"stepCount": "10",
"steps": [
"128.91679",
"231.08321",
"360.00000",
"497.83359",
"626.75038",
"702.16641",
"831.08321",
"933.24962",
"1062.16641",
"2/1"
]
},
{
"id": "c_126_cp",
"desc": "126/125 comma pump scale in 185-tET",
"stepCount": "11",
"steps": [
"45.40541",
"77.83784",
"123.24324",
"311.35135",
"389.18919",
"467.02703",
"622.70270",
"700.54054",
"966.48649",
"1011.89189",
"2/1"
]
},
{
"id": "c_225_cp",
"desc": "225/224 comma pump scale in 197-tET",
"stepCount": "12",
"steps": [
"115.73604",
"152.28426",
"268.02030",
"383.75635",
"499.49239",
"584.77157",
"700.50761",
"767.51269",
"852.79188",
"968.52792",
"1084.26396",
"2/1"
]
},
{
"id": "c_385_cp",
"desc": "385/384 comma pump scale in 284-tET",
"stepCount": "16",
"steps": [
"50.70423",
"202.81690",
"283.09859",
"316.90141",
"384.50704",
"435.21127",
"549.29577",
"701.40845",
"752.11268",
"781.69014",
"866.19718",
"933.80282",
"967.60563",
"1047.88732",
"1098.59155",
"2/1"
]
},
{
"id": "c_1029_cp",
"desc": "1029/1024 comma pump scale in 190-tET",
"stepCount": "16",
"steps": [
"82.10526",
"202.10526",
"233.68421",
"385.26316",
"467.36842",
"618.94737",
"701.05263",
"783.15789",
"852.63158",
"884.21053",
"934.73684",
"966.31579",
"1086.31579",
"1117.89474",
"1168.42105",
"2/1"
]
},
{
"id": "c_1728_cp",
"desc": "1728/1715 comma pump scale in 111-tET",
"stepCount": "14",
"steps": [
"43.24324",
"270.27027",
"313.51351",
"389.18919",
"540.54054",
"583.78378",
"659.45946",
"702.70270",
"810.81081",
"854.05405",
"929.72973",
"972.97297",
"1124.32432",
"2/1"
]
},
{
"id": "c_3136_cp",
"desc": "3136/3125 comma pump scale in 446-tET",
"stepCount": "20",
"steps": [
"121.07623",
"156.05381",
"193.72197",
"266.36771",
"277.13004",
"314.79821",
"387.44395",
"508.52018",
"581.16592",
"702.24215",
"774.88789",
"812.55605",
"895.96413",
"968.60987",
"1006.27803",
"1078.92377",
"1089.68610",
"1127.35426",
"1162.33184",
"2/1"
]
},
{
"id": "c_5120_cp",
"desc": "5120/5103 comma pump scale in 391-tET",
"stepCount": "28",
"steps": [
"70.58824",
"85.93350",
"95.14066",
"156.52174",
"181.07417",
"205.62660",
"291.56010",
"300.76726",
"386.70077",
"411.25320",
"472.63427",
"497.18670",
"567.77494",
"592.32737",
"653.70844",
"678.26087",
"702.81330",
"788.74680",
"797.95396",
"883.88747",
"908.43990",
"969.82097",
"1028.13299",
"1089.51407",
"1114.06650",
"1150.89514",
"1175.44757",
"2/1"
]
},
{
"id": "c_6144_cp",
"desc": "6144/6125 comma pump scale in 381-tET",
"stepCount": "21",
"steps": [
"47.24409",
"85.03937",
"119.68504",
"157.48031",
"204.72441",
"277.16535",
"314.96063",
"387.40157",
"434.64567",
"472.44094",
"544.88189",
"655.11811",
"702.36220",
"774.80315",
"859.84252",
"932.28346",
"970.07874",
"1017.32283",
"1089.76378",
"1127.55906",
"2/1"
]
},
{
"id": "c_10976_cp",
"desc": "10976/10935 comma pump scale in 695-tET",
"stepCount": "28",
"steps": [
"60.43165",
"120.86331",
"145.03597",
"205.46763",
"265.89928",
"326.33094",
"386.76259",
"436.83453",
"447.19424",
"471.36691",
"497.26619",
"531.79856",
"557.69784",
"581.87050",
"592.23022",
"642.30216",
"702.73381",
"763.16547",
"823.59712",
"884.02878",
"908.20144",
"968.63309",
"1029.06475",
"1079.13669",
"1089.49640",
"1139.56835",
"1149.92806",
"2/1"
]
},
{
"id": "c_64827_cp",
"desc": "64827/64000 comma pump scale in 122-tET",
"stepCount": "16",
"steps": [
"147.54098",
"226.22951",
"304.91803",
"383.60656",
"462.29508",
"540.98361",
"619.67213",
"649.18033",
"698.36066",
"727.86885",
"806.55738",
"885.24590",
"963.93443",
"1042.62295",
"1121.31148",
"2/1"
]
},
{
"id": "cairo",
"desc": "d'Erlanger vol.5, p. 42. Congress of Arabic Music, Cairo, 1932",
"stepCount": "26",
"steps": [
"625/607",
"5000/4739",
"400/367",
"1000/891",
"1250/1087",
"2000/1689",
"500/419",
"400/327",
"5000/3989",
"2500/1937",
"4/3",
"250/183",
"10000/7111",
"10000/6881",
"3/2",
"2500/1631",
"1000/631",
"1000/627",
"2500/1529",
"500/297",
"10000/5789",
"500/279",
"200/109",
"250/133",
"125/64",
"2/1"
]
},
{
"id": "cal_46",
"desc": "Gene Ward Smith, 46 note scale for Caleb",
"stepCount": "46",
"steps": [
"22.92510",
"56.25760",
"80.63690",
"104.06120",
"126.61710",
"160.40260",
"184.73570",
"208.17100",
"231.93080",
"263.21920",
"288.77110",
"311.22890",
"336.78080",
"368.06920",
"391.82900",
"415.26430",
"439.59740",
"473.38290",
"495.93880",
"519.36310",
"543.74240",
"577.07490",
"600.00000",
"622.92510",
"656.25760",
"680.63690",
"704.06120",
"726.61710",
"760.40260",
"784.73570",
"808.17100",
"831.93080",
"863.21920",
"888.77110",
"911.22890",
"936.78080",
"968.06920",
"991.82900",
"1015.26430",
"1039.59740",
"1073.38290",
"1095.93880",
"1119.36310",
"1143.74240",
"1177.07490",
"2/1"
]
},
{
"id": "canright",
"desc": "David Canright's piano tuning for \"Fibonacci Suite\"(2001). Also 84-tET version of 11-limit \"Orwell\"",
"stepCount": "9",
"steps": [
"157.14286",
"271.42857",
"428.57143",
"542.85714",
"700.00000",
"814.28571",
"971.42857",
"1085.71429",
"2/1"
]
},
{
"id": "cantonpenta",
"desc": "Freivald's Canton scale in 13-limit pentacircle (351/350 and 364/363) temperament, 271-tET",
"stepCount": "12",
"steps": [
"128.41328",
"208.11808",
"287.82288",
"416.23616",
"495.94096",
"575.64576",
"704.05904",
"783.76384",
"912.17712",
"991.88192",
"1071.58672",
"2/1"
]
},
{
"id": "capurso",
"desc": "Equal temperament with equal beating 3/1 = 4/1 opposite (2009). Circular Harmonic System C.HA.S.",
"stepCount": "12",
"steps": [
"100.03832",
"200.07664",
"300.11496",
"400.15327",
"500.19159",
"600.22991",
"700.26823",
"800.30655",
"900.34487",
"1000.38318",
"1100.42150",
"1200.45982"
]
},
{
"id": "carlos_alpha",
"desc": "Wendy Carlos' Alpha scale with perfect fifth divided in nine",
"stepCount": "18",
"steps": [
"78.00000",
"156.00000",
"234.00000",
"312.00000",
"390.00000",
"468.00000",
"546.00000",
"624.00000",
"702.00000",
"780.00000",
"858.00000",
"936.00000",
"1014.00000",
"1092.00000",
"1170.00000",
"1248.00000",
"1326.00000",
"1404.00000"
]
},
{
"id": "carlos_alpha_2",
"desc": "Wendy Carlos' Alpha prime scale with perfect fifth divided by eightteen",
"stepCount": "36",
"steps": [
"39.00000",
"78.00000",
"117.00000",
"156.00000",
"195.00000",
"234.00000",
"273.00000",
"312.00000",
"351.00000",
"390.00000",
"429.00000",
"468.00000",
"507.00000",
"546.00000",
"585.00000",
"624.00000",
"663.00000",
"702.00000",
"741.00000",
"780.00000",
"819.00000",
"858.00000",
"897.00000",
"936.00000",
"975.00000",
"1014.00000",
"1053.00000",
"1092.00000",
"1131.00000",
"1170.00000",
"1209.00000",
"1248.00000",
"1287.00000",
"1326.00000",
"1365.00000",
"1404.00000"
]
},
{
"id": "carlos_beta",
"desc": "Wendy Carlos' Beta scale with perfect fifth divided by eleven",
"stepCount": "22",
"steps": [
"63.80000",
"127.60000",
"191.40000",
"255.20000",
"319.00000",
"382.80000",
"446.60000",
"510.40000",
"574.20000",
"638.00000",
"701.80000",
"765.60000",
"829.40000",
"893.20000",
"957.00000",
"1020.80000",
"1084.60000",
"1148.40000",
"1212.20000",
"1276.00000",
"1339.80000",
"1403.60000"
]
},
{
"id": "carlos_beta_2",
"desc": "Wendy Carlos' Beta prime scale with perfect fifth divided by twentytwo",
"stepCount": "44",
"steps": [
"31.90000",
"63.80000",
"95.70000",
"127.60000",
"159.50000",
"191.40000",
"223.30000",
"255.20000",
"287.10000",
"319.00000",
"350.90000",
"382.80000",
"414.70000",
"446.60000",
"478.50000",
"510.40000",
"542.30000",
"574.20000",
"606.10000",
"638.00000",
"669.90000",
"701.80000",
"733.70000",
"765.60000",
"797.50000",
"829.40000",
"861.30000",
"893.20000",
"925.10000",
"957.00000",
"988.90000",
"1020.80000",
"1052.70000",
"1084.60000",
"1116.50000",
"1148.40000",
"1180.30000",
"1212.20000",
"1244.10000",
"1276.00000",
"1307.90000",
"1339.80000",
"1371.70000",
"1403.60000"
]
},
{
"id": "carlos_gamma",
"desc": "Wendy Carlos' Gamma scale with third divided by eleven or fifth by twenty",
"stepCount": "35",
"steps": [
"35.09900",
"70.19800",
"105.29700",
"140.39600",
"175.49500",
"210.59400",
"245.69300",
"280.79200",
"315.89100",
"350.99000",
"386.08900",
"421.18800",
"456.28700",
"491.38600",
"526.48500",
"561.58400",
"596.68300",
"631.78200",
"666.88100",
"701.98000",
"737.07900",
"772.17800",
"807.27700",
"842.37600",
"877.47500",
"912.57400",
"947.67300",
"982.77200",
"1017.87100",
"1052.97000",
"1088.06900",
"1123.16800",
"1158.26700",
"1193.36600",
"1228.46500"
]
},
{
"id": "carlos_harm",
"desc": "Carlos Harmonic & Ben Johnston's scale of 'Blues' from Suite f.micr.piano (1977) & David Beardsley's scale of 'Science Friction'",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"21/16",
"11/8",
"3/2",
"13/8",
"27/16",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "carlos_super",
"desc": "Carlos Super Just",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"6/5",
"5/4",
"4/3",
"11/8",
"3/2",
"13/8",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "carlson",
"desc": "Brian Carlson's guitar scale (or 7 is 21/16 instead) fretted by Mark Rankin",
"stepCount": "19",
"steps": [
"21/20",
"35/32",
"9/8",
"7/6",
"6/5",
"5/4",
"35/27",
"4/3",
"7/5",
"35/24",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"9/5",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "cartwheel",
"desc": "Andrew Heathwite's 13-limit wakalix",
"stepCount": "17",
"steps": [
"28/27",
"13/12",
"9/8",
"7/6",
"11/9",
"5/4",
"4/3",
"11/8",
"13/9",
"3/2",
"14/9",
"13/8",
"5/3",
"7/4",
"11/6",
"15/8",
"2/1"
]
},
{
"id": "cassandra_1",
"desc": "Cassandra temperament (Erv Wilson), 13-limit, g=497.866",
"stepCount": "41",
"steps": [
"25.60083",
"63.73216",
"89.33299",
"114.93381",
"140.53464",
"178.66598",
"204.26680",
"229.86763",
"267.99897",
"293.59979",
"319.20062",
"344.80144",
"382.93278",
"408.53361",
"434.13443",
"472.26577",
"497.86660",
"523.46742",
"549.06825",
"587.19959",
"612.80041",
"638.40124",
"676.53258",
"702.13340",
"727.73423",
"765.86557",
"791.46639",
"817.06722",
"842.66804",
"880.79938",
"906.40021",
"932.00103",
"970.13237",
"995.73320",
"1021.33402",
"1046.93485",
"1085.06619",
"1110.66701",
"1136.26784",
"1174.39917",
"2/1"
]
},
{
"id": "cassandra_2",
"desc": "Cassandra temperament, schismic variant, 13-limit, g=497.395",
"stepCount": "41",
"steps": [
"24.44514",
"55.70922",
"86.97330",
"111.41844",
"142.68252",
"173.94660",
"198.39174",
"229.65582",
"260.91990",
"292.18398",
"316.62912",
"347.89320",
"379.15728",
"403.60242",
"434.86650",
"466.13058",
"497.39466",
"521.83980",
"553.10388",
"584.36796",
"608.81310",
"640.07718",
"671.34126",
"702.60534",
"727.05048",
"758.31456",
"789.57864",
"814.02378",
"845.28786",
"876.55194",
"900.99708",
"932.26116",
"963.52524",
"994.78932",
"1019.23446",
"1050.49854",
"1081.76262",
"1106.20776",
"1137.47184",
"1168.73592",
"2/1"
]
},
{
"id": "cassmagmirrod",
"desc": "Cassandra-magic-miracle-rodan Fokker block 385/384, 441/440, 225/224, 896/891 all generators -20..20",
"stepCount": "41",
"steps": [
"56/55",
"28/27",
"21/20",
"16/15",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"32/27",
"6/5",
"11/9",
"5/4",
"14/11",
"9/7",
"21/16",
"4/3",
"224/165",
"11/8",
"7/5",
"10/7",
"16/11",
"165/112",
"3/2",
"32/21",
"14/9",
"11/7",
"8/5",
"18/11",
"5/3",
"27/16",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"15/8",
"40/21",
"27/14",
"55/28",
"2/1"
]
},
{
"id": "cassmagmonkrod",
"desc": "Cassandra-magic-monkey-rodan Fokker block 385/384, 5120/5103, 100/99, 896/891 all generators -20..20",
"stepCount": "41",
"steps": [
"81/80",
"33/32",
"21/20",
"16/15",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"32/27",
"6/5",
"11/9",
"5/4",
"81/64",
"128/99",
"21/16",
"4/3",
"27/20",
"11/8",
"891/640",
"1280/891",
"16/11",
"40/27",
"3/2",
"32/21",
"99/64",
"128/81",
"8/5",
"18/11",
"5/3",
"27/16",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"15/8",
"40/21",
"64/33",
"160/81",
"2/1"
]
},
{
"id": "cassmagoctrod",
"desc": "Cassandra-magic-octacot-rodan Fokker block 245/243, 441/440, 896/891, 100/99 all generators -20..20 (Paul Erlich, 1999)",
"stepCount": "41",
"steps": [
"81/80",
"28/27",
"21/20",
"297/280",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"33/28",
"6/5",
"11/9",
"5/4",
"14/11",
"9/7",
"21/16",
"4/3",
"27/20",
"11/8",
"7/5",
"10/7",
"16/11",
"40/27",
"3/2",
"32/21",
"14/9",
"11/7",
"8/5",
"18/11",
"5/3",
"56/33",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"560/297",
"40/21",
"27/14",
"160/81",
"2/1"
]
},
{
"id": "cassmagsuprod",
"desc": "Cassandra-magic-superkliesmic-rodan Fokker block 385/384, 441/440, 100/99, 896/891 all generators -20..20",
"stepCount": "41",
"steps": [
"56/55",
"33/32",
"21/20",
"16/15",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"33/28",
"6/5",
"11/9",
"5/4",
"14/11",
"128/99",
"21/16",
"4/3",
"27/20",
"11/8",
"7/5",
"10/7",
"16/11",
"40/27",
"3/2",
"32/21",
"99/64",
"11/7",
"8/5",
"18/11",
"5/3",
"56/33",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"15/8",
"40/21",
"64/33",
"55/28",
"2/1"
]
},
{
"id": "cat_22",
"desc": "5-limit Dwarf(22) in catakleismic tempering, <197 312 457 553 681 728| tuning",
"stepCount": "22",
"steps": [
"48.73096",
"85.27919",
"134.01015",
"201.01523",
"249.74619",
"316.75127",
"383.75635",
"432.48731",
"450.76142",
"517.76650",
"584.77157",
"633.50254",
"700.50761",
"749.23858",
"816.24365",
"834.51777",
"901.52284",
"950.25381",
"1017.25888",
"1084.26396",
"1132.99492",
"2/1"
]
},
{
"id": "catakleismic_34",
"desc": "Catakleismic[34] 11-limit 3.5 cents lesfip optimized",
"stepCount": "34",
"steps": [
"16.49695",
"66.29540",
"84.05375",
"134.00830",
"150.79237",
"199.33786",
"249.33368",
"266.98536",
"316.80742",
"333.19956",
"383.02162",
"400.67330",
"450.66912",
"499.21461",
"515.99868",
"565.95323",
"583.71158",
"633.51003",
"650.00698",
"700.38204",
"717.29515",
"766.76698",
"816.00493",
"832.67380",
"882.78493",
"899.92196",
"950.08502",
"967.22205",
"1017.33318",
"1034.00205",
"1083.24000",
"1132.71183",
"1149.62494",
"2/1"
]
},
{
"id": "catakleismic_34_fok",
"desc": "Catakleismic[34] 5-limit 15625/15552&20000/19683 Fokker transversal",
"stepCount": "34",
"steps": [
"250/243",
"25/24",
"3125/2916",
"27/25",
"10/9",
"9/8",
"125/108",
"729/625",
"6/5",
"100/81",
"5/4",
"625/486",
"162/125",
"4/3",
"27/20",
"25/18",
"3125/2187",
"36/25",
"40/27",
"3/2",
"125/81",
"25/16",
"8/5",
"81/50",
"5/3",
"1250/729",
"125/72",
"16/9",
"9/5",
"50/27",
"15/8",
"625/324",
"243/125",
"2/1"
]
},
{
"id": "catakleismic_34_semitransversal",
"desc": "17 note 2.3.7 semitransversal of Catakleismic[34]",
"stepCount": "17",
"steps": [
"28/27",
"243/224",
"9/8",
"7/6",
"243/196",
"9/7",
"4/3",
"112/81",
"81/56",
"3/2",
"14/9",
"392/243",
"12/7",
"16/9",
"448/243",
"27/14",
"2/1"
]
},
{
"id": "catakleismic_34_trans",
"desc": "Catakleismic[34] 2.5.7 transversal",
"stepCount": "34",
"steps": [
"128/125",
"401408/390625",
"48828125/44957696",
"15625/14336",
"125/112",
"28/25",
"3584/3125",
"11239424/9765625",
"1953125/1605632",
"15625/12544",
"5/4",
"32/25",
"100352/78125",
"12845056/9765625",
"78125/57344",
"625/448",
"7/5",
"896/625",
"114688/78125",
"9765625/6422528",
"78125/50176",
"25/16",
"8/5",
"25088/15625",
"3211264/1953125",
"9765625/5619712",
"3125/1792",
"25/14",
"224/125",
"28672/15625",
"89915392/48828125",
"390625/200704",
"125/64",
"2/1"
]
},
{
"id": "catler",
"desc": "Catler 24-tone JI from \"Over and Under the 13 Limit\", 1/1 3(3)",
"stepCount": "24",
"steps": [
"33/32",
"16/15",
"9/8",
"8/7",
"7/6",
"6/5",
"128/105",
"16/13",
"5/4",
"21/16",
"4/3",
"11/8",
"45/32",
"16/11",
"3/2",
"8/5",
"13/8",
"5/3",
"27/16",
"7/4",
"16/9",
"24/13",
"15/8",
"2/1"
]
},
{
"id": "cauldron",
"desc": "Circulating temperament with two pure 9/7 thirds and 7 meantone, 2 slightly wide, 3 superpyth fifths",
"stepCount": "12",
"steps": [
"70.31346",
"189.20489",
"291.90367",
"378.40979",
"505.39755",
"567.61468",
"694.60245",
"781.10856",
"883.80734",
"1002.69878",
"1073.01223",
"2/1"
]
},
{
"id": "cbrat_19",
"desc": "Circulating 19-tone temperament with exact brats, G.W. Smith",
"stepCount": "19",
"steps": [
"3688037/3546660",
"9545591/8866650",
"197729/177333",
"686317/591110",
"6815759/5674656",
"441637/354666",
"1149379/886665",
"395458/295555",
"2468497/1773330",
"1280918/886665",
"264304/177333",
"28241/18188",
"1141103/709332",
"493284/295555",
"1026089/591110",
"528608/295555",
"329881/177333",
"686317/354666",
"2/1"
]
},
{
"id": "cdia_22",
"desc": "Circulating 22 note scale, two 11-tET cycles 5/4 apart, 11 pure major thirds",
"stepCount": "22",
"steps": [
"59.04099",
"109.09091",
"168.13190",
"218.18182",
"277.22280",
"327.27273",
"5/4",
"436.36364",
"495.40462",
"545.45454",
"604.49553",
"654.54545",
"713.58644",
"763.63636",
"822.67735",
"872.72727",
"931.76826",
"981.81818",
"1040.85917",
"1090.90909",
"1149.95008",
"2/1"
]
},
{
"id": "ceb_88_f",
"desc": "88 cents steps with equal beating fifths",
"stepCount": "13",
"steps": [
"88.21897",
"175.92057",
"264.44880",
"352.44257",
"439.93133",
"528.25538",
"616.05624",
"704.67971",
"792.76342",
"880.33719",
"968.74280",
"1056.62072",
"1144.00000"
]
},
{
"id": "ceb_88_s",
"desc": "88 cents steps with equal beating sevenths",
"stepCount": "14",
"steps": [
"88.05984",
"175.91216",
"264.14035",
"352.15228",
"439.95917",
"528.14400",
"616.11482",
"703.88273",
"792.03035",
"879.96589",
"967.70033",
"1055.81601",
"1143.72127",
"1232.00000"
]
},
{
"id": "ceb_88_t",
"desc": "88 cents steps with equal beating 7/6 thirds",
"stepCount": "14",
"steps": [
"87.59652",
"175.92414",
"262.95957",
"350.74928",
"439.26203",
"526.47086",
"614.42684",
"703.09889",
"790.45689",
"878.55589",
"967.36495",
"1054.85122",
"1143.07317",
"1232.00000"
]
},
{
"id": "cet_7",
"desc": "271th root of 3, Heinz Bohlen (1972)",
"stepCount": "271",
"steps": [
"7.01828",
"14.03657",
"21.05485",
"28.07314",
"35.09142",
"42.10970",
"49.12799",
"56.14627",
"63.16456",
"70.18284",
"77.20113",
"84.21941",
"91.23769",
"98.25598",
"105.27426",
"112.29255",
"119.31083",
"126.32911",
"133.34740",
"140.36568",
"147.38397",
"154.40225",
"161.42054",
"168.43882",
"175.45710",
"182.47539",
"189.49367",
"196.51196",
"203.53024",
"210.54852",
"217.56681",
"224.58509",
"231.60338",
"238.62166",
"245.63994",
"252.65823",
"259.67651",
"266.69480",
"273.71308",
"280.73137",
"287.74965",
"294.76793",
"301.78622",
"308.80450",
"315.82279",
"322.84107",
"329.85935",
"336.87764",
"343.89592",
"350.91421",
"357.93249",
"364.95078",
"371.96906",
"378.98734",
"386.00563",
"393.02391",
"400.04220",
"407.06048",
"414.07876",
"421.09705",
"428.11533",
"435.13362",
"442.15190",
"449.17018",
"456.18847",
"463.20675",
"470.22504",
"477.24332",
"484.26161",
"491.27989",
"498.29817",
"505.31646",
"512.33474",
"519.35303",
"526.37131",
"533.38959",
"540.40788",
"547.42616",
"554.44445",
"561.46273",
"568.48102",
"575.49930",
"582.51758",
"589.53587",
"596.55415",
"603.57244",
"610.59072",
"617.60900",
"624.62729",
"631.64557",
"638.66386",
"645.68214",
"652.70042",
"659.71871",
"666.73699",
"673.75528",
"680.77356",
"687.79185",
"694.81013",
"701.82841",
"708.84670",
"715.86498",
"722.88327",
"729.90155",
"736.91983",
"743.93812",
"750.95640",
"757.97469",
"764.99297",
"772.01125",
"779.02954",
"786.04782",
"793.06611",
"800.08439",
"807.10268",
"814.12096",
"821.13924",
"828.15753",
"835.17581",
"842.19410",
"849.21238",
"856.23066",
"863.24895",
"870.26723",
"877.28552",
"884.30380",
"891.32209",
"898.34037",
"905.35865",
"912.37694",
"919.39522",
"926.41351",
"933.43179",
"940.45007",
"947.46836",
"954.48664",
"961.50493",
"968.52321",
"975.54149",
"982.55978",
"989.57806",
"996.59635",
"1003.61463",
"1010.63292",
"1017.65120",
"1024.66948",
"1031.68777",
"1038.70605",
"1045.72434",
"1052.74262",
"1059.76090",
"1066.77919",
"1073.79747",
"1080.81576",
"1087.83404",
"1094.85233",
"1101.87061",
"1108.88889",
"1115.90718",
"1122.92546",
"1129.94375",
"1136.96203",
"1143.98031",
"1150.99860",
"1158.01688",
"1165.03517",
"1172.05345",
"1179.07173",
"1186.09002",
"1193.10830",
"1200.12659",
"1207.14487",
"1214.16316",
"1221.18144",
"1228.19972",
"1235.21801",
"1242.23629",
"1249.25458",
"1256.27286",
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"3/1"
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},
{
"id": "cet_10",
"desc": "20th root of 9/8, on Antonio Soler's tuning box, afinador or templante",
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"81/64",
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"729/512",
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{
"id": "cet_11",
"desc": "36th root of 5/4, Mohajeri Shahin",
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"25/16",
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"125/64",
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},
{
"id": "cet_14",
"desc": "Delta scale, 8th root of 16/15",
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},
{
"id": "cet_16",
"desc": "30th root of 4/3, Aristoxenos",
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},
{
"id": "cet_21",
"desc": "32nd root of 3/2",
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"3/2"
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},
{
"id": "cet_21_k",
"desc": "scale of syntonic comma's, almost 56-tET",
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"steps": [
"81/80",
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},
{
"id": "cet_22",
"desc": "9th root of 9/8",
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"steps": [
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},
{
"id": "cet_22_a",
"desc": "84th root of 3, almost equal to 53-tET",
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"3/1"
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},
{
"id": "cet_29",
"desc": "95th root of 5",
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"steps": [
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"2756.98410",
"5/1"
]
},
{
"id": "cet_33",
"desc": "25th root of phi, Walter O�Connell (1993)",
"stepCount": "25",
"steps": [
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},
{
"id": "cet_33_a",
"desc": "57th root of 3",
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},
{
"id": "cet_35",
"desc": "45th root of 5/2, Caleb Morgan (2010)",
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},
{
"id": "cet_39",
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{
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{
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{
"id": "cet_39_c",
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{
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{
"id": "cet_39_e",
"desc": "15th root of 7/5, X.J. Scott",
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{
"id": "cet_39_f",
"desc": "10th root of 5/4",
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"125/64",
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{
"id": "cet_39_g",
"desc": "31-tET 11-limit TOP-RMS tuning",
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{
"id": "cet_43",
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{
"id": "cet_44",
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{
"id": "cet_44_a",
"desc": "91th root of 10, Jim Kukula",
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"10/1"
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{
"id": "cet_44_b",
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"3/2"
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{
"id": "cet_45",
"desc": "11th root of 4/3",
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{
"id": "cet_45_a",
"desc": "13th root of 7/5, X.J. Scott",
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},
{
"id": "cet_46",
"desc": "18th root of phi, Walter O�Connell (1993)",
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{
"id": "cet_48",
"desc": "30th root of 7/3",
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"steps": [
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"7/3"
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{
"id": "cet_49",
"desc": "39th root of 3, Triple Bohlen-Pierce, good 3.5.7.11.13 system",
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"steps": [
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"3/1"
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{
"id": "cet_50",
"desc": "14th root of 3/2, stretched 24-tET",
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"steps": [
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{
"id": "cet_51",
"desc": "47nd root of 4",
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},
{
"id": "cet_53",
"desc": "5th root of 7/6, X.J. Scott",
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"steps": ["53.37418", "106.74836", "160.12254", "213.49672", "7/6"]
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{
"id": "cet_54",
"desc": "62nd root of 7",
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{
"id": "cet_54_a",
"desc": "101st root of 24",
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{
"id": "cet_54_b",
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"1630.24714",
"1684.58872",
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"1793.27186",
"1847.61343",
"3/1"
]
},
{
"id": "cet_54_c",
"desc": "22-tET 11-limit TOP tuning",
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"steps": [
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},
{
"id": "cet_54_d",
"desc": "22-tET 11-limit TOP-RMS tuning",
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"steps": [
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"108.99038",
"163.48557",
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},
{
"id": "cet_55",
"desc": "51th root of 5",
"stepCount": "51",
"steps": [
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"5/1"
]
},
{
"id": "cet_55_a",
"desc": "9th root of 4/3, 'Noleta' Scale",
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"steps": [
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"442.70667",
"4/3"
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},
{
"id": "cet_55_b",
"desc": "7th root of 5/4",
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"steps": [
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"25/16",
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"125/64",
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]
},
{
"id": "cet_59",
"desc": "12th root of 3/2, Gary Morrison",
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"steps": [
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"3/2",
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]
},
{
"id": "cet_59_a",
"desc": "32th root of 3",
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"steps": [
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"1842.51891",
"3/1"
]
},
{
"id": "cet_63",
"desc": "30th root of 3 or stretched 19-tET",
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"steps": [
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"1711.75950",
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"1838.55650",
"3/1"
]
},
{
"id": "cet_63_a",
"desc": "44th root of 5",
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"steps": [
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"5/1"
]
},
{
"id": "cet_63_b",
"desc": "19-tET 7-limit TOP tuning",
"stepCount": "19",
"steps": [
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},
{
"id": "cet_63_c",
"desc": "19-tET 7-limit TOP-RMS tuning",
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"steps": [
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},
{
"id": "cet_63_d",
"desc": "5th root of 6/5",
"stepCount": "19",
"steps": [
"63.12826",
"126.25651",
"189.38477",
"252.51303",
"6/5",
"378.76954",
"441.89780",
"505.02606",
"568.15432",
"36/25",
"694.41083",
"757.53909",
"820.66735",
"883.79560",
"216/125",
"1010.05212",
"1073.18038",
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"1199.43689"
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},
{
"id": "cet_63_e",
"desc": "16th root of 9/5",
"stepCount": "19",
"steps": [
"63.59977",
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"9/5",
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"1144.79582",
"1208.39559"
]
},
{
"id": "cet_63_f",
"desc": "93th root of 30 or stretched 19-tET",
"stepCount": "93",
"steps": [
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"5001.86267",
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"5128.49211",
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"5255.12154",
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"5445.06569",
"5508.38041",
"5571.69513",
"5635.00985",
"5698.32456",
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"5824.95400",
"30/1"
]
},
{
"id": "cet_63_g",
"desc": "49th root of 6",
"stepCount": "49",
"steps": [
"63.30520",
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"189.91561",
"253.22082",
"316.52602",
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"2658.81857",
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"2848.73418",
"2912.03939",
"2975.34459",
"3038.64980",
"6/1"
]
},
{
"id": "cet_63_h",
"desc": "25th root of 5/2",
"stepCount": "25",
"steps": [
"63.45255",
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"190.35765",
"253.81019",
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"1332.50352",
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"5/2"
]
},
{
"id": "cet_63_i",
"desc": "11th root of 3/2, half of Carlos Beta",
"stepCount": "11",
"steps": [
"63.81409",
"127.62818",
"191.44227",
"255.25636",
"319.07045",
"382.88455",
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"510.51273",
"574.32682",
"638.14091",
"3/2"
]
},
{
"id": "cet_65",
"desc": "65cET by Andrew Heathwaite",
"stepCount": "20",
"steps": [
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"130.00000",
"195.00000",
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"1105.00000",
"1170.00000",
"1235.00000",
"1300.00000"
]
},
{
"id": "cet_65_a",
"desc": "37th root of 4",
"stepCount": "37",
"steps": [
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"129.72973",
"194.59459",
"259.45946",
"324.32432",
"389.18919",
"454.05405",
"518.91892",
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"648.64865",
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"2140.54054",
"2205.40541",
"2270.27027",
"2335.13514",
"4/1"
]
},
{
"id": "cet_67",
"desc": "14th root of 12/7, X.J. Scott",
"stepCount": "14",
"steps": [
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"199.95623",
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"333.26039",
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"12/7"
]
},
{
"id": "cet_68",
"desc": "3rd root of 9/8",
"stepCount": "18",
"steps": [
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"135.94000",
"9/8",
"271.88000",
"339.85000",
"81/64",
"475.79000",
"543.76000",
"729/512",
"679.70001",
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"6561/4096",
"883.61001",
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"59049/32768",
"1087.52001",
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"531441/262144"
]
},
{
"id": "cet_68_a",
"desc": "49th root of 7",
"stepCount": "49",
"steps": [
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"3025.06816",
"3093.81971",
"3162.57126",
"3231.32281",
"3300.07436",
"7/1"
]
},
{
"id": "cet_69",
"desc": "12th root of phi",
"stepCount": "12",
"steps": [
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},
{
"id": "cet_70",
"desc": "27th root of 3",
"stepCount": "27",
"steps": [
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"915.75611",
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"1479.29833",
"1549.74111",
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"1831.51222",
"3/1"
]
},
{
"id": "cet_71",
"desc": "39th root of 5",
"stepCount": "39",
"steps": [
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"142.88788",
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"357.21971",
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"5/1"
]
},
{
"id": "cet_72",
"desc": "33rd root of 4, Birgit Maus",
"stepCount": "33",
"steps": [
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"145.45455",
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"2327.27273",
"4/1"
]
},
{
"id": "cet_73",
"desc": "26th root of 3, Gene Smith",
"stepCount": "26",
"steps": [
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"1170.43385",
"1243.58596",
"1316.73808",
"1389.89019",
"1463.04231",
"1536.19442",
"1609.34654",
"1682.49865",
"1755.65077",
"1828.80289",
"3/1"
]
},
{
"id": "cet_75",
"desc": "16-tET 13-limit TOP tuning",
"stepCount": "16",
"steps": [
"75.46561",
"150.93121",
"226.39682",
"301.86242",
"377.32803",
"452.79363",
"528.25924",
"603.72485",
"679.19045",
"754.65606",
"830.12166",
"905.58727",
"981.05287",
"1056.51848",
"1131.98409",
"1207.44969"
]
},
{
"id": "cet_75_a",
"desc": "16-tET 13-limit TOP-RMS tuning",
"stepCount": "16",
"steps": [
"75.32739",
"150.65478",
"225.98217",
"301.30956",
"376.63695",
"451.96434",
"527.29173",
"602.61912",
"677.94651",
"753.27390",
"828.60129",
"903.92868",
"979.25607",
"1054.58346",
"1129.91085",
"1205.23824"
]
},
{
"id": "cet_76",
"desc": "25th root of 3 or stretched 16-tET",
"stepCount": "25",
"steps": [
"76.07820",
"152.15640",
"228.23460",
"304.31280",
"380.39100",
"456.46920",
"532.54740",
"608.62560",
"684.70380",
"760.78200",
"836.86020",
"912.93840",
"989.01660",
"1065.09480",
"1141.17300",
"1217.25120",
"1293.32940",
"1369.40760",
"1445.48580",
"1521.56400",
"1597.64220",
"1673.72040",
"1749.79860",
"1825.87680",
"3/1"
]
},
{
"id": "cet_77",
"desc": "19th root of 7/3",
"stepCount": "19",
"steps": [
"77.20373",
"154.40746",
"231.61120",
"308.81493",
"386.01866",
"463.22239",
"540.42612",
"617.62985",
"694.83359",
"772.03732",
"849.24105",
"926.44478",
"1003.64851",
"1080.85225",
"1158.05598",
"1235.25971",
"1312.46344",
"1389.66717",
"7/3"
]
},
{
"id": "cet_78",
"desc": "9th root of 3/2",
"stepCount": "9",
"steps": [
"77.99500",
"155.99000",
"233.98500",
"311.98000",
"389.97500",
"467.97000",
"545.96500",
"623.96000",
"3/2"
]
},
{
"id": "cet_79",
"desc": "24th root of 3, James Heffernan (1906)",
"stepCount": "24",
"steps": [
"79.24813",
"158.49625",
"237.74438",
"316.99250",
"396.24063",
"475.48875",
"554.73688",
"633.98500",
"713.23313",
"792.48125",
"871.72938",
"950.97750",
"1030.22563",
"1109.47375",
"1188.72188",
"1267.97000",
"1347.21813",
"1426.46625",
"1505.71438",
"1584.96250",
"1664.21063",
"1743.45875",
"1822.70688",
"3/1"
]
},
{
"id": "cet_80",
"desc": "35th root of 5",
"stepCount": "35",
"steps": [
"79.60896",
"159.21793",
"238.82689",
"318.43585",
"398.04482",
"477.65378",
"557.26274",
"636.87171",
"716.48067",
"796.08963",
"875.69860",
"955.30756",
"1034.91652",
"1114.52549",
"1194.13445",
"1273.74341",
"1353.35238",
"1432.96134",
"1512.57030",
"1592.17927",
"1671.78823",
"1751.39719",
"1831.00615",
"1910.61512",
"1990.22408",
"2069.83304",
"2149.44201",
"2229.05097",
"2308.65993",
"2388.26890",
"2467.87786",
"2547.48682",
"2627.09579",
"2706.70475",
"5/1"
]
},
{
"id": "cet_83",
"desc": "83.33333 cent steps by Alexander Nemtin (1963)",
"stepCount": "15",
"steps": [
"83.33333",
"166.66667",
"250.00000",
"333.33333",
"416.66667",
"500.00000",
"583.33333",
"666.66667",
"750.00000",
"833.33333",
"916.66667",
"1000.00000",
"1083.33333",
"1166.66667",
"1250.00000"
]
},
{
"id": "cet_83_a",
"desc": "48th root of 10",
"stepCount": "48",
"steps": [
"83.04820",
"166.09640",
"249.14461",
"332.19281",
"415.24101",
"498.28921",
"581.33742",
"664.38562",
"747.43382",
"830.48202",
"913.53023",
"996.57843",
"1079.62663",
"1162.67483",
"1245.72304",
"1328.77124",
"1411.81944",
"1494.86764",
"1577.91585",
"1660.96405",
"1744.01225",
"1827.06045",
"1910.10865",
"1993.15686",
"2076.20506",
"2159.25326",
"2242.30146",
"2325.34967",
"2408.39787",
"2491.44607",
"2574.49427",
"2657.54248",
"2740.59068",
"2823.63888",
"2906.68708",
"2989.73529",
"3072.78349",
"3155.83169",
"3238.87989",
"3321.92809",
"3404.97630",
"3488.02450",
"3571.07270",
"3654.12090",
"3737.16911",
"3820.21731",
"3903.26551",
"10/1"
]
},
{
"id": "cet_84",
"desc": "33rd root of 5",
"stepCount": "33",
"steps": [
"84.43375",
"168.86750",
"253.30125",
"337.73500",
"422.16874",
"506.60249",
"591.03624",
"675.46999",
"759.90374",
"844.33749",
"928.77124",
"1013.20499",
"1097.63874",
"1182.07248",
"1266.50623",
"1350.93998",
"1435.37373",
"1519.80748",
"1604.24123",
"1688.67498",
"1773.10873",
"1857.54248",
"1941.97622",
"2026.40997",
"2110.84372",
"2195.27747",
"2279.71122",
"2364.14497",
"2448.57872",
"2533.01247",
"2617.44622",
"2701.87996",
"5/1"
]
},
{
"id": "cet_87",
"desc": "Least-squares stretched ET to telephone dial tones. 1/1=697 Hz",
"stepCount": "15",
"steps": [
"86.67933",
"173.35867",
"260.03800",
"346.71733",
"433.39667",
"520.07600",
"606.75533",
"693.43467",
"780.11400",
"866.79333",
"953.47267",
"1040.15200",
"1126.83133",
"1213.51067",
"1300.19000"
]
},
{
"id": "cet_88_snake",
"desc": "3+1 mode of 88cET, nicknamed Snake by Andrew Heathwaite",
"stepCount": "21",
"steps": [
"264.00000",
"352.00000",
"616.00000",
"704.00000",
"968.00000",
"1056.00000",
"1320.00000",
"1408.00000",
"1672.00000",
"1760.00000",
"2024.00000",
"2112.00000",
"2376.00000",
"2464.00000",
"2728.00000",
"2816.00000",
"3080.00000",
"3168.00000",
"3432.00000",
"3520.00000",
"3608.00000"
]
},
{
"id": "cet_88",
"desc": "88.0 cents steps by Gary Morrison alias mr88cet",
"stepCount": "14",
"steps": [
"88.00000",
"176.00000",
"264.00000",
"352.00000",
"440.00000",
"528.00000",
"616.00000",
"704.00000",
"792.00000",
"880.00000",
"968.00000",
"1056.00000",
"1144.00000",
"1232.00000"
]
},
{
"id": "cet_88_b",
"desc": "87.97446 cent steps. Least squares for 7/6, 11/9, 10/7, 3/2, 7/4",
"stepCount": "14",
"steps": [
"87.97446",
"175.94891",
"263.92337",
"351.89782",
"439.87228",
"527.84674",
"615.82119",
"703.79565",
"791.77010",
"879.74456",
"967.71902",
"1055.69347",
"1143.66793",
"1231.64238"
]
},
{
"id": "cet_88_b_2",
"desc": "87.75412 cent steps. Minimax for 7/6, 11/9, 10/7, 3/2, 7/4",
"stepCount": "14",
"steps": [
"87.75412",
"175.50824",
"263.26236",
"351.01648",
"438.77060",
"526.52472",
"614.27884",
"702.03296",
"789.78708",
"877.54120",
"965.29532",
"1053.04944",
"1140.80356",
"1228.55768"
]
},
{
"id": "cet_88_b_3",
"desc": "87.84635 cent steps. Minimax for 3, 5, 7, 8, 11",
"stepCount": "14",
"steps": [
"87.84635",
"175.69270",
"263.53905",
"351.38539",
"439.23174",
"527.07809",
"614.92444",
"702.77079",
"790.61714",
"878.46348",
"966.30983",
"1054.15618",
"1142.00253",
"1229.84888"
]
},
{
"id": "cet_88_b_4",
"desc": "87.80488 cent steps. Least squares for 3, 5, 7, 8, 11",
"stepCount": "14",
"steps": [
"87.80488",
"175.60976",
"263.41463",
"351.21951",
"439.02439",
"526.82927",
"614.63415",
"702.43902",
"790.24390",
"878.04878",
"965.85366",
"1053.65854",
"1141.46341",
"1229.26829"
]
},
{
"id": "cet_88_c",
"desc": "38th root of 7, McLaren 'Microtonal Music', volume 3, track 7",
"stepCount": "38",
"steps": [
"88.65331",
"177.30663",
"265.95994",
"354.61325",
"443.26657",
"531.91988",
"620.57319",
"709.22651",
"797.87982",
"886.53313",
"975.18645",
"1063.83976",
"1152.49307",
"1241.14639",
"1329.79970",
"1418.45301",
"1507.10633",
"1595.75964",
"1684.41295",
"1773.06627",
"1861.71958",
"1950.37289",
"2039.02621",
"2127.67952",
"2216.33283",
"2304.98615",
"2393.63946",
"2482.29277",
"2570.94609",
"2659.59940",
"2748.25271",
"2836.90603",
"2925.55934",
"3014.21265",
"3102.86597",
"3191.51928",
"3280.17259",
"7/1"
]
},
{
"id": "cet_88_d",
"desc": "41th root of 8",
"stepCount": "41",
"steps": [
"87.80488",
"175.60976",
"263.41463",
"351.21951",
"439.02439",
"526.82927",
"614.63415",
"702.43902",
"790.24390",
"878.04878",
"965.85366",
"1053.65854",
"1141.46341",
"1229.26829",
"1317.07317",
"1404.87805",
"1492.68293",
"1580.48780",
"1668.29268",
"1756.09756",
"1843.90244",
"1931.70732",
"2019.51220",
"2107.31707",
"2195.12195",
"2282.92683",
"2370.73171",
"2458.53659",
"2546.34146",
"2634.14634",
"2721.95122",
"2809.75610",
"2897.56098",
"2985.36585",
"3073.17073",
"3160.97561",
"3248.78049",
"3336.58537",
"3424.39024",
"3512.19512",
"8/1"
]
},
{
"id": "cet_88_e",
"desc": "35th root of 6",
"stepCount": "35",
"steps": [
"88.62729",
"177.25457",
"265.88186",
"354.50914",
"443.13643",
"531.76371",
"620.39100",
"709.01829",
"797.64557",
"886.27286",
"974.90014",
"1063.52743",
"1152.15471",
"1240.78200",
"1329.40929",
"1418.03657",
"1506.66386",
"1595.29114",
"1683.91843",
"1772.54571",
"1861.17300",
"1949.80029",
"2038.42757",
"2127.05486",
"2215.68214",
"2304.30943",
"2392.93671",
"2481.56400",
"2570.19129",
"2658.81857",
"2747.44586",
"2836.07314",
"2924.70043",
"3013.32772",
"6/1"
]
},
{
"id": "cet_88_f",
"desc": "18th root of 5/2",
"stepCount": "18",
"steps": [
"88.12854",
"176.25708",
"264.38562",
"352.51416",
"440.64270",
"528.77124",
"616.89978",
"705.02832",
"793.15686",
"881.28540",
"969.41394",
"1057.54248",
"1145.67102",
"1233.79956",
"1321.92809",
"1410.05663",
"1498.18517",
"5/2"
]
},
{
"id": "cet_88_g",
"desc": "27th root of 4",
"stepCount": "27",
"steps": [
"88.88889",
"177.77778",
"266.66667",
"355.55556",
"444.44444",
"533.33333",
"622.22222",
"711.11111",
"800.00000",
"888.88889",
"977.77778",
"1066.66667",
"1155.55556",
"1244.44444",
"1333.33333",
"1422.22222",
"1511.11111",
"1600.00000",
"1688.88889",
"1777.77778",
"1866.66667",
"1955.55556",
"2044.44444",
"2133.33333",
"2222.22222",
"2311.11111",
"4/1"
]
},
{
"id": "cet_89",
"desc": "31st root of 5, McLaren 'Microtonal Music', volume 2, track 22",
"stepCount": "31",
"steps": [
"89.88109",
"179.76218",
"269.64326",
"359.52435",
"449.40544",
"539.28653",
"629.16761",
"719.04870",
"808.92979",
"898.81088",
"988.69196",
"1078.57305",
"1168.45414",
"1258.33523",
"1348.21631",
"1438.09740",
"1527.97849",
"1617.85958",
"1707.74066",
"1797.62175",
"1887.50284",
"1977.38393",
"2067.26501",
"2157.14610",
"2247.02719",
"2336.90828",
"2426.78936",
"2516.67045",
"2606.55154",
"2696.43263",
"5/1"
]
},
{
"id": "cet_90",
"desc": "Scale with limma steps",
"stepCount": "17",
"steps": [
"256/243",
"65536/59049",
"16777216/14348907",
"360.89998",
"451.12498",
"541.34997",
"631.57497",
"721.79997",
"812.02496",
"902.24996",
"992.47495",
"1082.69995",
"1172.92494",
"1263.14994",
"1353.37494",
"1443.59993",
"1533.82493"
]
},
{
"id": "cet_93",
"desc": "Tuning used in John Chowning's Stria (1977), 9th root of Phi",
"stepCount": "9",
"steps": [
"92.56559",
"185.13118",
"277.69677",
"370.26235",
"462.82794",
"555.39353",
"647.95912",
"740.52471",
"833.09030"
]
},
{
"id": "cet_95",
"desc": "20th root of 3",
"stepCount": "20",
"steps": [
"95.09775",
"190.19550",
"285.29325",
"380.39100",
"475.48875",
"570.58650",
"665.68425",
"760.78200",
"855.87975",
"950.97750",
"1046.07525",
"1141.17300",
"1236.27075",
"1331.36850",
"1426.46625",
"1521.56400",
"1616.66175",
"1711.75950",
"1806.85725",
"3/1"
]
},
{
"id": "cet_96",
"desc": "4th root of 5/4",
"stepCount": "16",
"steps": [
"96.57843",
"193.15686",
"289.73529",
"5/4",
"482.89214",
"579.47057",
"676.04900",
"25/16",
"869.20586",
"965.78428",
"1062.36271",
"125/64",
"1255.51957",
"1352.09800",
"1448.67643",
"625/256"
]
},
{
"id": "cet_97",
"desc": "Manfred Stahnke, PARTCH HARP synth tuning. Minimax for 5/4 and 7/4, acceptable 11/4",
"stepCount": "12",
"steps": [
"96.79569",
"193.59138",
"290.38707",
"387.18276",
"483.97845",
"580.77414",
"677.56983",
"774.36551",
"871.16120",
"967.95689",
"1064.75258",
"1161.54827"
]
},
{
"id": "cet_97_a",
"desc": "15th root of 7/3",
"stepCount": "15",
"steps": [
"97.79139",
"195.58279",
"293.37418",
"391.16557",
"488.95697",
"586.74836",
"684.53976",
"782.33115",
"880.12254",
"977.91394",
"1075.70533",
"1173.49672",
"1271.28812",
"1369.07951",
"7/3"
]
},
{
"id": "cet_98",
"desc": "8th root of 11/7, X.J. Scott",
"stepCount": "8",
"steps": [
"97.81150",
"195.62301",
"293.43451",
"391.24602",
"489.05752",
"586.86903",
"684.68053",
"11/7"
]
},
{
"id": "cet_98_phi",
"desc": "Phi + 1 equal division by 17, Brouncker (1653)",
"stepCount": "17",
"steps": [
"98.01062",
"196.02125",
"294.03187",
"392.04249",
"490.05312",
"588.06374",
"686.07436",
"784.08498",
"882.09561",
"980.10623",
"1078.11685",
"1176.12748",
"1274.13810",
"1372.14872",
"1470.15935",
"1568.16997",
"1666.18059"
]
},
{
"id": "cet_99",
"desc": "16th root of 5/2",
"stepCount": "16",
"steps": [
"99.14461",
"198.28921",
"297.43382",
"396.57843",
"495.72304",
"594.86764",
"694.01225",
"793.15686",
"892.30146",
"991.44607",
"1090.59068",
"1189.73529",
"1288.87989",
"1388.02450",
"1487.16911",
"5/2"
]
},
{
"id": "cet_100",
"desc": "28th root of 5",
"stepCount": "28",
"steps": [
"99.51120",
"199.02241",
"298.53361",
"398.04482",
"497.55602",
"597.06722",
"696.57843",
"796.08963",
"895.60084",
"995.11204",
"1094.62324",
"1194.13445",
"1293.64565",
"1393.15686",
"1492.66806",
"1592.17927",
"1691.69047",
"1791.20167",
"1890.71288",
"1990.22408",
"2089.73529",
"2189.24649",
"2288.75769",
"2388.26890",
"2487.78010",
"2587.29131",
"2686.80251",
"5/1"
]
},
{
"id": "cet_100_a",
"desc": "12-tET 5-limit TOP tuning",
"stepCount": "12",
"steps": [
"99.80617",
"199.61234",
"299.41852",
"399.22469",
"499.03086",
"598.83703",
"698.64321",
"798.44938",
"898.25555",
"998.06172",
"1097.86790",
"1197.67407"
]
},
{
"id": "cet_100_b",
"desc": "12-tET 5-limit TOP-RMS tuning",
"stepCount": "12",
"steps": [
"99.87003",
"199.74006",
"299.61009",
"399.48012",
"499.35014",
"599.22017",
"699.09020",
"798.96023",
"898.83026",
"998.70029",
"1098.57032",
"1198.44035"
]
},
{
"id": "cet_104",
"desc": "23rd root of 4, T�tim Dennsuul",
"stepCount": "23",
"steps": [
"104.34783",
"208.69565",
"313.04348",
"417.39130",
"521.73913",
"626.08696",
"730.43478",
"834.78261",
"939.13043",
"1043.47826",
"1147.82609",
"1252.17391",
"1356.52174",
"1460.86957",
"1565.21739",
"1669.56522",
"1773.91304",
"1878.26087",
"1982.60870",
"2086.95652",
"2191.30435",
"2295.65217",
"4/1"
]
},
{
"id": "cet_104_a",
"desc": "38th root of 10",
"stepCount": "38",
"steps": [
"104.90299",
"209.80598",
"314.70898",
"419.61197",
"524.51496",
"629.41795",
"734.32095",
"839.22394",
"944.12693",
"1049.02992",
"1153.93292",
"1258.83591",
"1363.73890",
"1468.64189",
"1573.54489",
"1678.44788",
"1783.35087",
"1888.25386",
"1993.15686",
"2098.05985",
"2202.96284",
"2307.86583",
"2412.76883",
"2517.67182",
"2622.57481",
"2727.47780",
"2832.38080",
"2937.28379",
"3042.18678",
"3147.08977",
"3251.99277",
"3356.89576",
"3461.79875",
"3566.70174",
"3671.60474",
"3776.50773",
"3881.41072",
"10/1"
]
},
{
"id": "cet_105",
"desc": "13th root of 11/5, has very good 6/5 and 13/8",
"stepCount": "13",
"steps": [
"105.00033",
"210.00065",
"315.00098",
"420.00130",
"525.00163",
"630.00195",
"735.00228",
"840.00260",
"945.00293",
"1050.00325",
"1155.00358",
"1260.00390",
"11/5"
]
},
{
"id": "cet_105_a",
"desc": "18th root of 3",
"stepCount": "18",
"steps": [
"105.66417",
"211.32833",
"316.99250",
"422.65667",
"528.32083",
"633.98500",
"739.64917",
"845.31333",
"950.97750",
"1056.64167",
"1162.30583",
"1267.97000",
"1373.63417",
"1479.29833",
"1584.96250",
"1690.62667",
"1796.29083",
"3/1"
]
},
{
"id": "cet_108",
"desc": "4th root of 9/7, Chris Vaisvil",
"stepCount": "11",
"steps": [
"108.77102",
"217.54205",
"326.31307",
"9/7",
"543.85512",
"652.62614",
"761.39717",
"81/49",
"978.93921",
"1087.71024",
"1196.48126"
]
},
{
"id": "cet_109",
"desc": "LS optimal 11-tET 2.7.9.11.15.17 JI subgroup tuning",
"stepCount": "11",
"steps": [
"108.91867",
"217.83734",
"326.75600",
"435.67467",
"544.59334",
"653.51201",
"762.43068",
"871.34934",
"980.26801",
"1089.18668",
"1198.10535"
]
},
{
"id": "cet_111",
"desc": "25th root of 5, Karlheinz Stockhausen in \"Studie II\"(1954)",
"stepCount": "25",
"steps": [
"111.45255",
"222.90510",
"334.35765",
"445.81019",
"557.26274",
"668.71529",
"780.16784",
"891.62039",
"1003.07294",
"1114.52549",
"1225.97803",
"1337.43058",
"1448.88313",
"1560.33568",
"1671.78823",
"1783.24078",
"1894.69333",
"2006.14587",
"2117.59842",
"2229.05097",
"2340.50352",
"2451.95607",
"2563.40862",
"2674.86117",
"5/1"
]
},
{
"id": "cet_111_a",
"desc": "17th root of 3. McLaren 'Microtonal Music', volume 1, track 8",
"stepCount": "17",
"steps": [
"111.87971",
"223.75941",
"335.63912",
"447.51882",
"559.39853",
"671.27824",
"783.15794",
"895.03765",
"1006.91735",
"1118.79706",
"1230.67677",
"1342.55647",
"1454.43618",
"1566.31588",
"1678.19559",
"1790.07529",
"3/1"
]
},
{
"id": "cet_112",
"desc": "53rd root of 31. McLaren 'Microtonal Music', volume 4, track 16",
"stepCount": "53",
"steps": [
"112.17048",
"224.34096",
"336.51145",
"448.68193",
"560.85241",
"673.02289",
"785.19338",
"897.36386",
"1009.53434",
"1121.70482",
"1233.87531",
"1346.04579",
"1458.21627",
"1570.38675",
"1682.55724",
"1794.72772",
"1906.89820",
"2019.06868",
"2131.23917",
"2243.40965",
"2355.58013",
"2467.75061",
"2579.92110",
"2692.09158",
"2804.26206",
"2916.43254",
"3028.60303",
"3140.77351",
"3252.94399",
"3365.11447",
"3477.28496",
"3589.45544",
"3701.62592",
"3813.79640",
"3925.96689",
"4038.13737",
"4150.30785",
"4262.47833",
"4374.64882",
"4486.81930",
"4598.98978",
"4711.16026",
"4823.33075",
"4935.50123",
"5047.67171",
"5159.84219",
"5272.01268",
"5384.18316",
"5496.35364",
"5608.52412",
"5720.69461",
"5832.86509",
"31/1"
]
},
{
"id": "cet_112_a",
"desc": "30th root of 7",
"stepCount": "30",
"steps": [
"112.29420",
"224.58839",
"336.88259",
"449.17679",
"561.47098",
"673.76518",
"786.05938",
"898.35358",
"1010.64777",
"1122.94197",
"1235.23617",
"1347.53036",
"1459.82456",
"1572.11876",
"1684.41295",
"1796.70715",
"1909.00135",
"2021.29554",
"2133.58974",
"2245.88394",
"2358.17813",
"2470.47233",
"2582.76653",
"2695.06073",
"2807.35492",
"2919.64912",
"3031.94332",
"3144.23751",
"3256.53171",
"7/1"
]
},
{
"id": "cet_114",
"desc": "21st root of 4",
"stepCount": "21",
"steps": [
"114.28571",
"228.57143",
"342.85714",
"457.14286",
"571.42857",
"685.71429",
"800.00000",
"914.28571",
"1028.57143",
"1142.85714",
"1257.14286",
"1371.42857",
"1485.71429",
"1600.00000",
"1714.28571",
"1828.57143",
"1942.85714",
"2057.14286",
"2171.42857",
"2285.71429",
"4/1"
]
},
{
"id": "cet_115",
"desc": "2nd root of 8/7. Werner Linden, Musiktheorie, 2003 no.1 midi 15.Eb=19.44544 Hz",
"stepCount": "10",
"steps": [
"115.58705",
"8/7",
"346.76114",
"64/49",
"577.93523",
"512/343",
"809.10933",
"4096/2401",
"1040.28342",
"32768/16807"
]
},
{
"id": "cet_116",
"desc": "31st root of 8, Jake Freivald in \"A Call in Summer\"",
"stepCount": "31",
"steps": [
"116.12903",
"232.25806",
"348.38710",
"464.51613",
"580.64516",
"696.77419",
"812.90323",
"929.03226",
"1045.16129",
"1161.29032",
"1277.41935",
"1393.54839",
"1509.67742",
"1625.80645",
"1741.93548",
"1858.06452",
"1974.19355",
"2090.32258",
"2206.45161",
"2322.58065",
"2438.70968",
"2554.83871",
"2670.96774",
"2787.09677",
"2903.22581",
"3019.35484",
"3135.48387",
"3251.61290",
"3367.74194",
"3483.87097",
"8/1"
]
},
{
"id": "cet_117",
"desc": "72nd root of 128, step = generator of Miracle",
"stepCount": "36",
"steps": [
"116.66667",
"233.33333",
"350.00000",
"466.66667",
"583.33333",
"700.00000",
"816.66667",
"933.33333",
"1050.00000",
"1166.66667",
"1283.33333",
"1400.00000",
"1516.66667",
"1633.33333",
"1750.00000",
"1866.66667",
"1983.33333",
"2100.00000",
"2216.66667",
"2333.33333",
"2450.00000",
"2566.66667",
"2683.33333",
"2800.00000",
"2916.66667",
"3033.33333",
"3150.00000",
"3266.66667",
"3383.33333",
"3500.00000",
"3616.66667",
"3733.33333",
"3850.00000",
"3966.66667",
"4083.33333",
"4200.00000"
]
},
{
"id": "cet_117_a",
"desc": "6th root of 3/2",
"stepCount": "11",
"steps": [
"116.99250",
"233.98500",
"350.97750",
"467.97000",
"584.96250",
"3/2",
"818.94750",
"935.94000",
"1052.93250",
"1169.92500",
"1286.91750"
]
},
{
"id": "cet_118",
"desc": "16th root of 3. McLaren 'Microtonal Music', volume 1, track 7",
"stepCount": "16",
"steps": [
"118.87219",
"237.74438",
"356.61656",
"475.48875",
"594.36094",
"713.23313",
"832.10531",
"950.97750",
"1069.84969",
"1188.72188",
"1307.59406",
"1426.46625",
"1545.33844",
"1664.21063",
"1783.08281",
"3/1"
]
},
{
"id": "cet_119",
"desc": "7th root of phi",
"stepCount": "10",
"steps": [
"119.01290",
"238.02580",
"357.03870",
"476.05160",
"595.06450",
"714.07740",
"833.09030",
"952.10320",
"1071.11610",
"1190.12899"
]
},
{
"id": "cet_125",
"desc": "125 cents steps",
"stepCount": "10",
"steps": [
"125.00000",
"250.00000",
"375.00000",
"500.00000",
"625.00000",
"750.00000",
"875.00000",
"1000.00000",
"1125.00000",
"1250.00000"
]
},
{
"id": "cet_126",
"desc": "15th root of 3. McLaren 'Microtonal Music', volume 1, track 6",
"stepCount": "15",
"steps": [
"126.79700",
"253.59400",
"380.39100",
"507.18800",
"633.98500",
"760.78200",
"887.57900",
"1014.37600",
"1141.17300",
"1267.97000",
"1394.76700",
"1521.56400",
"1648.36100",
"1775.15800",
"3/1"
]
},
{
"id": "cet_126_a",
"desc": "19th root of 4",
"stepCount": "19",
"steps": [
"126.31579",
"252.63158",
"378.94737",
"505.26316",
"631.57895",
"757.89474",
"884.21053",
"1010.52632",
"1136.84211",
"1263.15789",
"1389.47368",
"1515.78947",
"1642.10526",
"1768.42105",
"1894.73684",
"2021.05263",
"2147.36842",
"2273.68421",
"4/1"
]
},
{
"id": "cet_126_b",
"desc": "22th root of 5. Close to every second step of 19-tET",
"stepCount": "22",
"steps": [
"126.65062",
"253.30125",
"379.95187",
"506.60249",
"633.25312",
"759.90374",
"886.55436",
"1013.20499",
"1139.85561",
"1266.50623",
"1393.15686",
"1519.80748",
"1646.45810",
"1773.10873",
"1899.75935",
"2026.40997",
"2153.06060",
"2279.71122",
"2406.36184",
"2533.01247",
"2659.66309",
"5/1"
]
},
{
"id": "cet_133",
"desc": "13th root of e",
"stepCount": "13",
"steps": [
"133.17185",
"266.34370",
"399.51555",
"532.68740",
"665.85925",
"799.03110",
"932.20295",
"1065.37480",
"1198.54665",
"1331.71850",
"1464.89035",
"1598.06220",
"1731.23405"
]
},
{
"id": "cet_139",
"desc": "20th root of 5, Hieronymus' tuning",
"stepCount": "20",
"steps": [
"139.31569",
"278.63137",
"417.94706",
"557.26274",
"696.57843",
"835.89411",
"975.20980",
"1114.52549",
"1253.84117",
"1393.15686",
"1532.47254",
"1671.78823",
"1811.10391",
"1950.41960",
"2089.73529",
"2229.05097",
"2368.36666",
"2507.68234",
"2646.99803",
"5/1"
]
},
{
"id": "cet_140",
"desc": "24th root of 7",
"stepCount": "24",
"steps": [
"140.36775",
"280.73549",
"421.10324",
"561.47098",
"701.83873",
"842.20648",
"982.57422",
"1122.94197",
"1263.30971",
"1403.67746",
"1544.04521",
"1684.41295",
"1824.78070",
"1965.14845",
"2105.51619",
"2245.88394",
"2386.25168",
"2526.61943",
"2666.98718",
"2807.35492",
"2947.72267",
"3088.09041",
"3228.45816",
"7/1"
]
},
{
"id": "cet_141",
"desc": "17th root of 4",
"stepCount": "17",
"steps": [
"141.17647",
"282.35294",
"423.52941",
"564.70588",
"705.88235",
"847.05882",
"988.23529",
"1129.41176",
"1270.58824",
"1411.76471",
"1552.94118",
"1694.11765",
"1835.29412",
"1976.47059",
"2117.64706",
"2258.82353",
"4/1"
]
},
{
"id": "cet_148",
"desc": "21th root of 6, Moreno's C-21",
"stepCount": "21",
"steps": [
"147.71214",
"295.42429",
"443.13643",
"590.84857",
"738.56071",
"886.27286",
"1033.98500",
"1181.69714",
"1329.40929",
"1477.12143",
"1624.83357",
"1772.54571",
"1920.25786",
"2067.97000",
"2215.68214",
"2363.39429",
"2511.10643",
"2658.81857",
"2806.53072",
"2954.24286",
"6/1"
]
},
{
"id": "cet_152",
"desc": "13th root of pi",
"stepCount": "13",
"steps": [
"152.44600",
"304.89200",
"457.33700",
"609.78300",
"762.22900",
"914.67500",
"1067.12100",
"1219.56600",
"1372.01200",
"1524.45800",
"1676.90400",
"1829.35000",
"1981.79600"
]
},
{
"id": "cet_156",
"desc": "9th root of 9/4",
"stepCount": "9",
"steps": [
"155.99000",
"311.98000",
"467.97000",
"623.96000",
"779.95000",
"935.94000",
"1091.93000",
"1247.92000",
"9/4"
]
},
{
"id": "cet_158",
"desc": "12th root of 3, Moreno's A-12, see dissertation \"Embedding Equal Pitch Spaces\"",
"stepCount": "12",
"steps": [
"158.49625",
"316.99250",
"475.48875",
"633.98500",
"792.48125",
"950.97750",
"1109.47375",
"1267.97000",
"1426.46625",
"1584.96250",
"1743.45875",
"3/1"
]
},
{
"id": "cet_159",
"desc": "4e-th root of e. e-th root of e is highest x-th root of x",
"stepCount": "8",
"steps": [
"159.22135",
"318.44271",
"477.66406",
"636.88541",
"796.10677",
"955.32812",
"1114.54948",
"1273.77083"
]
},
{
"id": "cet_160",
"desc": "15th root of 4, Rudolf Escher in \"The Long Christmas Dinner\"(1960)",
"stepCount": "15",
"steps": [
"160.00000",
"320.00000",
"480.00000",
"640.00000",
"800.00000",
"960.00000",
"1120.00000",
"1280.00000",
"1440.00000",
"1600.00000",
"1760.00000",
"1920.00000",
"2080.00000",
"2240.00000",
"4/1"
]
},
{
"id": "cet_160_a",
"desc": "37th root of 31, McLaren 'Microtonal Music', volume 2, track 7",
"stepCount": "37",
"steps": [
"160.67664",
"321.35327",
"482.02991",
"642.70655",
"803.38319",
"964.05982",
"1124.73646",
"1285.41310",
"1446.08973",
"1606.76637",
"1767.44301",
"1928.11965",
"2088.79628",
"2249.47292",
"2410.14956",
"2570.82619",
"2731.50283",
"2892.17947",
"3052.85610",
"3213.53274",
"3374.20938",
"3534.88602",
"3695.56265",
"3856.23929",
"4016.91593",
"4177.59256",
"4338.26920",
"4498.94584",
"4659.62248",
"4820.29911",
"4980.97575",
"5141.65239",
"5302.32902",
"5463.00566",
"5623.68230",
"5784.35894",
"31/1"
]
},
{
"id": "cet_163",
"desc": "9th root of 7/3. Jeff Scott in \"Quiet Moonlight\"(2001)",
"stepCount": "9",
"steps": [
"162.98566",
"325.97131",
"488.95697",
"651.94262",
"814.92828",
"977.91394",
"1140.89959",
"1303.88525",
"7/3"
]
},
{
"id": "cet_163_a",
"desc": "5th root of 8/5",
"stepCount": "8",
"steps": [
"162.73726",
"325.47451",
"488.21177",
"650.94903",
"8/5",
"976.42354",
"1139.16080",
"1301.89806"
]
},
{
"id": "cet_166",
"desc": "3rd root of 4/3",
"stepCount": "3",
"steps": ["166.01500", "332.03000", "4/3"]
},
{
"id": "cet_167",
"desc": "5th root of phi",
"stepCount": "7",
"steps": [
"166.61806",
"333.23612",
"499.85418",
"666.47224",
"833.09030",
"999.70836",
"1166.32641"
]
},
{
"id": "cet_168",
"desc": "20th root of 7",
"stepCount": "20",
"steps": [
"168.44130",
"336.88259",
"505.32389",
"673.76518",
"842.20648",
"1010.64777",
"1179.08907",
"1347.53036",
"1515.97166",
"1684.41295",
"1852.85425",
"2021.29554",
"2189.73684",
"2358.17813",
"2526.61943",
"2695.06073",
"2863.50202",
"3031.94332",
"3200.38461",
"7/1"
]
},
{
"id": "cet_173",
"desc": "11th root of 3, Moreno's A-11",
"stepCount": "11",
"steps": [
"172.90500",
"345.81000",
"518.71500",
"691.62000",
"864.52500",
"1037.43000",
"1210.33500",
"1383.24000",
"1556.14500",
"1729.05000",
"3/1"
]
},
{
"id": "cet_175",
"desc": "175 cents steps (Georgian)",
"stepCount": "7",
"steps": [
"175.00000",
"350.00000",
"525.00000",
"700.00000",
"875.00000",
"1050.00000",
"1225.00000"
]
},
{
"id": "cet_175_a",
"desc": "4th root of 3/2",
"stepCount": "7",
"steps": [
"175.48875",
"350.97750",
"526.46625",
"3/2",
"877.44375",
"1052.93250",
"1228.42125"
]
},
{
"id": "cet_175_b",
"desc": "28th root of 7. McLaren 'Microtonal Music', volume 6, track 3",
"stepCount": "28",
"steps": [
"175.17698",
"350.35396",
"525.53094",
"700.70792",
"875.88489",
"1051.06187",
"1226.23885",
"1401.41583",
"1576.59281",
"1751.76979",
"1926.94677",
"2102.12375",
"2277.30073",
"2452.47770",
"2627.65468",
"2802.83166",
"2978.00864",
"3153.18562",
"3328.36260",
"3503.53958",
"3678.71656",
"3853.89354",
"4029.07051",
"4204.24749",
"4379.42447",
"4554.60145",
"4729.77843",
"17/1"
]
},
{
"id": "cet_178",
"desc": "27th root of 16",
"stepCount": "27",
"steps": [
"177.77778",
"355.55556",
"533.33333",
"711.11111",
"888.88889",
"1066.66667",
"1244.44444",
"1422.22222",
"1600.00000",
"1777.77778",
"1955.55556",
"2133.33333",
"2311.11111",
"2488.88889",
"2666.66667",
"2844.44444",
"3022.22222",
"3200.00000",
"3377.77778",
"3555.55556",
"3733.33333",
"3911.11111",
"4088.88889",
"4266.66667",
"4444.44444",
"4622.22222",
"16/1"
]
},
{
"id": "cet_181",
"desc": "6.625 tET. The 16/3 is the so-called Kidjel Ratio promoted by Maurice Kidjel in 1958",
"stepCount": "16",
"steps": [
"181.12781",
"362.25562",
"543.38344",
"724.51125",
"905.63906",
"1086.76687",
"1267.89469",
"1449.02250",
"1630.15031",
"1811.27812",
"1992.40594",
"2173.53375",
"2354.66156",
"2535.78937",
"2716.91719",
"16/3"
]
},
{
"id": "cet_182",
"desc": "17th root of 6, Moreno's C-17",
"stepCount": "17",
"steps": [
"182.46794",
"364.93588",
"547.40382",
"729.87176",
"912.33971",
"1094.80765",
"1277.27559",
"1459.74353",
"1642.21147",
"1824.67941",
"2007.14735",
"2189.61529",
"2372.08324",
"2554.55118",
"2737.01912",
"2919.48706",
"6/1"
]
},
{
"id": "cet_182_a",
"desc": "10/9 equal temperament",
"stepCount": "14",
"steps": [
"10/9",
"100/81",
"1000/729",
"10000/6561",
"100000/59049",
"1000000/531441",
"10000000/4782969",
"100000000/43046721",
"1000000000/387420489",
"10000000000/3486784401",
"100000000000/31381059609",
"1000000000000/282429536481",
"10000000000000/2541865828329",
"100000000000000/22876792454961"
]
},
{
"id": "cet_185",
"desc": "15th root of 5",
"stepCount": "15",
"steps": [
"185.75425",
"371.50850",
"557.26274",
"743.01699",
"928.77124",
"1114.52549",
"1300.27973",
"1486.03398",
"1671.78823",
"1857.54248",
"2043.29672",
"2229.05097",
"2414.80522",
"2600.55947",
"5/1"
]
},
{
"id": "cet_195",
"desc": "7th root of 11/5",
"stepCount": "7",
"steps": [
"195.00060",
"390.00121",
"585.00181",
"780.00242",
"975.00302",
"1170.00362",
"11/5"
]
},
{
"id": "cet_198",
"desc": "10th root of pi",
"stepCount": "10",
"steps": [
"198.17954",
"396.35907",
"594.53861",
"792.71814",
"990.89768",
"1189.07721",
"1387.25675",
"1585.43628",
"1783.61582",
"1981.79536"
]
},
{
"id": "cet_203",
"desc": "9/8 equal temperament",
"stepCount": "12",
"steps": [
"9/8",
"81/64",
"729/512",
"6561/4096",
"59049/32768",
"531441/262144",
"4782969/2097152",
"43046721/16777216",
"387420489/134217728",
"3486784401/1073741824",
"31381059609/8589934592",
"282429536481/68719476736"
]
},
{
"id": "cet_214",
"desc": "13th root of 5",
"stepCount": "13",
"steps": [
"214.33182",
"428.66365",
"642.99547",
"857.32730",
"1071.65912",
"1285.99094",
"1500.32277",
"1714.65459",
"1928.98642",
"2143.31824",
"2357.65007",
"2571.98189",
"5/1"
]
},
{
"id": "cet_222",
"desc": "14th root of 6, Moreno's C-14",
"stepCount": "14",
"steps": [
"221.56821",
"443.13643",
"664.70464",
"886.27286",
"1107.84107",
"1329.40929",
"1550.97750",
"1772.54571",
"1994.11393",
"2215.68214",
"2437.25036",
"2658.81857",
"2880.38679",
"6/1"
]
},
{
"id": "cet_227",
"desc": "square root of 13/10",
"stepCount": "2",
"steps": ["227.10697", "13/10"]
},
{
"id": "cet_231",
"desc": "8/7 equal temperament",
"stepCount": "11",
"steps": [
"8/7",
"64/49",
"512/343",
"4096/2401",
"32768/16807",
"262144/117649",
"2097152/823543",
"16777216/5764801",
"134217728/40353607",
"1073741824/282475249",
"8589934592/1977326743"
]
},
{
"id": "cet_233",
"desc": "21st root of 17, McLaren 'Microtonal Music', volume 2, track 15",
"stepCount": "21",
"steps": [
"233.56931",
"467.13861",
"700.70792",
"934.27722",
"1167.84653",
"1401.41583",
"1634.98514",
"1868.55444",
"2102.12375",
"2335.69305",
"2569.26236",
"2802.83166",
"3036.40097",
"3269.97027",
"3503.53958",
"3737.10888",
"3970.67819",
"4204.24749",
"4437.81680",
"4671.38610",
"17/1"
]
},
{
"id": "cet_258",
"desc": "12th root of 6, Moreno's C-12",
"stepCount": "12",
"steps": [
"258.49625",
"516.99250",
"775.48875",
"1033.98500",
"1292.48125",
"1550.97750",
"1809.47375",
"2067.97000",
"2326.46625",
"2584.96250",
"2843.45875",
"6/1"
]
},
{
"id": "chahargah",
"desc": "Chahargah in C",
"stepCount": "12",
"steps": [
"100.00000",
"140.00000",
"300.00000",
"386.00000",
"498.00000",
"590.00000",
"702.00000",
"800.00000",
"840.00000",
"1000.00000",
"1100.00000",
"2/1"
]
},
{
"id": "chahargah_2",
"desc": "Dastgah Chahargah in C, Mohammad Reza Gharib",
"stepCount": "7",
"steps": [
"140.00000",
"390.00000",
"498.00000",
"702.00000",
"840.00000",
"1100.00000",
"2/1"
]
},
{
"id": "chahargah_3",
"desc": "Iranian Chahargah, Julien J. Weiss",
"stepCount": "7",
"steps": ["13/12", "5/4", "4/3", "3/2", "13/8", "15/8", "2/1"]
},
{
"id": "chalmers_17",
"desc": "7-limit figurative scale, Chalmers '96 Adnexed S&H decads",
"stepCount": "17",
"steps": [
"36/35",
"35/32",
"9/8",
"6/5",
"5/4",
"9/7",
"21/16",
"36/25",
"72/49",
"3/2",
"49/32",
"25/16",
"12/7",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "chalmers_17_marvwoo",
"desc": "Marvel woo version of chalmers_17",
"stepCount": "17",
"steps": [
"49.41539",
"151.28207",
"200.69746",
"316.92773",
"383.74261",
"433.15800",
"468.20980",
"633.85547",
"665.61854",
"700.67034",
"735.72214",
"767.48522",
"933.13088",
"968.18268",
"1017.59808",
"1084.41295",
"1200.64322"
]
},
{
"id": "chalmers_19",
"desc": "7-limit figurative scale. Reversed S&H decads",
"stepCount": "19",
"steps": [
"36/35",
"10/9",
"9/8",
"7/6",
"6/5",
"9/7",
"4/3",
"49/36",
"25/18",
"36/25",
"72/49",
"3/2",
"14/9",
"5/3",
"12/7",
"16/9",
"9/5",
"35/18",
"2/1"
]
},
{
"id": "chalmers_csurd",
"desc": "Combined Surd Scale, combination of Surd and Inverted Surd, JHC, 26-6-97",
"stepCount": "15",
"steps": [
"75.90187",
"160.53817",
"256.34665",
"325.85509",
"366.90634",
"4/3",
"539.98536",
"660.01995",
"3/2",
"833.08148",
"874.14491",
"943.65335",
"1039.46183",
"1124.09813",
"2/1"
]
},
{
"id": "chalmers_isurd",
"desc": "Inverted Surd Scale, of the form 4/(SQRT(N)+1, JHC, 26-6-97",
"stepCount": "8",
"steps": [
"75.90187",
"160.53817",
"256.34665",
"366.90634",
"4/3",
"660.01995",
"874.14491",
"2/1"
]
},
{
"id": "chalmers_ji_1",
"desc": "Based loosely on Wronski's and similar JI scales, May 2, 1997.",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"4/3",
"17/12",
"3/2",
"19/12",
"5/3",
"57/32",
"15/8",
"2/1"
]
},
{
"id": "chalmers_ji_2",
"desc": "Based loosely on Wronski's and similar JI scales, May 2, 1997.",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"4/3",
"17/12",
"3/2",
"51/32",
"27/16",
"57/32",
"15/8",
"2/1"
]
},
{
"id": "chalmers_ji_3",
"desc": "15 16 17 18 19 20 21 on 1/1, 15-20 on 3/2, May 2, 1997. See other scales",
"stepCount": "12",
"steps": [
"16/15",
"17/15",
"6/5",
"19/15",
"4/3",
"7/5",
"3/2",
"8/5",
"17/10",
"9/5",
"19/10",
"2/1"
]
},
{
"id": "chalmers_ji_4",
"desc": "15 16 17 18 19 20 on 1/1, same on 4/3, + 16/15 on 16/9",
"stepCount": "12",
"steps": [
"16/15",
"17/15",
"6/5",
"19/15",
"4/3",
"64/45",
"68/45",
"8/5",
"76/45",
"16/9",
"256/135",
"2/1"
]
},
{
"id": "chalmers_surd",
"desc": "Surd Scale, Surds of the form (SQRT(N)+1)/2, JHC, 26-6-97",
"stepCount": "8",
"steps": [
"325.85509",
"539.98536",
"3/2",
"833.08148",
"943.65335",
"1039.46183",
"1124.09813",
"2/1"
]
},
{
"id": "chalmers_surd_2",
"desc": "Surd Scale, Surds of the form (SQRT(N)+1)/4",
"stepCount": "40",
"steps": [
"68.84785",
"131.88444",
"190.04384",
"244.04863",
"294.46971",
"341.76635",
"5/4",
"428.42236",
"468.35241",
"506.32393",
"542.52489",
"577.11709",
"610.24088",
"642.01879",
"672.55847",
"3/2",
"730.29280",
"757.64716",
"784.08555",
"809.66863",
"834.45119",
"858.48284",
"881.80870",
"904.46987",
"926.50396",
"947.94541",
"7/4",
"989.17461",
"1009.01845",
"1028.38235",
"1047.28941",
"1065.76109",
"1083.81735",
"1101.47681",
"1118.75684",
"1135.67369",
"1152.24258",
"1168.47780",
"1184.39273",
"2/1"
]
},
{
"id": "chalmers",
"desc": "Chalmers' 19-tone with more hexanies than Perrett's Tierce-Tone",
"stepCount": "19",
"steps": [
"21/20",
"16/15",
"9/8",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"35/24",
"3/2",
"63/40",
"8/5",
"5/3",
"7/4",
"9/5",
"28/15",
"63/32",
"2/1"
]
},
{
"id": "chalung",
"desc": "Tuning of chalung from Tasikmalaya, slendro-like. 1/1=185 Hz",
"stepCount": "11",
"steps": [
"391.91944",
"562.34225",
"692.57160",
"1048.51200",
"1213.98043",
"1569.38679",
"1772.45659",
"1984.19266",
"2253.61137",
"2413.98043",
"2776.93031"
]
},
{
"id": "chan_34",
"desc": "34 note hanson based circulating scale with 15 pure major thirds and 18 -1 brats",
"stepCount": "34",
"steps": [
"254754959781491/249729352508160",
"30071722855/28903860244",
"38421792648/36129825305",
"6759548793775/6243233812704",
"1081527807004/975505283235",
"14412856352274025/12786142848417792",
"576514254090961/499458705016320",
"991798286653/843680244960",
"960013575180847/799133928026112",
"30614793048041/24972935250816",
"5/4",
"638254280871377/499458705016320",
"150358614275/115615440976",
"48114756568/36129825305",
"1459280021371/1076419622880",
"270381951751/195101056647",
"60205443660021679/42620476161392640",
"576514254090961/399566964013056",
"30663265517723/20810779375680",
"4800067875904235/3196535712104448",
"21305517838327/13873852917120",
"25/16",
"8/5",
"50840497270643/31216169063520",
"12028689142/7225965061",
"424031442260527/249729352508160",
"1351909758755/780404226588",
"1727914373344/975505283235",
"2882571270454805/1598267856052224",
"230425355849681/124864676254080",
"24000339379521175/12786142848417792",
"960013575180847/499458705016320",
"412730869507/210920061240",
"2/1"
]
},
{
"id": "chargah_pentachord_7_limit",
"desc": "Chargah pentachord 150:162:189:200:225",
"stepCount": "4",
"steps": ["27/25", "63/50", "4/3", "3/2"]
},
{
"id": "chargah_tetrachord_7_limit",
"desc": "Chargah tetrachord 150:162:189:200",
"stepCount": "3",
"steps": ["27/25", "63/50", "4/3"]
},
{
"id": "chaumont",
"desc": "Lambert Chaumont organ temperament (1695), 1st interpretation",
"stepCount": "12",
"steps": [
"76.04900",
"193.15686",
"290.90905",
"5/4",
"503.42157",
"579.47057",
"696.57843",
"25/16",
"889.73529",
"997.16531",
"1082.89214",
"2/1"
]
},
{
"id": "chaumont_2",
"desc": "Lambert Chaumont organ temperament (1695), 2nd interpretation",
"stepCount": "12",
"steps": [
"83.57620",
"195.30749",
"289.83374",
"390.61497",
"502.34626",
"585.92246",
"697.65374",
"781.22994",
"892.96123",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "chimes_peck",
"desc": "Kris Peck, 9-tone windchime tuning. TL 7-3-2001",
"stepCount": "8",
"steps": ["5/4", "3/2", "7/4", "9/4", "11/4", "13/4", "15/4", "4/1"]
},
{
"id": "chimes",
"desc": "Heavenly Chimes",
"stepCount": "3",
"steps": ["32/29", "1/2", "16/29"]
},
{
"id": "chin_5",
"desc": "Chinese pentatonic from Zhou period",
"stepCount": "5",
"steps": ["9/8", "4/3", "3/2", "27/16", "2/1"]
},
{
"id": "chin_7",
"desc": "Chinese heptatonic scale and tritriadic of 64:81:96 triad",
"stepCount": "7",
"steps": ["9/8", "81/64", "4/3", "3/2", "27/16", "243/128", "2/1"]
},
{
"id": "chin_12",
"desc": "Chinese scale, 4th cent.",
"stepCount": "12",
"steps": [
"99.20000",
"199.50000",
"296.70000",
"398.00000",
"492.90000",
"595.20000",
"699.00000",
"790.90000",
"896.10000",
"984.90000",
"1091.40000",
"2/1"
]
},
{
"id": "chin_60",
"desc": "Chinese scale of fifths (the 60 l�)",
"stepCount": "60",
"steps": [
"3.61505",
"531441/524288",
"46.92002",
"70.38003",
"93.84004",
"2187/2048",
"1162261467/1073741824",
"160.60503",
"184.06504",
"9/8",
"207.52505",
"4782969/4194304",
"250.83002",
"274.29003",
"297.75004",
"19683/16384",
"341.05502",
"364.51503",
"387.97504",
"81/64",
"411.43505",
"43046721/33554432",
"454.74002",
"478.20003",
"501.66005",
"177147/131072",
"544.96502",
"568.42503",
"591.88504",
"729/512",
"615.34505",
"387420489/268435456",
"658.65003",
"682.11004",
"3/2",
"705.57005",
"1594323/1048576",
"748.87502",
"772.33503",
"795.79504",
"6561/4096",
"839.10002",
"862.56003",
"886.02004",
"27/16",
"909.48005",
"14348907/8388608",
"952.78502",
"976.24503",
"999.70504",
"59049/32768",
"1043.01002",
"1066.47003",
"1089.93004",
"243/128",
"1113.39005",
"129140163/67108864",
"1156.69503",
"1180.15504",
"2/1"
]
},
{
"id": "chin_bianzhong",
"desc": "Pitches of Bianzhong bells (Xinyang). 1/1=b, Liang Mingyue, 1975.",
"stepCount": "12",
"steps": [
"104.00000",
"308.00000",
"624.00000",
"820.00000",
"1012.00000",
"1144.00000",
"1329.00000",
"1515.00000",
"1857.00000",
"2039.00000",
"2231.00000",
"2674.00000"
]
},
{
"id": "chin_bianzhong_2_a",
"desc": "A-tones (GU) of 13 Xinyang bells (Ma Cheng-Yuan) 1/1=d#=619 Hz",
"stepCount": "12",
"steps": [
"147.00000",
"308.00000",
"612.00000",
"792.00000",
"931.00000",
"1092.00000",
"1326.00000",
"1581.00000",
"1693.00000",
"2068.00000",
"2252.00000",
"2598.00000"
]
},
{
"id": "chin_bianzhong_2_b",
"desc": "B-tones (SUI) of 13 Xinyang bells (Ma Cheng-Yuan) 1/1=b+=506.6 Hz",
"stepCount": "12",
"steps": [
"114.98540",
"308.99317",
"624.99652",
"812.98131",
"1009.98545",
"1138.97957",
"1323.94786",
"1506.01750",
"1852.96980",
"2039.00232",
"2206.96993",
"2658.99308"
]
},
{
"id": "chin_bianzhong_3",
"desc": "A and B-tones of 13 Xinyang bells (Ma Cheng-Yuan) abs. pitches wrt middle-C",
"stepCount": "26",
"steps": [
"1150.00000",
"1262.00000",
"1460.00000",
"1491.00000",
"1638.00000",
"1776.00000",
"1799.00000",
"1962.00000",
"2103.00000",
"2160.00000",
"2283.00000",
"2290.00000",
"2422.00000",
"2474.00000",
"2583.00000",
"2656.00000",
"2817.00000",
"3004.00000",
"3072.00000",
"3184.00000",
"3188.00000",
"3357.00000",
"3559.00000",
"3743.00000",
"3810.00000",
"4089.00000"
]
},
{
"id": "chin_bronze",
"desc": "Scale found on ancient Chinese bronze instrument 3rd c.BC & \"Scholar's Lute\"",
"stepCount": "7",
"steps": ["8/7", "6/5", "5/4", "4/3", "3/2", "5/3", "2/1"]
},
{
"id": "chin_chime",
"desc": "Pitches of 12 stone chimes, F. Kuttner, 1951, ROMA Toronto. 1/1=b4",
"stepCount": "12",
"steps": [
"88.00000",
"550.50000",
"790.50000",
"1370.50000",
"1660.50000",
"1827.00000",
"1991.50000",
"2201.50000",
"2207.00000",
"2396.50000",
"2484.00000",
"2898.00000"
]
},
{
"id": "chin_ching",
"desc": "Scale of Ching Fang, c.45 BC. Pyth.steps 0 1 2 3 4 5 47 48 49 50 51 52 53",
"stepCount": "12",
"steps": [
"93.84004",
"9/8",
"297.75004",
"81/64",
"501.66005",
"591.88504",
"3/2",
"795.79504",
"27/16",
"999.70504",
"243/128",
"1203.61505"
]
},
{
"id": "chin_di",
"desc": "Chinese di scale",
"stepCount": "6",
"steps": [
"229.46929",
"329.97080",
"555.03167",
"777.52793",
"875.24684",
"1213.57835"
]
},
{
"id": "chin_di_2",
"desc": "Observed tuning from Chinese flute dizi, Helmholtz/Ellis p. 518, nr.103",
"stepCount": "7",
"steps": [
"178.00000",
"339.00000",
"448.00000",
"662.00000",
"888.00000",
"1103.00000",
"1196.00000"
]
},
{
"id": "chin_huang",
"desc": "Huang Zhong qin tuning",
"stepCount": "6",
"steps": ["81/64", "3/2", "27/16", "2/1", "9/4", "81/32"]
},
{
"id": "chin_liu_an",
"desc": "Scale of Liu An, in: \"Huai Nan Tzu\", c.122 BC, 1st known corr. to Pyth. scale",
"stepCount": "11",
"steps": [
"81/76",
"9/8",
"81/68",
"81/64",
"27/20",
"27/19",
"3/2",
"27/17",
"27/16",
"9/5",
"27/14"
]
},
{
"id": "chin_lu",
"desc": "Chinese L� scale by Huai Nan zi, Han era. P�re Amiot 1780, Kurt Reinhard",
"stepCount": "12",
"steps": [
"18/17",
"9/8",
"6/5",
"54/43",
"4/3",
"27/19",
"3/2",
"27/17",
"27/16",
"9/5",
"36/19",
"2/1"
]
},
{
"id": "chin_lu_2",
"desc": "Chinese L� (Lushi chunqiu, by Lu Buwei). Mingyue: Music of the billion, p.67",
"stepCount": "12",
"steps": [
"2187/2048",
"9/8",
"19683/16384",
"81/64",
"177147/131072",
"729/512",
"3/2",
"6561/4096",
"27/16",
"59049/32768",
"243/128",
"2/1"
]
},
{
"id": "chin_lu_3",
"desc": "Chinese L� scale by Ho Ch'�ng-T'ien, reported in Sung Shu (500 AD)",
"stepCount": "12",
"steps": [
"101.00000",
"200.00000",
"297.00000",
"398.00000",
"493.00000",
"596.00000",
"699.00000",
"791.00000",
"897.00000",
"985.00000",
"1092.00000",
"2/1"
]
},
{
"id": "chin_lu_3_a",
"desc": "Chinese L� scale by Ho Ch'�ng-T'ien, calc. basis is \"big number\"177147",
"stepCount": "12",
"steps": [
"17714700/16727831",
"2952450/2631019",
"590490/497483",
"1476225/1173019",
"708588/533029",
"177147/125686",
"708588/473185",
"885735/560906",
"1771470/1055723",
"8857350/5014657",
"177147/94357",
"2/1"
]
},
{
"id": "chin_lu_4",
"desc": "Chinese L� \"749-Temperament\"",
"stepCount": "12",
"steps": [
"97.51604",
"561001/500000",
"296.80634",
"398.58059",
"496.09663",
"597.87089",
"749/500",
"797.16119",
"420189749/250000000",
"996.45149",
"1098.22574",
"2/1"
]
},
{
"id": "chin_lu_5",
"desc": "Chinese L� scale by Ch'ien Lo-Chih, c.450 AD Pyth.steps 0 154 255 103 204 etc.",
"stepCount": "12",
"steps": [
"101.07013",
"198.52522",
"301.36509",
"398.82018",
"499.89031",
"599.11513",
"700.18527",
"799.41009",
"900.48022",
"999.70504",
"1100.77518",
"1198.23000"
]
},
{
"id": "chin_lusheng",
"desc": "Observed tuning of a small Lusheng, 1/1=d, OdC '97",
"stepCount": "5",
"steps": ["329.00000", "498.00000", "688.00000", "1003.00000", "1191.00000"]
},
{
"id": "chin_pan",
"desc": "Pan Huai-su pure Pythagorean system, in: Sin-Yan Shen, 1991",
"stepCount": "23",
"steps": [
"256/243",
"2187/2048",
"65536/59049",
"9/8",
"32/27",
"8192/6561",
"81/64",
"2097152/1594323",
"4/3",
"1024/729",
"729/512",
"262144/177147",
"3/2",
"128/81",
"6561/4096",
"32768/19683",
"27/16",
"8388608/4782969",
"16/9",
"4096/2187",
"243/128",
"1048576/531441",
"2/1"
]
},
{
"id": "chin_pipa",
"desc": "Observed tuning from Chinese balloon lute p'i-p'a, Helmholtz/Ellis p. 518, nr.109",
"stepCount": "5",
"steps": ["145.00000", "351.00000", "647.00000", "874.00000", "1195.00000"]
},
{
"id": "chin_sheng",
"desc": "Observed tuning from Chinese sheng or mouth organ, Helmholtz/Ellis p. 518, nr.105",
"stepCount": "7",
"steps": [
"210.00000",
"338.00000",
"498.00000",
"715.00000",
"908.00000",
"1040.00000",
"1199.00000"
]
},
{
"id": "chin_shierlu",
"desc": "Old Chinese L� scale, from http://en.wikipedia.org/wiki/Shi_Er_L%C3%BC",
"stepCount": "12",
"steps": [
"2187/2048 ! * &#22823;&#21525; (D� L&#474;) ..... 3^7/2^11",
"9/8 ! * &#22826;&#31751; (T�i C�).... 3^2/2^3",
"1968/1683 ! *&#22841;&#38047;(Ji�Zh&#333;ng)41*3*2^4/17/11/3^2 41-limit",
"81/64 ! * &#22993;&#27927; (G&#363; Xi&#462;n) .... 3^4/2^5",
"1771/1311 ! *&#20013;&#21525;(Zh�ngL&#474;) .. 23*11*7/23*19*3=77/57=",
"729/512 ! * &#34148;&#23486; (Ru� B&#299;n). 3^6/2^9=(9/8)^3 tritone",
"3/2 ! * &#26519;&#38047; (L�n Zh&#333;ng)... 5th",
"6561/4096 ! * &#22839;&#21017; (Y� Z�) ...... 3^8/2^12",
"27/16 ! * &#21335;&#21525; (N�n L&#474;) .... 3^3/2^4",
"5905/3277 ! * &#26080;&#23556; (W� Y�)....1181*5/113/29 1181-limit",
"243/128 ! * &#24212;&#38047; (Y�ng Zh&#333;ng) .. 3^5/2^7",
"2/1"
]
},
{
"id": "chin_sientsu",
"desc": "Observed tuning from Chinese tamboura sienzi, Helmholtz/Ellis p. 518, nr.108",
"stepCount": "5",
"steps": ["189.00000", "386.00000", "702.00000", "893.00000", "2/1"]
},
{
"id": "chin_sona",
"desc": "Observed tuning from Chinese oboe (so-na), Helmholtz/Ellis p. 518, nr.104",
"stepCount": "7",
"steps": [
"145.00000",
"297.00000",
"440.00000",
"637.00000",
"813.00000",
"1014.00000",
"1216.00000"
]
},
{
"id": "chin_wang_po",
"desc": "Scale of Wang Po, 958 AD. H. Pischner: Musik in China, Berlin, 1955, p.20",
"stepCount": "7",
"steps": [
"9/8",
"403.22751",
"609.26340",
"3/2",
"903.70231",
"1106.39699",
"1180.87015"
]
},
{
"id": "chin_yangqin",
"desc": "Observed tuning from Chinese dulcimer yangqin, Helmholtz/Ellis p. 518, nr.107",
"stepCount": "7",
"steps": [
"169.00000",
"274.00000",
"491.00000",
"661.00000",
"878.00000",
"996.00000",
"1198.00000"
]
},
{
"id": "chin_yunlo",
"desc": "Observed tuning from Chinese gong-chime (y�n-lo), Helmholtz/Ellis p. 518, nr.106",
"stepCount": "7",
"steps": [
"169.00000",
"367.00000",
"586.00000",
"674.00000",
"775.00000",
"1062.00000",
"1208.00000"
]
},
{
"id": "chopsticks",
"desc": "Symmetrical non-octave MOS, subset of 15-tET",
"stepCount": "10",
"steps": [
"320.00000",
"480.00000",
"800.00000",
"960.00000",
"1280.00000",
"1440.00000",
"1760.00000",
"1920.00000",
"2240.00000",
"4/1"
]
},
{
"id": "choquel",
"desc": "Choquel/Barbour/Marpurg?",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"5/3",
"20/11",
"15/8",
"2/1"
]
},
{
"id": "chordal",
"desc": "Chordal Notes subharmonic and harmonic",
"stepCount": "40",
"steps": [
"3/2",
"5/4",
"7/4",
"9/4",
"11/4",
"13/4",
"15/4",
"15/4",
"15/8",
"17/8",
"19/8",
"19/16",
"2/1",
"4/3",
"8/5",
"8/7",
"16/9",
"16/11",
"16/13",
"16/15",
"7/3",
"7/2",
"10/3",
"8/3",
"5/2",
"12/5",
"12/7",
"11/9",
"13/9",
"17/10",
"17/5",
"9/7",
"9/8",
"16/9",
"11/7",
"7/6",
"7/5",
"10/7",
"6/5",
"9/5"
]
},
{
"id": "chrom_new",
"desc": "New Chromatic genus 4.5 + 9 + 16.5",
"stepCount": "7",
"steps": [
"75.00000",
"225.00000",
"500.00000",
"700.00000",
"775.00000",
"925.00000",
"2/1"
]
},
{
"id": "chrom_new_2",
"desc": "New Chromatic genus 14/3 + 28/3 + 16 parts",
"stepCount": "7",
"steps": [
"77.77778",
"233.33333",
"500.00000",
"700.00000",
"777.77778",
"933.33333",
"2/1"
]
},
{
"id": "chrom_soft",
"desc": "100/81 Chromatic. This genus is a good approximation to the soft chromatic",
"stepCount": "7",
"steps": ["27/26", "27/25", "4/3", "3/2", "81/52", "81/50", "2/1"]
},
{
"id": "chrom_soft_2",
"desc": "1:2 Soft Chromatic",
"stepCount": "7",
"steps": [
"44.44444",
"133.33333",
"500.00000",
"700.00000",
"744.44444",
"833.33333",
"2/1"
]
},
{
"id": "chrom_soft_3",
"desc": "Soft chromatic genus from Kathleen Schlesinger's modified Mixolydian Harmonia",
"stepCount": "7",
"steps": ["28/27", "14/13", "4/3", "3/2", "14/9", "21/13", "2/1"]
},
{
"id": "chrom_15_inv",
"desc": "Inverted Chromatic Tonos-15 Harmonia",
"stepCount": "7",
"steps": ["6/5", "19/15", "4/3", "22/15", "26/15", "28/15", "2/1"]
},
{
"id": "chrom_15_inv_2",
"desc": "A harmonic form of the Chromatic Tonos-15 inverted",
"stepCount": "7",
"steps": ["16/15", "17/15", "4/3", "22/15", "23/15", "8/5", "2/1"]
},
{
"id": "chrom_15",
"desc": "Tonos-15 Chromatic",
"stepCount": "7",
"steps": ["15/14", "15/13", "15/11", "3/2", "30/19", "5/3", "2/1"]
},
{
"id": "chrom_17_con",
"desc": "Conjunct Tonos-17 Chromatic",
"stepCount": "7",
"steps": ["17/16", "17/15", "17/12", "34/23", "17/11", "17/9", "2/1"]
},
{
"id": "chrom_17",
"desc": "Tonos-17 Chromatic",
"stepCount": "7",
"steps": ["17/16", "17/15", "17/12", "17/11", "34/21", "17/10", "2/1"]
},
{
"id": "chrom_19_con",
"desc": "Conjunct Tonos-19 Chromatic",
"stepCount": "7",
"steps": ["19/18", "19/17", "19/14", "38/27", "19/13", "19/11", "2/1"]
},
{
"id": "chrom_19",
"desc": "Tonos-19 Chromatic",
"stepCount": "7",
"steps": ["19/18", "19/17", "19/14", "19/13", "38/25", "19/12", "2/1"]
},
{
"id": "chrom_21_inv",
"desc": "Inverted Chromatic Tonos-21 Harmonia",
"stepCount": "7",
"steps": ["26/21", "9/7", "4/3", "32/21", "38/21", "40/21", "2/1"]
},
{
"id": "chrom_21_inv_2",
"desc": "Inverted harmonic form of the Chromatic Tonos-21",
"stepCount": "7",
"steps": ["16/15", "8/7", "4/3", "32/21", "34/21", "12/7", "2/1"]
},
{
"id": "chrom_21",
"desc": "Tonos-21 Chromatic",
"stepCount": "7",
"steps": ["21/20", "21/19", "21/16", "3/2", "14/9", "21/13", "2/1"]
},
{
"id": "chrom_23_con",
"desc": "Conjunct Tonos-23 Chromatic",
"stepCount": "7",
"steps": ["23/22", "23/21", "23/18", "23/17", "23/16", "23/13", "2/1"]
},
{
"id": "chrom_23",
"desc": "Tonos-23 Chromatic",
"stepCount": "7",
"steps": ["23/22", "23/21", "23/18", "23/16", "23/15", "23/14", "2/1"]
},
{
"id": "chrom_25_con",
"desc": "Conjunct Tonos-25 Chromatic",
"stepCount": "7",
"steps": ["50/47", "25/22", "25/18", "25/17", "25/16", "25/13", "2/1"]
},
{
"id": "chrom_25",
"desc": "Tonos-25 Chromatic",
"stepCount": "7",
"steps": ["50/47", "25/22", "25/18", "25/16", "5/3", "25/14", "2/1"]
},
{
"id": "chrom_27_inv",
"desc": "Inverted Chromatic Tonos-27 Harmonia",
"stepCount": "7",
"steps": ["32/27", "34/27", "4/3", "40/27", "16/9", "17/9", "2/1"]
},
{
"id": "chrom_27_inv_2",
"desc": "Inverted harmonic form of the Chromatic Tonos-27",
"stepCount": "7",
"steps": ["28/27", "29/27", "4/3", "40/27", "14/9", "5/3", "2/1"]
},
{
"id": "chrom_27",
"desc": "Tonos-27 Chromatic",
"stepCount": "7",
"steps": ["18/17", "9/8", "27/20", "3/2", "27/17", "27/16", "2/1"]
},
{
"id": "chrom_29_con",
"desc": "Conjunct Tonos-29 Chromatic",
"stepCount": "7",
"steps": ["29/28", "29/27", "29/22", "29/21", "29/20", "29/16", "2/1"]
},
{
"id": "chrom_29",
"desc": "Tonos-29 Chromatic",
"stepCount": "7",
"steps": ["29/28", "29/27", "29/22", "29/20", "29/19", "29/18", "2/1"]
},
{
"id": "chrom_31_con",
"desc": "Conjunct Tonos-31 Chromatic",
"stepCount": "8",
"steps": [
"31/29",
"31/27",
"31/24",
"31/23",
"31/22",
"31/21",
"31/18",
"2/1"
]
},
{
"id": "chrom_31",
"desc": "Tonos-31 Chromatic. Tone 24 alternates with 23 as MESE or A",
"stepCount": "8",
"steps": [
"31/29",
"31/27",
"31/24",
"31/23",
"31/22",
"31/21",
"31/20",
"2/1"
]
},
{
"id": "chrom_33_con",
"desc": "Conjunct Tonos-33 Chromatic",
"stepCount": "7",
"steps": ["33/31", "33/29", "11/8", "33/23", "3/2", "11/6", "2/1"]
},
{
"id": "chrom_33",
"desc": "Tonos-33 Chromatic. A variant is 66 63 60 48",
"stepCount": "7",
"steps": ["33/31", "33/29", "11/8", "3/2", "11/7", "33/20", "2/1"]
},
{
"id": "chrys_diat_1st_ji",
"desc": "Chrysanthos JI Diatonic and 1st Byzantine Liturgical mode",
"stepCount": "7",
"steps": ["12/11", "32/27", "4/3", "3/2", "18/11", "16/9", "2/1"]
},
{
"id": "chrys_diatenh_var_ji",
"desc": "JI interpretation of Chrysanthos Diatonic-Enharmonic Byzantine mode",
"stepCount": "7",
"steps": ["12/11", "32/27", "4/3", "3/2", "14/9", "16/9", "2/1"]
},
{
"id": "chrys_enhdiat_var_ji",
"desc": "JI interpretation of Chrysanthos Enharmonic-Diatonic Byzantine Mode",
"stepCount": "7",
"steps": ["8/7", "9/7", "4/3", "3/2", "18/11", "16/9", "2/1"]
},
{
"id": "cifariello",
"desc": "F. Cifariello Ciardi, ICMC 86 Proc. 15-tone 5-limit tuning",
"stepCount": "15",
"steps": [
"16/15",
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"25/18",
"36/25",
"3/2",
"8/5",
"5/3",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "circ_5120",
"desc": "Circle of seven minor, six major, and one subminor thirds in 531-tET",
"stepCount": "14",
"steps": [
"24.858757",
"205.649718",
"230.508475",
"316.384181",
"411.299435",
"522.033898",
"616.949153",
"702.824859",
"727.683616",
"908.474576",
"933.333333",
"1019.209040",
"1114.124294",
"2/1"
]
},
{
"id": "circb_22",
"desc": "circulating scale from pipedum_22c in 50/49 (-1,5) tuning; approximate pajara",
"stepCount": "22",
"steps": [
"56.609169",
"108.337097",
"165.798940",
"217.526867",
"274.136036",
"325.863964",
"382.473133",
"434.201060",
"491.662903",
"543.390831",
"600.000000",
"656.609169",
"708.337097",
"765.798940",
"817.526867",
"874.136036",
"925.863964",
"982.473133",
"1034.201060",
"1091.662903",
"1143.390831",
"2/1"
]
},
{
"id": "circle_31",
"desc": "Approximate 31-tET with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)",
"stepCount": "31",
"steps": [
"39.04564",
"76.04900",
"117.10786",
"153.61881",
"193.15686",
"233.21637",
"269.20586",
"310.26471",
"347.78954",
"5/4",
"427.38710",
"462.36271",
"503.42157",
"541.96027",
"579.47057",
"620.52943",
"656.53344",
"696.57843",
"736.13100",
"25/16",
"8/5",
"850.70417",
"889.73529",
"930.30173",
"965.78428",
"1006.84314",
"1044.87491",
"1082.89214",
"1123.95100",
"1159.44808",
"2/1"
]
},
{
"id": "circls_12",
"desc": "Least squares circulating temperament",
"stepCount": "12",
"steps": [
"79.70961",
"198.27445",
"285.43857",
"390.29238",
"495.14619",
"582.31031",
"700.87514",
"780.58476",
"894.97858",
"990.29238",
"1085.60618",
"2/1"
]
},
{
"id": "circos",
"desc": "[1, 3] weight range weighted least squares circulating temperament",
"stepCount": "12",
"steps": [
"89.617502",
"195.633226",
"300.984164",
"391.528643",
"501.698852",
"587.325482",
"697.824592",
"796.007518",
"893.677492",
"1002.402613",
"1088.884819",
"2/1"
]
},
{
"id": "ckring_9",
"desc": "Double-tie circular mirroring with common pivot of 3:5:7:9",
"stepCount": "13",
"steps": [
"10/9",
"7/6",
"6/5",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"5/3",
"12/7",
"9/5",
"2/1"
]
},
{
"id": "clampitt_phi",
"desc": "David Clampitt, phi+1 mod 3phi+2, from \"Pairwise Well-Formed Scales\", 1997",
"stepCount": "7",
"steps": [
"175.07764",
"350.15528",
"458.35921",
"633.43685",
"916.71842",
"1091.79607",
"2/1"
]
},
{
"id": "classr",
"desc": "Marvel projection to the 5-limit of class",
"stepCount": "12",
"steps": [
"135/128",
"1125/1024",
"6/5",
"5/4",
"675/512",
"45/32",
"3/2",
"25/16",
"27/16",
"225/128",
"15/8",
"2/1"
]
},
{
"id": "claudi_enigma",
"desc": "Claudi Meneghin's 11-limit JI Enigma theme scale",
"stepCount": "15",
"steps": [
"9/8",
"7/6",
"5/4",
"21/16",
"4/3",
"45/32",
"3/2",
"14/9",
"44/27",
"5/3",
"27/16",
"7/4",
"11/6",
"15/8",
"2/1"
]
},
{
"id": "clipper_81",
"desc": "Clipper(81/80), 5-limit, POTE tuning",
"stepCount": "9",
"steps": [
"118.80670",
"192.47732",
"311.28402",
"503.76134",
"696.23866",
"815.04536",
"888.71598",
"1007.52268",
"2/1"
]
},
{
"id": "clipper_99",
"desc": "Clipper(99/98), 2.3.7.11, POTE tuning",
"stepCount": "17",
"steps": [
"27.34889",
"73.52244",
"119.69599",
"227.00036",
"273.17391",
"319.34746",
"346.69635",
"500.17427",
"546.34782",
"573.69671",
"727.17463",
"773.34818",
"819.52173",
"972.99964",
"1000.34853",
"1046.52208",
"2/1"
]
},
{
"id": "clipper_100",
"desc": "Clipper(100/99), 2.3.5.11, POTE tuning",
"stepCount": "17",
"steps": [
"110.97925",
"174.16103",
"237.34280",
"348.32205",
"384.06751",
"495.04676",
"558.22853",
"606.02601",
"669.20779",
"732.38956",
"815.93249",
"879.11427",
"942.29604",
"990.09352",
"1053.27529",
"1164.25455",
"2/1"
]
},
{
"id": "clipper_105",
"desc": "Clipper(105/104), 2.3.5.7.13, POTE tuning",
"stepCount": "15",
"steps": [
"197.65902",
"238.18605",
"317.83053",
"340.47195",
"460.64346",
"556.01658",
"578.65800",
"698.82951",
"819.00102",
"841.64244",
"937.01556",
"1057.18707",
"1079.82849",
"1159.47297",
"2/1"
]
},
{
"id": "clipper_121",
"desc": "Clipper(121/120), 2.3.5.11, POTE tuning",
"stepCount": "11",
"steps": [
"228.21813",
"340.79562",
"385.96469",
"498.54218",
"543.71125",
"656.28875",
"884.50687",
"929.67595",
"1042.25344",
"1154.83093",
"2/1"
]
},
{
"id": "clipper_126",
"desc": "Clipper(126/125) 7-limit, POTE tuning",
"stepCount": "23",
"steps": [
"78.94254",
"108.65147",
"157.88508",
"187.59400",
"266.53654",
"311.15449",
"390.09702",
"419.80595",
"469.03956",
"498.74849",
"577.69103",
"656.63357",
"686.34249",
"701.25151",
"809.90298",
"859.13659",
"888.84551",
"918.55444",
"967.78805",
"1076.43952",
"1091.34853",
"1121.05746",
"2/1"
]
},
{
"id": "clipper_144",
"desc": "Clipper(144/143), 2.3.11.13, POTE tuning",
"stepCount": "11",
"steps": [
"144.91886",
"289.83773",
"349.44325",
"497.73781",
"642.65667",
"702.26219",
"787.57553",
"847.18106",
"992.09992",
"1140.39448",
"2/1"
]
},
{
"id": "clipper_169",
"desc": "Clipper(169/168), 2.3.7.13, POTE tuning",
"stepCount": "11",
"steps": [
"133.55330",
"267.10660",
"364.80229",
"498.35559",
"603.94872",
"631.90889",
"835.19771",
"863.15788",
"968.75101",
"1102.30431",
"2/1"
]
},
{
"id": "clipper_176",
"desc": "Clipper(176/175), 2.5.7.11, POTE tuning",
"stepCount": "11",
"steps": [
"161.87535",
"227.88872",
"389.76408",
"551.63943",
"617.65280",
"779.52815",
"810.23592",
"941.40351",
"1038.12465",
"1169.29223",
"2/1"
]
},
{
"id": "clipper_225",
"desc": "Clipper(225/224), 7-limit, POTE tuning",
"stepCount": "17",
"steps": [
"49.08706",
"115.95486",
"200.81497",
"231.90973",
"316.76984",
"383.63765",
"432.72470",
"548.67957",
"584.45262",
"615.54738",
"700.40749",
"816.36235",
"932.31722",
"1017.17733",
"1048.27208",
"1084.04514",
"2/1"
]
},
{
"id": "clipper_243",
"desc": "Clipper(243/242), 2.3.11, POTE tuning",
"stepCount": "17",
"steps": [
"94.74626",
"148.42388",
"202.10149",
"296.84776",
"350.52537",
"404.20299",
"498.94925",
"552.62687",
"647.37313",
"701.05075",
"795.79701",
"849.47463",
"903.15224",
"997.89851",
"1051.57612",
"1105.25374",
"2/1"
]
},
{
"id": "clipper_245",
"desc": "Clipper(245/243), 7-limit, POTE tuning",
"stepCount": "35",
"steps": [
"25.93232",
"55.35554",
"122.70610",
"152.12932",
"178.06164",
"207.48486",
"233.41718",
"262.84039",
"288.77271",
"359.61418",
"385.54650",
"411.47882",
"440.90203",
"470.32525",
"496.25757",
"522.18989",
"593.03136",
"618.96367",
"648.38689",
"674.31921",
"703.74243",
"729.67475",
"759.09797",
"826.44853",
"855.87175",
"881.80407",
"907.73639",
"937.15961",
"966.58282",
"992.51514",
"1089.28893",
"1115.22124",
"1144.64446",
"1174.06768",
"2/1"
]
},
{
"id": "clipper_385",
"desc": "Clipper(385/384), 11-limit, POTE tuning",
"stepCount": "15",
"steps": [
"101.60799",
"152.25568",
"265.75961",
"334.39669",
"385.04439",
"418.01529",
"498.54831",
"650.80399",
"803.05967",
"883.59270",
"916.56360",
"967.21129",
"1035.84838",
"1149.35231",
"2/1"
]
},
{
"id": "clipper_625",
"desc": "Clipper(625/624), 2.3.5.13, POTE tuning",
"stepCount": "19",
"steps": [
"26.09351",
"43.22463",
"69.31814",
"316.27365",
"342.36716",
"385.59179",
"428.81642",
"454.90993",
"701.86544",
"727.95895",
"745.09007",
"771.18358",
"814.40821",
"840.50172",
"883.72635",
"1087.45723",
"1130.68186",
"1156.77537",
"2/1"
]
},
{
"id": "clipper_640",
"desc": "Clipper(640/637), 2.5.7.13, POTE tuning",
"stepCount": "11",
"steps": [
"30.96384",
"100.32422",
"228.28077",
"259.24461",
"387.20115",
"456.56153",
"487.52538",
"615.48192",
"843.76269",
"1072.04346",
"2/1"
]
},
{
"id": "clipper_896",
"desc": "Clipper(896/891), 2.3.7.11, POTE tuning",
"stepCount": "19",
"steps": [
"22.45891",
"58.36883",
"80.82774",
"207.66891",
"230.12782",
"288.49664",
"346.86547",
"437.79672",
"496.16555",
"554.53437",
"576.99328",
"703.83445",
"726.29336",
"762.20328",
"784.66219",
"933.96227",
"992.33109",
"1050.69992",
"2/1"
]
},
{
"id": "clipper_1029",
"desc": "clipper(1029/1024), 2.3.7, POTE tuning",
"stepCount": "7",
"steps": [
"31.56229",
"233.68754",
"265.24983",
"498.93738",
"732.62492",
"966.31246",
"2/1"
]
},
{
"id": "clipper_2048",
"desc": "Clipper(2048/2025) 5-limit, POTE tuning",
"stepCount": "14",
"steps": [
"104.89817",
"180.40732",
"209.79634",
"314.69451",
"390.20366",
"495.10183",
"600.00000",
"704.89817",
"809.79634",
"885.30549",
"990.20366",
"1019.59268",
"1095.10183",
"2/1"
]
},
{
"id": "clipper_3125",
"desc": "Clipper(3125/3072), 5-limit, POTE tuning",
"stepCount": "11",
"steps": [
"59.82464",
"119.64929",
"380.05845",
"439.88310",
"499.70774",
"760.11690",
"819.94155",
"879.76619",
"939.59083",
"1140.17536",
"2/1"
]
},
{
"id": "clipper_3136",
"desc": "Clipper(3136/3125), 2.5.7, POTE tuning",
"stepCount": "17",
"steps": [
"37.36988",
"74.73975",
"193.77169",
"231.14156",
"350.17350",
"387.54337",
"424.91325",
"462.28313",
"581.31506",
"618.68494",
"775.08675",
"812.45663",
"849.82650",
"1006.22831",
"1043.59819",
"1162.63012",
"2/1"
]
},
{
"id": "clipper_4000",
"desc": "Clipper(4000/3993), 2.3.5.11, POTE tuning",
"stepCount": "31",
"steps": [
"54.32322",
"95.60807",
"124.67273",
"149.93129",
"165.95758",
"220.28080",
"261.56565",
"274.60402",
"315.88887",
"370.21209",
"386.23838",
"411.49694",
"440.56160",
"481.84645",
"536.16967",
"552.19596",
"647.80404",
"702.12725",
"772.47676",
"797.73532",
"813.76162",
"826.79998",
"868.08484",
"909.36969",
"922.40805",
"938.43435",
"963.69291",
"1034.04242",
"1088.36564",
"1183.97371",
"2/1"
]
},
{
"id": "clipper_5120",
"desc": "Clipper(5120/5103), 7-limit, POTE tuning",
"stepCount": "27",
"steps": [
"61.35474",
"85.85389",
"110.35304",
"205.65844",
"267.01318",
"291.51233",
"316.01148",
"377.36622",
"472.67163",
"497.17078",
"521.66993",
"583.02467",
"607.52382",
"678.33007",
"702.82922",
"764.18396",
"788.68311",
"813.18226",
"874.53700",
"908.48767",
"969.84241",
"994.34156",
"1018.84071",
"1080.19545",
"1104.69460",
"1175.50085",
"2/1"
]
},
{
"id": "clipper_6144",
"desc": "Clipper(6144/6125), 7-limit, POTE tuning",
"stepCount": "23",
"steps": [
"72.47746",
"110.23900",
"157.46768",
"229.94514",
"267.70668",
"302.42261",
"340.18415",
"387.41282",
"497.65182",
"544.88050",
"582.64204",
"617.35796",
"655.11950",
"727.59697",
"774.82564",
"812.58718",
"885.06464",
"970.05486",
"1004.77078",
"1042.53232",
"1080.29386",
"1115.00979",
"2/1"
]
},
{
"id": "clipper_65536",
"desc": "Clipper(65536/65219), 2.7.11, POTE tuning",
"stepCount": "11",
"steps": [
"93.48674",
"186.97348",
"323.37169",
"416.85843",
"553.25663",
"646.74337",
"740.23011",
"833.71685",
"970.11506",
"1063.60180",
"2/1"
]
},
{
"id": "clipper_65625",
"desc": "Clipper(65625/65536), 7-limit, POTE tuning",
"stepCount": "23",
"steps": [
"119.21337",
"161.39847",
"189.29818",
"231.48328",
"273.66838",
"315.85349",
"385.93830",
"428.12340",
"505.15167",
"547.33677",
"617.42158",
"659.60668",
"701.79179",
"771.87660",
"814.06170",
"891.08997",
"933.27507",
"1003.35988",
"1045.54498",
"1087.73009",
"1129.91519",
"1157.81490",
"2/1"
]
},
{
"id": "clipper_245242",
"desc": "Clipper(245/242), 2.5.7.11",
"stepCount": "17",
"steps": [
"87.18417",
"148.60607",
"172.01159",
"235.79025",
"384.39632",
"407.80184",
"471.58050",
"556.40791",
"643.59209",
"728.41950",
"792.19816",
"815.60368",
"964.20975",
"1027.98841",
"1051.39393",
"1112.81583",
"2/1"
]
},
{
"id": "cluster",
"desc": "13-tone 5-limit Tritriadic Cluster",
"stepCount": "13",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"4/3",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "cluster_6_c",
"desc": "Six-Tone Triadic Cluster 3:4:5",
"stepCount": "6",
"steps": ["10/9", "6/5", "4/3", "8/5", "5/3", "2/1"]
},
{
"id": "cluster_6_d",
"desc": "Six-Tone Triadic Cluster 3:5:4",
"stepCount": "6",
"steps": ["10/9", "5/4", "4/3", "3/2", "5/3", "2/1"]
},
{
"id": "cluster_6_e",
"desc": "Six-Tone Triadic Cluster 5:6:8",
"stepCount": "6",
"steps": ["6/5", "5/4", "3/2", "8/5", "48/25", "2/1"]
},
{
"id": "cluster_6_f",
"desc": "Six-Tone Triadic Cluster 5:8:6",
"stepCount": "6",
"steps": ["6/5", "4/3", "8/5", "5/3", "48/25", "2/1"]
},
{
"id": "cluster_6_g",
"desc": "Six-Tone Triadic Cluster 4:5:7, genus [577]",
"stepCount": "6",
"steps": ["35/32", "8/7", "5/4", "10/7", "7/4", "2/1"]
},
{
"id": "cluster_6_i",
"desc": "Six-Tone Triadic Cluster 5:6:7",
"stepCount": "6",
"steps": ["6/5", "7/5", "10/7", "42/25", "12/7", "2/1"]
},
{
"id": "cluster_6_j",
"desc": "Six-Tone Triadic Cluster 5:7:6",
"stepCount": "6",
"steps": ["7/6", "6/5", "7/5", "5/3", "42/25", "2/1"]
},
{
"id": "cluster_8_b",
"desc": "Eight-Tone Triadic Cluster 4:6:5, genus [3555]",
"stepCount": "8",
"steps": ["75/64", "6/5", "5/4", "3/2", "25/16", "8/5", "15/8", "2/1"]
},
{
"id": "cluster_8_c",
"desc": "Eight-Tone Triadic Cluster 3:4:5",
"stepCount": "8",
"steps": ["10/9", "6/5", "4/3", "25/18", "8/5", "5/3", "50/27", "2/1"]
},
{
"id": "cluster_8_d",
"desc": "Eight-Tone Triadic Cluster 3:5:4",
"stepCount": "8",
"steps": ["10/9", "5/4", "4/3", "40/27", "3/2", "5/3", "16/9", "2/1"]
},
{
"id": "cluster_8_e",
"desc": "Eight-Tone Triadic Cluster 5:6:8",
"stepCount": "8",
"steps": ["6/5", "5/4", "32/25", "3/2", "192/125", "8/5", "48/25", "2/1"]
},
{
"id": "cluster_8_f",
"desc": "Eight-Tone Triadic Cluster 5:8:6",
"stepCount": "8",
"steps": ["144/125", "6/5", "4/3", "36/25", "8/5", "5/3", "48/25", "2/1"]
},
{
"id": "cluster_8_h",
"desc": "Eight-Tone Triadic Cluster 4:7:5, genus [5557]",
"stepCount": "8",
"steps": ["35/32", "5/4", "175/128", "7/5", "25/16", "8/5", "7/4", "2/1"]
},
{
"id": "cluster_8_i",
"desc": "Eight-Tone Triadic Cluster 5:6:7",
"stepCount": "8",
"steps": ["147/125", "6/5", "7/5", "10/7", "42/25", "12/7", "49/25", "2/1"]
},
{
"id": "cluster_8_j",
"desc": "Eight-Tone Triadic Cluster 5:7:6",
"stepCount": "8",
"steps": ["126/125", "7/6", "6/5", "7/5", "36/25", "5/3", "42/25", "2/1"]
},
{
"id": "cohenf_11",
"desc": "Flynn Cohen, 7-limit scale of \"Rameau's nephew\"(1996)",
"stepCount": "11",
"steps": [
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"2/1"
]
},
{
"id": "coherent_49",
"desc": "Generator is the positive root of x^4 - x^2 - 1, Raph, Meta-Sidi, 72&121 temperament sqrtphi <30 35 38 39 ... |",
"stepCount": "49",
"steps": [
"30.17385",
"49.63544",
"79.80930",
"99.27089",
"129.44474",
"148.90633",
"179.08019",
"198.54178",
"228.71563",
"248.17722",
"278.35108",
"297.81267",
"317.27426",
"347.44811",
"366.90970",
"397.08356",
"416.54515",
"446.71900",
"466.18059",
"496.35445",
"515.81604",
"545.98989",
"565.45148",
"595.62533",
"615.08693",
"645.26078",
"664.72237",
"694.89622",
"714.35782",
"733.81941",
"763.99326",
"783.45485",
"813.62870",
"833.09030",
"863.26415",
"882.72574",
"912.89959",
"932.36119",
"962.53504",
"981.99663",
"1012.17048",
"1031.63207",
"1061.80593",
"1081.26752",
"1111.44137",
"1130.90296",
"1150.36456",
"1180.53841",
"2/1"
]
},
{
"id": "coleman_4",
"desc": "Coleman IV from Jim Coleman Sr.",
"stepCount": "12",
"steps": [
"98.00000",
"198.00000",
"298.00000",
"396.00000",
"500.00000",
"598.00000",
"698.00000",
"798.00000",
"898.00000",
"998.00000",
"1096.00000",
"2/1"
]
},
{
"id": "coleman_10",
"desc": "Coleman 10 (2001)",
"stepCount": "12",
"steps": [
"98.50000",
"198.50000",
"298.50000",
"397.00000",
"500.50000",
"597.50000",
"699.50000",
"798.50000",
"898.00000",
"999.50000",
"1096.50000",
"2/1"
]
},
{
"id": "c_scalamake_src_2_coleman_11_scl",
"desc": "Jim Coleman's XI piano temperament. TL 16 Mar 1999",
"stepCount": "12",
"steps": [
"97.00000",
"197.00000",
"297.00000",
"394.00000",
"501.00000",
"595.00000",
"699.00000",
"797.00000",
"896.00000",
"999.00000",
"1093.00000",
"2/1"
]
},
{
"id": "coleman_16",
"desc": "Balanced 16 from Jim Coleman Sr. (2001)",
"stepCount": "12",
"steps": [
"94.00000",
"196.00000",
"296.00000",
"392.00000",
"500.00000",
"592.00000",
"698.00000",
"795.00000",
"894.00000",
"998.00000",
"1092.00000",
"2/1"
]
},
{
"id": "coll_7",
"desc": "Seven note Collatz cycle scale, -17 starting point",
"stepCount": "7",
"steps": ["37/34", "41/34", "91/68", "25/17", "55/34", "61/34", "2/1"]
},
{
"id": "collangettes",
"desc": "d'Erlanger vol.5, p. 23. P�re Maurice Collangettes, 24 tone Arabic system",
"stepCount": "24",
"steps": [
"36/35",
"256/243",
"12/11",
"9/8",
"81/70",
"32/27",
"27/22",
"81/64",
"729/560",
"4/3",
"48/35",
"1024/729",
"16/11",
"3/2",
"54/35",
"128/81",
"18/11",
"27/16",
"243/140",
"16/9",
"64/35",
"243/128",
"64/33",
"2/1"
]
},
{
"id": "collapsar",
"desc": "An 11-limit patent val superwakalix",
"stepCount": "12",
"steps": [
"15/14",
"49/44",
"7/6",
"5/4",
"15/11",
"7/5",
"3/2",
"35/22",
"5/3",
"7/4",
"21/11",
"2/1"
]
},
{
"id": "colonna_1",
"desc": "Colonna's irregular Just Intonation no. 1 (1618)",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"85/72",
"5/4",
"4/3",
"25/18",
"3/2",
"55/36",
"5/3",
"85/48",
"15/8",
"2/1"
]
},
{
"id": "colonna_2",
"desc": "Colonna's irregular Just Intonation no. 2 (1618)",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "compton_48",
"desc": "Compton[48] 11-limit tweaked",
"stepCount": "48",
"steps": [
"50.02948",
"66.62693",
"83.40254",
"100.00000",
"150.02948",
"166.62693",
"183.40254",
"200.00000",
"250.02948",
"266.62693",
"283.40254",
"300.00000",
"350.02948",
"366.62693",
"383.40254",
"400.00000",
"450.02948",
"466.62693",
"483.40254",
"500.00000",
"550.02948",
"566.62693",
"583.40254",
"600.00000",
"650.02948",
"666.62693",
"683.40254",
"700.00000",
"750.02948",
"766.62693",
"783.40254",
"800.00000",
"850.02948",
"866.62693",
"883.40254",
"900.00000",
"950.02948",
"966.62693",
"983.40254",
"1000.00000",
"1050.02948",
"1066.62693",
"1083.40254",
"1100.00000",
"1150.02948",
"1166.62693",
"1183.40254",
"2/1"
]
},
{
"id": "concertina",
"desc": "English Concertina, Helmholtz/Ellis, p. 470",
"stepCount": "14",
"steps": [
"25/24",
"10/9",
"9/8",
"75/64",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"5/3",
"27/16",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "cons_5",
"desc": "Set of consonant 5-limit intervals within the octave",
"stepCount": "7",
"steps": ["6/5", "5/4", "4/3", "3/2", "8/5", "5/3", "9/5"]
},
{
"id": "cons_7",
"desc": "Set of consonant 7-limit intervals of tetrad 4:5:6:7 and inverse",
"stepCount": "10",
"steps": [
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4"
]
},
{
"id": "cons_7_a",
"desc": "Set of consonant 7-limit intervals, harmonic entropy minima",
"stepCount": "11",
"steps": [
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"7/4"
]
},
{
"id": "cons_8",
"desc": "Set of intervals with num + den <= 8 not exceeding 2/1",
"stepCount": "4",
"steps": ["4/3", "3/2", "5/3", "2/1"]
},
{
"id": "cons_9",
"desc": "Set of intervals with num + den <= 9 not exceeding 2/1",
"stepCount": "5",
"steps": ["5/4", "4/3", "3/2", "5/3", "2/1"]
},
{
"id": "cons_11",
"desc": "Set of intervals with num + den <= 11 not exceeding 2/1",
"stepCount": "7",
"steps": ["6/5", "5/4", "4/3", "3/2", "5/3", "7/4", "2/1"]
},
{
"id": "cons_12",
"desc": "Set of intervals with num + den <= 12 not exceeding 2/1",
"stepCount": "8",
"steps": ["6/5", "5/4", "4/3", "7/5", "3/2", "5/3", "7/4", "2/1"]
},
{
"id": "cons_13",
"desc": "Set of intervals with num + den <= 13 not exceeding 2/1",
"stepCount": "10",
"steps": [
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"2/1"
]
},
{
"id": "cons_14",
"desc": "Set of intervals with num + den <= 14 not exceeding 2/1",
"stepCount": "11",
"steps": [
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "cons_15",
"desc": "Set of intervals with num + den <= 15 not exceeding 2/1",
"stepCount": "12",
"steps": [
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "cons_16",
"desc": "Set of intervals with num + den <= 16 not exceeding 2/1",
"stepCount": "13",
"steps": [
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "cons_17",
"desc": "Set of intervals with num + den <= 17 not exceeding 2/1",
"stepCount": "16",
"steps": [
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "cons_18",
"desc": "Set of intervals with num + den <= 18 not exceeding 2/1",
"stepCount": "17",
"steps": [
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"11/7",
"8/5",
"5/3",
"7/4",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "cons_19",
"desc": "Set of intervals with num + den <= 19 not exceeding 2/1",
"stepCount": "20",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"11/7",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "cons_20",
"desc": "Set of intervals with num + den <= 20 not exceeding 2/1",
"stepCount": "22",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"11/7",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"11/6",
"13/7",
"2/1"
]
},
{
"id": "cons_21",
"desc": "Set of intervals with num + den <= 21 not exceeding 2/1",
"stepCount": "24",
"steps": [
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"11/7",
"8/5",
"13/8",
"5/3",
"12/7",
"7/4",
"9/5",
"11/6",
"13/7",
"2/1"
]
},
{
"id": "cont_frac_1",
"desc": "Continued fraction scale 1, see McLaren in Xenharmonikon 15, pp.33-38",
"stepCount": "14",
"steps": [
"17.586 cents",
"35.324 cents",
"144.501 cents",
"170.140 cents",
"262.822 cents",
"393.347 cents",
"466.181 cents",
"591.807 cents",
"692.773 cents",
"770.284 cents",
"818.652 cents",
"932.366 cents",
"1080.764 cents",
"1115.066 cents"
]
},
{
"id": "cont_frac_2",
"desc": "Continued fraction scale 2, see McLaren in Xenharmonikon 15, pp.33-38",
"stepCount": "15",
"steps": [
"46.003 cents",
"135.968 cents",
"165.005 cents",
"257.376 cents",
"272.981 cents",
"400.028 cents",
"422.067 cents",
"518.453 cents",
"646.633 cents",
"704.876 cents",
"845.880 cents",
"871.569 cents",
"1024.875 cents",
"1064.813 cents",
"1187.312 cents"
]
},
{
"id": "corner_7",
"desc": "Quadratic corner 7-limit. Chalmers '96",
"stepCount": "10",
"steps": [
"35/32",
"9/8",
"5/4",
"21/16",
"3/2",
"49/32",
"25/16",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "corner_9",
"desc": "First 9 harmonics of 5th through 9th harmonics",
"stepCount": "14",
"steps": [
"35/32",
"9/8",
"5/4",
"81/64",
"21/16",
"45/32",
"3/2",
"49/32",
"25/16",
"27/16",
"7/4",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "corner_11",
"desc": "Quadratic Corner 11-limit. Chalmers '96",
"stepCount": "15",
"steps": [
"33/32",
"35/32",
"9/8",
"77/64",
"5/4",
"21/16",
"11/8",
"3/2",
"49/32",
"25/16",
"55/32",
"7/4",
"15/8",
"121/64",
"2/1"
]
},
{
"id": "corner_13",
"desc": "Quadratic Corner 13-limit. Chalmers '96",
"stepCount": "21",
"steps": [
"65/64",
"33/32",
"35/32",
"143/128",
"9/8",
"77/64",
"39/32",
"5/4",
"21/16",
"169/128",
"11/8",
"91/64",
"3/2",
"49/32",
"25/16",
"13/8",
"55/32",
"7/4",
"15/8",
"121/64",
"2/1"
]
},
{
"id": "corner_17",
"desc": "Quadratic Corner 17-limit.",
"stepCount": "28",
"steps": [
"65/64",
"33/32",
"17/16",
"35/32",
"143/128",
"9/8",
"289/256",
"77/64",
"39/32",
"5/4",
"21/16",
"169/128",
"85/64",
"11/8",
"91/64",
"187/128",
"3/2",
"49/32",
"25/16",
"51/32",
"13/8",
"55/32",
"221/128",
"7/4",
"119/64",
"15/8",
"121/64",
"2/1"
]
},
{
"id": "corner_17_a",
"desc": "Quadratic Corner 17 odd limit.",
"stepCount": "42",
"steps": [
"65/64",
"33/32",
"135/128",
"17/16",
"35/32",
"143/128",
"9/8",
"289/256",
"75/64",
"153/128",
"77/64",
"39/32",
"5/4",
"81/64",
"165/128",
"21/16",
"169/128",
"85/64",
"11/8",
"45/32",
"91/64",
"187/128",
"3/2",
"195/128",
"49/32",
"99/64",
"25/16",
"51/32",
"13/8",
"105/64",
"27/16",
"55/32",
"221/128",
"7/4",
"225/128",
"117/64",
"119/64",
"15/8",
"121/64",
"63/32",
"255/128",
"2/1"
]
},
{
"id": "corners_7",
"desc": "Quadratic Corners 7-limit. Chalmers '96",
"stepCount": "19",
"steps": [
"16/15",
"35/32",
"9/8",
"8/7",
"5/4",
"32/25",
"64/49",
"21/16",
"4/3",
"3/2",
"32/21",
"49/32",
"25/16",
"8/5",
"7/4",
"16/9",
"64/35",
"15/8",
"2/1"
]
},
{
"id": "corners_11",
"desc": "Quadratic Corners 11-limit, John Chalmers (1996)",
"stepCount": "29",
"steps": [
"33/32",
"128/121",
"16/15",
"35/32",
"9/8",
"8/7",
"64/55",
"77/64",
"5/4",
"32/25",
"64/49",
"21/16",
"4/3",
"11/8",
"16/11",
"3/2",
"32/21",
"49/32",
"25/16",
"8/5",
"128/77",
"55/32",
"7/4",
"16/9",
"64/35",
"15/8",
"121/64",
"64/33",
"2/1"
]
},
{
"id": "corners_13",
"desc": "Quadratic Corners 13-limit. Chalmers '96",
"stepCount": "41",
"steps": [
"65/64",
"33/32",
"128/121",
"16/15",
"35/32",
"143/128",
"9/8",
"8/7",
"64/55",
"77/64",
"39/32",
"16/13",
"5/4",
"32/25",
"64/49",
"21/16",
"169/128",
"4/3",
"11/8",
"128/91",
"91/64",
"16/11",
"3/2",
"256/169",
"32/21",
"49/32",
"25/16",
"8/5",
"13/8",
"64/39",
"128/77",
"55/32",
"7/4",
"16/9",
"256/143",
"64/35",
"15/8",
"121/64",
"64/33",
"128/65",
"2/1"
]
},
{
"id": "corrette",
"desc": "Corrette temperament, modified 1/4-comma meantone",
"stepCount": "12",
"steps": [
"76.04900",
"193.15686",
"288.75843",
"5/4",
"503.42157",
"579.47057",
"696.57843",
"783.38100",
"889.73529",
"16/9",
"1082.89214",
"2/1"
]
},
{
"id": "corrette_2",
"desc": "Michel Corrette, modified meantone temperament (1753)",
"stepCount": "12",
"steps": [
"72.62999",
"192.18000",
"296.09000",
"8192/6561",
"503.91000",
"576.53999",
"696.09000",
"776.53999",
"888.26999",
"1000.00000",
"1080.44999",
"2/1"
]
},
{
"id": "corrette_3",
"desc": "Corrette's monochord (1753), also Marpurg 4 and Yamaha Pure Minor",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "coul_12",
"desc": "Scale 1 5/4 3/2 2 successively split largest intervals by smallest interval",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"6/5",
"5/4",
"125/96",
"25/18",
"3/2",
"25/16",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "coul_12_a",
"desc": "Scale 1 6/5 3/2 2 successively split largest intervals by smallest interval",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"6/5",
"5/4",
"4/3",
"36/25",
"3/2",
"25/16",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "coul_12_sup",
"desc": "Superparticular approximation to Pythagorean scale. Op de Coul, 2003",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"19/16",
"19/15",
"4/3",
"10/7",
"3/2",
"45/28",
"27/16",
"57/32",
"19/10",
"2/1"
]
},
{
"id": "coul_13",
"desc": "Symmetrical 13-tone 5-limit JI scale",
"stepCount": "13",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"25/18",
"36/25",
"3/2",
"8/5",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "coul_17_sup",
"desc": "Superparticular approximation to Pythagorean 17-tone scale. Op de Coul, 2003",
"stepCount": "17",
"steps": [
"19/18",
"16/15",
"152/135",
"32/27",
"6/5",
"19/15",
"4/3",
"38/27",
"64/45",
"608/405",
"128/81",
"8/5",
"76/45",
"16/9",
"9/5",
"19/10",
"2/1"
]
},
{
"id": "coul_20",
"desc": "Tuning for a 3-row symmetrical keyboard, Op de Coul (1989)",
"stepCount": "20",
"steps": [
"100.00000",
"131.28300",
"200.00000",
"268.71700",
"300.00000",
"400.00000",
"431.28300",
"500.00000",
"25/18",
"600.00000",
"700.00000",
"731.28300",
"800.00000",
"868.71700",
"900.00000",
"1000.00000",
"1031.28300",
"1100.00000",
"1168.71700",
"2/1"
]
},
{
"id": "coul_27",
"desc": "Symmetrical 27-tone 5-limit just system, 67108864/66430125 and 25/24",
"stepCount": "27",
"steps": [
"256/243",
"135/128",
"16/15",
"4096/3645",
"9/8",
"32/27",
"1215/1024",
"5/4",
"512/405",
"81/64",
"4/3",
"1024/729",
"45/32",
"64/45",
"729/512",
"3/2",
"128/81",
"405/256",
"8/5",
"2048/1215",
"27/16",
"16/9",
"3645/2048",
"15/8",
"256/135",
"243/128",
"2/1"
]
},
{
"id": "counterschismic",
"desc": "Counterschismic temperament, g=498.082318, 5-limit",
"stepCount": "53",
"steps": [
"23.01218",
"46.02437",
"69.03655",
"90.41159",
"113.42377",
"136.43596",
"159.44814",
"182.46033",
"203.83536",
"226.84755",
"249.85973",
"272.87192",
"294.24695",
"317.25914",
"340.27132",
"363.28351",
"386.29569",
"407.67073",
"430.68291",
"453.69510",
"476.70728",
"498.08232",
"521.09450",
"544.10669",
"567.11887",
"588.49391",
"611.50609",
"634.51828",
"657.53046",
"680.54264",
"701.91768",
"724.92987",
"747.94205",
"770.95423",
"792.32927",
"815.34146",
"838.35364",
"861.36582",
"884.37801",
"905.75305",
"928.76523",
"951.77741",
"974.78960",
"996.16464",
"1019.17682",
"1042.18900",
"1065.20119",
"1086.57623",
"1109.58841",
"1132.60059",
"1155.61278",
"1178.62496",
"2/1"
]
},
{
"id": "couperin_org",
"desc": "F. Couperin organ temperament (1690), from C. di Veroli, 1985",
"stepCount": "12",
"steps": [
"76.04900",
"193.15686",
"297.10287",
"5/4",
"503.42157",
"579.47057",
"696.57843",
"783.38057",
"889.73529",
"1006.84314",
"1082.89214",
"2/1"
]
},
{
"id": "couperin",
"desc": "Couperin modified meantone",
"stepCount": "12",
"steps": [
"76.04900",
"193.15686",
"289.73598",
"5/4",
"503.42157",
"579.47057",
"696.57843",
"25/16",
"889.73529",
"996.57878",
"1082.89214",
"2/1"
]
},
{
"id": "cpak_19_a",
"desc": "First 19-epimorphic ordered tetrad pack scale, Gene Ward Smith, TL 23-10-2005",
"stepCount": "19",
"steps": [
"21/20",
"15/14",
"9/8",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"63/40",
"8/5",
"5/3",
"7/4",
"9/5",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "cpak_19_b",
"desc": "Second 19-epimorphic ordered tetrad pack scale, Gene Ward Smith, TL 23-10-2005",
"stepCount": "19",
"steps": [
"21/20",
"15/14",
"9/8",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"63/40",
"8/5",
"5/3",
"7/4",
"25/14",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "cross_7",
"desc": "3-5-7 cross reduced by 2/1, quasi diatonic, similar to Zalzal's, Flynn Cohen",
"stepCount": "7",
"steps": ["8/7", "5/4", "4/3", "3/2", "8/5", "7/4", "2/1"]
},
{
"id": "cross_7_a",
"desc": "2-5-7 cross reduced by 3/1",
"stepCount": "7",
"steps": ["9/7", "3/2", "5/3", "9/5", "2/1", "7/3", "3/1"]
},
{
"id": "cross_72",
"desc": "double 3-5-7 cross reduced by 2/1",
"stepCount": "13",
"steps": [
"16/15",
"9/8",
"7/6",
"6/5",
"21/16",
"4/3",
"3/2",
"32/21",
"5/3",
"12/7",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "cross_2_5",
"desc": "double 3-5 cross reduced by 2/1",
"stepCount": "9",
"steps": ["16/15", "9/8", "6/5", "4/3", "3/2", "5/3", "16/9", "15/8", "2/1"]
},
{
"id": "cross_2_7",
"desc": "longer 3-5-7 cross reduced by 2/1",
"stepCount": "13",
"steps": [
"9/8",
"8/7",
"5/4",
"32/25",
"64/49",
"4/3",
"3/2",
"49/32",
"25/16",
"8/5",
"7/4",
"16/9",
"2/1"
]
},
{
"id": "cross_2",
"desc": "John Pusey's double 5-7 cross reduced by 3/1",
"stepCount": "9",
"steps": [
"27/25",
"35/27",
"7/5",
"5/3",
"9/5",
"15/7",
"81/35",
"25/9",
"3/1"
]
},
{
"id": "cross_3",
"desc": "John Pusey's triple 5-7 cross reduced by 3/1",
"stepCount": "13",
"steps": [
"27/25",
"25/21",
"9/7",
"243/175",
"125/81",
"5/3",
"9/5",
"243/125",
"175/81",
"7/3",
"63/25",
"25/9",
"3/1"
]
},
{
"id": "cross_13",
"desc": "13-limit harmonic/subharmonic cross",
"stepCount": "19",
"steps": [
"14/13",
"12/11",
"10/9",
"8/7",
"7/6",
"16/13",
"14/11",
"9/7",
"7/5",
"10/7",
"14/9",
"11/7",
"13/8",
"12/7",
"7/4",
"9/5",
"11/6",
"13/7",
"2/1"
]
},
{
"id": "crossbone_1",
"desc": "7-limit Crossbone Scale (1st order, 1st sepent)",
"stepCount": "12",
"steps": [
"16/15",
"7/6",
"5/4",
"9/7",
"10/7",
"3/2",
"14/9",
"5/3",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "cruciform",
"desc": "Cruciform Lattice",
"stepCount": "12",
"steps": [
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"8/5",
"5/3",
"15/8",
"2/1"
]
},
{
"id": "cube_3",
"desc": "7-limit Cube[3] scale, Gene Ward Smith",
"stepCount": "32",
"steps": [
"49/48",
"25/24",
"21/20",
"15/14",
"35/32",
"9/8",
"8/7",
"7/6",
"6/5",
"60/49",
"49/40",
"5/4",
"9/7",
"21/16",
"4/3",
"7/5",
"10/7",
"35/24",
"3/2",
"49/32",
"25/16",
"8/5",
"105/64",
"5/3",
"42/25",
"12/7",
"7/4",
"25/14",
"9/5",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "cube_3_enn",
"desc": "7-limit Cube[3] scale, 3600-ET ennealimmal tempered",
"stepCount": "32",
"steps": [
"35.66667",
"70.66667",
"84.33333",
"119.33333",
"155.00000",
"204.00000",
"231.33333",
"267.00000",
"315.66667",
"350.66667",
"351.33333",
"386.33333",
"435.00000",
"470.66667",
"498.00000",
"582.66667",
"617.33333",
"653.33333",
"702.00000",
"737.66667",
"772.66667",
"813.66667",
"857.00000",
"884.33333",
"898.00000",
"933.00000",
"968.66667",
"1003.66667",
"1017.66667",
"1088.33333",
"1151.33333",
"2/1"
]
},
{
"id": "cube_4",
"desc": "7-limit Cube[4] scale, Gene Ward Smith",
"stepCount": "63",
"steps": [
"50/49",
"49/48",
"36/35",
"25/24",
"21/20",
"16/15",
"15/14",
"35/32",
"10/9",
"28/25",
"9/8",
"8/7",
"7/6",
"25/21",
"6/5",
"128/105",
"60/49",
"49/40",
"5/4",
"32/25",
"9/7",
"35/27",
"64/49",
"21/16",
"4/3",
"168/125",
"49/36",
"48/35",
"25/18",
"480/343",
"7/5",
"10/7",
"343/240",
"36/25",
"35/24",
"72/49",
"125/84",
"3/2",
"32/21",
"49/32",
"54/35",
"14/9",
"25/16",
"8/5",
"80/49",
"49/30",
"105/64",
"5/3",
"42/25",
"12/7",
"7/4",
"16/9",
"25/14",
"9/5",
"64/35",
"28/15",
"15/8",
"40/21",
"48/25",
"35/18",
"96/49",
"49/25",
"2/1"
]
},
{
"id": "cube_4_enn",
"desc": "7-limit Cube[4] scale, 3600-tET ennealimmal tempered",
"stepCount": "63",
"steps": [
"35.00000",
"35.66667",
"48.66667",
"70.66667",
"84.33333",
"111.66667",
"119.33333",
"155.00000",
"182.33333",
"196.33333",
"204.00000",
"231.33333",
"267.00000",
"302.00000",
"315.66667",
"343.00000",
"350.66667",
"351.33333",
"386.33333",
"427.33333",
"435.00000",
"449.33333",
"462.33333",
"470.66667",
"498.00000",
"512.00000",
"533.66667",
"546.66667",
"568.66667",
"581.66667",
"582.66667",
"617.33333",
"618.33333",
"631.33333",
"653.33333",
"666.33333",
"688.00000",
"702.00000",
"729.33333",
"737.66667",
"750.66667",
"765.00000",
"772.66667",
"813.66667",
"848.66667",
"849.33333",
"857.00000",
"884.33333",
"898.00000",
"933.00000",
"968.66667",
"996.00000",
"1003.66667",
"1017.66667",
"1045.00000",
"1080.66667",
"1088.33333",
"1115.66667",
"1129.33333",
"1151.33333",
"1164.33333",
"1165.00000",
"2/1"
]
},
{
"id": "cv_1",
"desc": "First 12/5 <12 19 28 34| epimorphic",
"stepCount": "12",
"steps": [
"16/15",
"8/7",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"28/15",
"2/1"
]
},
{
"id": "cv_5",
"desc": "Fifth 12/5 scale <12 19 28 34| epimorphic = inverse hen12",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"6/5",
"5/4",
"21/16",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "cv_7",
"desc": "Seventh 12/5 scale <12 19 28 34| epimorphic",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"6/5",
"9/7",
"21/16",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "cv_9",
"desc": "Ninth 12/5 scale <12 19 28 34| epimorphic",
"stepCount": "12",
"steps": [
"15/14",
"8/7",
"7/6",
"5/4",
"4/3",
"10/7",
"32/21",
"8/5",
"5/3",
"25/14",
"40/21",
"2/1"
]
},
{
"id": "cv_11",
"desc": "Eleventh 12/5 scale <12 19 28 34| epimorphic",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"6/5",
"9/7",
"21/16",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "cv_13",
"desc": "Thirteenth 12/5 scale <12 19 28 34| epimorphic",
"stepCount": "12",
"steps": [
"16/15",
"28/25",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"28/15",
"2/1"
]
},
{
"id": "cw_12_11",
"desc": "CalkinWilf(<12 19 28 34 42|)",
"stepCount": "12",
"steps": [
"12/11",
"8/7",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "cw_19_5",
"desc": "CalkinWilf(<19 30 44|)",
"stepCount": "19",
"steps": [
"135/128",
"27/25",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"128/75",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "cw_19_7",
"desc": "CalkinWilf(<19 30 44 53|)",
"stepCount": "19",
"steps": [
"21/20",
"35/32",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"9/5",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "cw_19_11",
"desc": "CalkinWilf(<19 30 44 53 66|)",
"stepCount": "19",
"steps": [
"35/33",
"12/11",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"9/5",
"11/6",
"40/21",
"2/1"
]
},
{
"id": "cx_4",
"desc": "Fourth 10/4 scale <10 16 23 28| epimorphic",
"stepCount": "10",
"steps": [
"35/32",
"9/8",
"5/4",
"21/16",
"35/24",
"3/2",
"105/64",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "cxi_1",
"desc": "First 11/5 <11 17 26 31| permutation epimorphic scale",
"stepCount": "11",
"steps": [
"15/14",
"6/5",
"5/4",
"9/7",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "cxi_3",
"desc": "Third 11/5 <11 17 26 31| permutation epimorphic scale",
"stepCount": "11",
"steps": [
"49/48",
"35/32",
"7/6",
"5/4",
"7/5",
"35/24",
"3/2",
"25/16",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "cycle_19",
"desc": "19-note lesfip scale, 9-limit, 10 cents tolerance",
"stepCount": "19",
"steps": [
"68.20867",
"136.05163",
"202.95562",
"268.42817",
"316.37773",
"386.43387",
"451.91444",
"519.78797",
"576.96741",
"634.14686",
"702.02039",
"767.50096",
"837.55710",
"885.50666",
"950.97921",
"1017.88320",
"1085.72616",
"1153.93483",
"2/1"
]
},
{
"id": "dan_seman",
"desc": "Semantix-Semantic, 5-limit, common tones to Semantic-36 and Semantix-36 with different A",
"stepCount": "12",
"steps": [
"27/25",
"9/8",
"243/200",
"100/81",
"4/3",
"25/18",
"3/2",
"81/50",
"400/243",
"729/400",
"50/27",
"2/1"
]
},
{
"id": "dan_semantic",
"desc": "The Semantic Scale, from Alain Dani�lou: \"S�mantique Musicale\"(1967)",
"stepCount": "35",
"steps": [
"25/24",
"256/243",
"16/15",
"10/9",
"9/8",
"256/225",
"75/64",
"32/27",
"6/5",
"100/81",
"5/4",
"81/64",
"675/512",
"4/3",
"27/20",
"25/18",
"45/32",
"64/45",
"40/27",
"3/2",
"243/160",
"25/16",
"128/81",
"8/5",
"400/243",
"5/3",
"27/16",
"225/128",
"16/9",
"9/5",
"50/27",
"15/8",
"243/128",
"160/81",
"2/1"
]
},
{
"id": "dan_semantix",
"desc": "Jacques Dudon, Semantix-36, 27/25 generator",
"stepCount": "36",
"steps": [
"49/48",
"25/24",
"200/189",
"27/25",
"54/49",
"9/8",
"8/7",
"7/6",
"25/21",
"243/200",
"100/81",
"63/50",
"9/7",
"21/16",
"4/3",
"49/36",
"25/18",
"567/400",
"36/25",
"72/49",
"3/2",
"49/32",
"14/9",
"100/63",
"81/50",
"81/49",
"42/25",
"12/7",
"7/4",
"25/14",
"49/27",
"50/27",
"189/100",
"27/14",
"96/49",
"2/1"
]
},
{
"id": "danielou_53",
"desc": "Dani�lou's Harmonic Division of the Octave, see p. 153",
"stepCount": "53",
"steps": [
"81/80",
"46/45",
"25/24",
"256/243",
"16/15",
"27/25",
"11/10",
"10/9",
"9/8",
"256/225",
"15/13",
"75/64",
"32/27",
"6/5",
"128/105",
"100/81",
"5/4",
"81/64",
"32/25",
"125/96",
"320/243",
"4/3",
"27/20",
"512/375",
"25/18",
"45/32",
"64/45",
"36/25",
"375/256",
"40/27",
"3/2",
"243/160",
"192/125",
"25/16",
"128/81",
"8/5",
"81/50",
"400/243",
"5/3",
"27/16",
"128/75",
"125/72",
"225/128",
"16/9",
"9/5",
"11/6",
"50/27",
"15/8",
"243/128",
"48/25",
"125/64",
"160/81",
"2/1"
]
},
{
"id": "danielou_5_53",
"desc": "Dani�lou's Harmonic Division in 5-limit, symmetrized",
"stepCount": "53",
"steps": [
"81/80",
"128/125",
"25/24",
"256/243",
"16/15",
"27/25",
"2048/1875",
"10/9",
"9/8",
"256/225",
"144/125",
"75/64",
"32/27",
"6/5",
"243/200",
"100/81",
"5/4",
"81/64",
"32/25",
"125/96",
"320/243",
"4/3",
"27/20",
"512/375",
"25/18",
"45/32",
"64/45",
"36/25",
"375/256",
"40/27",
"3/2",
"243/160",
"192/125",
"25/16",
"128/81",
"8/5",
"81/50",
"400/243",
"5/3",
"27/16",
"128/75",
"125/72",
"225/128",
"16/9",
"9/5",
"1875/1024",
"50/27",
"15/8",
"243/128",
"48/25",
"125/64",
"160/81",
"2/1"
]
},
{
"id": "darreg_ennea",
"desc": "Ivor Darreg's Mixed Enneatonic, a mixture of chromatic and enharmonic",
"stepCount": "9",
"steps": [
"50.00000",
"100.00000",
"200.00000",
"500.00000",
"700.00000",
"750.00000",
"800.00000",
"900.00000",
"2/1"
]
},
{
"id": "darreg_genus",
"desc": "Ivor Darreg's Mixed JI Genus (Archytas Enh, Ptolemy Soft Chrom, Didymos Chrom",
"stepCount": "9",
"steps": [
"28/27",
"16/15",
"10/9",
"4/3",
"3/2",
"14/9",
"8/5",
"5/3",
"2/1"
]
},
{
"id": "darreg_genus_2",
"desc": "Darreg's Mixed JI Genus 2 (Archytas Enharmonic and Chromatic Genera)",
"stepCount": "9",
"steps": [
"28/27",
"16/15",
"9/8",
"4/3",
"3/2",
"14/9",
"8/5",
"27/16",
"2/1"
]
},
{
"id": "darreg",
"desc": "This set of 19 ratios in 5-limit JI is for his megalyra family",
"stepCount": "19",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"64/45",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"225/128",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "david_7",
"desc": "Gary David's Constant Structure (1967). A mode of Fokker's 7-limit scale",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"9/7",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"28/15",
"2/1"
]
},
{
"id": "david_11",
"desc": "11-limit system from Gary David (1967)",
"stepCount": "22",
"steps": [
"33/32",
"21/20",
"12/11",
"9/8",
"7/6",
"77/64",
"5/4",
"14/11",
"21/16",
"11/8",
"7/5",
"63/44",
"3/2",
"14/9",
"77/48",
"18/11",
"27/16",
"7/4",
"11/6",
"15/8",
"21/11",
"2/1"
]
},
{
"id": "dcon_9_marvwoo",
"desc": "convex closure in marvel of 9-limit diamond, marvel woo tuning",
"stepCount": "21",
"steps": [
"116.23027",
"183.04515",
"200.69746",
"232.46054",
"267.51234",
"316.92773",
"383.74261",
"433.15800",
"499.97288",
"584.44007",
"616.20315",
"700.67034",
"767.48522",
"816.90061",
"883.71549",
"933.13088",
"968.18268",
"999.94576",
"1017.59808",
"1084.41295",
"1200.64322"
]
},
{
"id": "dconv_9_gam",
"desc": "Convex closure in gamelismic of 9-limit diamond in 190-tET",
"stepCount": "31",
"steps": [
"31.57895",
"82.10526",
"151.57895",
"183.15789",
"202.10526",
"233.68421",
"265.26316",
"315.78947",
"385.26316",
"416.84211",
"435.78947",
"467.36842",
"498.94737",
"549.47368",
"581.05263",
"618.94737",
"650.52632",
"701.05263",
"732.63158",
"764.21053",
"783.15789",
"814.73684",
"884.21053",
"934.73684",
"966.31579",
"997.89474",
"1016.84211",
"1048.42105",
"1117.89474",
"1168.42105",
"2/1"
]
},
{
"id": "dconv_9_marv",
"desc": "Convex closure in marvel of 9-limit diamond in 197-tET",
"stepCount": "21",
"steps": [
"115.73604",
"182.74112",
"201.01523",
"231.47208",
"268.02030",
"316.75127",
"383.75635",
"432.48731",
"499.49239",
"584.77157",
"615.22843",
"700.50761",
"767.51269",
"816.24365",
"883.24873",
"931.97970",
"968.52792",
"998.98477",
"1017.25888",
"1084.26396",
"2/1"
]
},
{
"id": "dconv_11_marv",
"desc": "Convex closure in marvel of 11-limit diamond in 166-tET",
"stepCount": "35",
"steps": [
"36.14458",
"115.66265",
"151.80723",
"166.26506",
"180.72289",
"202.40964",
"231.32530",
"267.46988",
"318.07229",
"346.98795",
"383.13253",
"419.27711",
"433.73494",
"498.79518",
"534.93976",
"549.39759",
"585.54217",
"614.45783",
"650.60241",
"665.06024",
"701.20482",
"766.26506",
"780.72289",
"816.86747",
"853.01205",
"881.92771",
"932.53012",
"968.67470",
"997.59036",
"1019.27711",
"1033.73494",
"1048.19277",
"1084.33735",
"1163.85542",
"2/1"
]
},
{
"id": "ddimlim_1",
"desc": "First 27/25&2048/1875 scale",
"stepCount": "14",
"steps": [
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"8/5",
"5/3",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "de_caus",
"desc": "De Caus (a mode of Ellis's duodene) (1615)",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"75/64",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "dean_81_primes",
"desc": "Roger Dean's 81 primes non-octave scale (2008)",
"stepCount": "80",
"steps": [
"3/2",
"5/2",
"7/2",
"11/2",
"13/2",
"17/2",
"19/2",
"23/2",
"29/2",
"31/2",
"37/2",
"41/2",
"43/2",
"47/2",
"53/2",
"59/2",
"61/2",
"67/2",
"71/2",
"73/2",
"79/2",
"83/2",
"89/2",
"97/2",
"101/2",
"103/2",
"107/2",
"109/2",
"113/2",
"127/2",
"131/2",
"137/2",
"139/2",
"149/2",
"151/2",
"157/2",
"163/2",
"167/2",
"173/2",
"179/2",
"181/2",
"191/2",
"193/2",
"197/2",
"199/2",
"211/2",
"223/2",
"227/2",
"229/2",
"233/2",
"239/2",
"241/2",
"251/2",
"257/2",
"263/2",
"269/2",
"271/2",
"277/2",
"281/2",
"283/2",
"293/2",
"307/2",
"311/2",
"313/2",
"317/2",
"331/2",
"337/2",
"347/2",
"349/2",
"353/2",
"359/2",
"367/2",
"373/2",
"379/2",
"383/2",
"389/2",
"397/2",
"401/2",
"409/2",
"419/2"
]
},
{
"id": "dean_91_primes",
"desc": "Roger Dean's 91 primes non-octave scale (2008)",
"stepCount": "90",
"steps": [
"3/2",
"5/2",
"7/2",
"11/2",
"13/2",
"17/2",
"19/2",
"23/2",
"29/2",
"31/2",
"37/2",
"41/2",
"43/2",
"47/2",
"53/2",
"59/2",
"61/2",
"67/2",
"71/2",
"73/2",
"79/2",
"83/2",
"89/2",
"97/2",
"101/2",
"103/2",
"107/2",
"109/2",
"113/2",
"127/2",
"131/2",
"137/2",
"139/2",
"149/2",
"151/2",
"157/2",
"163/2",
"167/2",
"173/2",
"179/2",
"181/2",
"191/2",
"193/2",
"197/2",
"199/2",
"211/2",
"223/2",
"227/2",
"229/2",
"233/2",
"239/2",
"241/2",
"251/2",
"257/2",
"263/2",
"269/2",
"271/2",
"277/2",
"281/2",
"283/2",
"293/2",
"307/2",
"311/2",
"313/2",
"317/2",
"331/2",
"337/2",
"347/2",
"349/2",
"353/2",
"359/2",
"367/2",
"373/2",
"379/2",
"383/2",
"389/2",
"397/2",
"401/2",
"409/2",
"419/2",
"421/2",
"431/2",
"433/2",
"439/2",
"443/2",
"449/2",
"457/2",
"461/2",
"463/2",
"467/2"
]
},
{
"id": "degung_sejati",
"desc": "pelog degung sejati, Sunda",
"stepCount": "5",
"steps": ["424.00000", "494.00000", "706.00000", "1130.00000", "2/1"]
},
{
"id": "degung_1",
"desc": "Gamelan Degung, Kabupaten Sukabumi. 1/1=363 Hz",
"stepCount": "5",
"steps": [
"155.003 cents",
"344.805 cents",
"693.988 cents",
"823.199 cents",
"2/1"
]
},
{
"id": "degung_2",
"desc": "Gamelan Degung, Kabupaten Bandung. 1/1=252 Hz",
"stepCount": "5",
"steps": [
"96.854 cents",
"380.809 cents",
"692.771 cents",
"799.892 cents",
"2/1"
]
},
{
"id": "degung_3",
"desc": "Gamelan Degung, Kabupaten Sumedang. 1/1=388.5 Hz",
"stepCount": "5",
"steps": [
"134.970 cents",
"351.656 cents",
"705.665 cents",
"847.882 cents",
"2/1"
]
},
{
"id": "degung_4",
"desc": "Gamelan Degung, Kasepuhan Cheribon. 1/1=250 Hz",
"stepCount": "5",
"steps": [
"146.014 cents",
"344.257 cents",
"645.650 cents",
"800.653 cents",
"2/1"
]
},
{
"id": "degung_5",
"desc": "Gamelan Degung, Kanoman Cheribon. 1/1=428 Hz",
"stepCount": "5",
"steps": [
"143.544 cents",
"337.081 cents",
"685.699 cents",
"861.558 cents",
"2/1"
]
},
{
"id": "degung_6",
"desc": "Gamelan Degung, Kacherbonan Cheribon. 1/1=426 Hz",
"stepCount": "5",
"steps": [
"75.542 cents",
"228.123 cents",
"644.104 cents",
"773.602 cents",
"2/1"
]
},
{
"id": "deka_126",
"desc": "Dekatesserany (2x2x2 chord cube) is convex in starling (126/125); 5-limit projection",
"stepCount": "14",
"steps": [
"25/24",
"27/25",
"625/576",
"9/8",
"5/4",
"125/96",
"625/432",
"3/2",
"15625/10368",
"25/16",
"625/384",
"125/72",
"15/8",
"2/1"
]
},
{
"id": "deka_225",
"desc": "Dekatesserany (2x2x2 chord cube) marvel (225/224) 5-limit convex closure",
"stepCount": "16",
"steps": [
"135/128",
"16/15",
"1125/1024",
"9/8",
"75/64",
"5/4",
"675/512",
"45/32",
"375/256",
"3/2",
"50625/32768",
"25/16",
"3375/2048",
"225/128",
"15/8",
"2/1"
]
},
{
"id": "deka_245",
"desc": "Dekatesserany (2x2x2 chord cube) sensamagic (245/243) 2.3.7 convex closure",
"stepCount": "26",
"steps": [
"49/48",
"343/324",
"729/686",
"243/224",
"9/8",
"7/6",
"6561/5488",
"243/196",
"81/64",
"9/7",
"21/16",
"49/36",
"2187/1568",
"81/56",
"3/2",
"49/32",
"59049/38416",
"2187/1372",
"729/448",
"81/49",
"27/16",
"7/4",
"729/392",
"27/14",
"63/32",
"2/1"
]
},
{
"id": "deka_875",
"desc": "Dekatesserany (2x2x2 chord cube) keemic (875/864) 5-limit convex closure",
"stepCount": "21",
"steps": [
"648/625",
"25/24",
"27/25",
"625/576",
"9/8",
"6/5",
"3888/3125",
"5/4",
"162/125",
"125/96",
"27/20",
"36/25",
"23328/15625",
"3/2",
"972/625",
"25/16",
"81/50",
"216/125",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "deka_1029",
"desc": "Dekatesserany (2x2x2 chord cube) gamelismic (1029/1024) 2.5.7 convex closure",
"stepCount": "20",
"steps": [
"256/245",
"2560/2401",
"35/32",
"131072/117649",
"8/7",
"5/4",
"64/49",
"10/7",
"12005/8192",
"512/343",
"49/32",
"25/16",
"80/49",
"1715/1024",
"4096/2401",
"7/4",
"640/343",
"245/128",
"32768/16807",
"2/1"
]
},
{
"id": "deka_1728",
"desc": "Dekatesserany (2x2x2 chord cube) orwellismic (1728/1715) 2.3.7 convex closure",
"stepCount": "21",
"steps": [
"49/48",
"2401/2304",
"2592/2401",
"54/49",
"9/8",
"432/343",
"9/7",
"21/16",
"72/49",
"3/2",
"49/32",
"186624/117649",
"3888/2401",
"81/49",
"12/7",
"7/4",
"343/192",
"31104/16807",
"648/343",
"27/14",
"2/1"
]
},
{
"id": "deka_2401",
"desc": "Dekatesserany (2x2x2 chord cube) breedsmic (1029/1024) 2.5.7 convex closure",
"stepCount": "22",
"steps": [
"50/49",
"16807/16000",
"343/320",
"35/32",
"5764801/5120000",
"117649/102400",
"49/40",
"5/4",
"16807/12800",
"343/256",
"10/7",
"500/343",
"2401/1600",
"49/32",
"25/16",
"823543/512000",
"16807/10240",
"7/4",
"25/14",
"117649/64000",
"2401/1280",
"2/1"
]
},
{
"id": "deka_3136",
"desc": "Dekatesserany (2x2x2 chord cube) hemimean (3136/3125) oblique transversal convex closure",
"stepCount": "24",
"steps": [
"375/32",
"12/125",
"78125/256",
"5/2",
"9/8",
"1875/64",
"6/25",
"390625/512",
"25/4",
"9375/128",
"3/5",
"1953125/1024",
"125/8",
"78125/192",
"46875/256",
"3/2",
"9765625/2048",
"625/16",
"234375/512",
"15/4",
"3125/32",
"75/8",
"15625/64",
"2/1"
]
},
{
"id": "deka_4375",
"desc": "Dekatesserany (2x2x2 chord cube) ragismic (4375/4374) 5-limit convex closure",
"stepCount": "34",
"steps": [
"81/80",
"25/24",
"6561/6250",
"3125/2916",
"2187/2000",
"9/8",
"125/108",
"59049/50000",
"243/200",
"5/4",
"6561/5000",
"27/20",
"25/18",
"177147/125000",
"729/500",
"3/2",
"4782969/3125000",
"25/16",
"19683/12500",
"81/50",
"6561/4000",
"5/3",
"27/16",
"531441/312500",
"125/72",
"2187/1250",
"9/5",
"729/400",
"15/8",
"59049/31250",
"625/324",
"243/125",
"19683/10000",
"2/1"
]
},
{
"id": "deka_5120",
"desc": "Dekatesserany (2x2x2 chord cube) hemifamity (5120/5103) 5-limit convex closure",
"stepCount": "38",
"steps": [
"25/24",
"256/243",
"135/128",
"2187/2048",
"800/729",
"10/9",
"9/8",
"204800/177147",
"2560/2187",
"32/27",
"100/81",
"5/4",
"81/64",
"25600/19683",
"320/243",
"4/3",
"25/18",
"45/32",
"729/512",
"3200/2187",
"40/27",
"3/2",
"819200/531441",
"10240/6561",
"25/16",
"128/81",
"400/243",
"5/3",
"27/16",
"102400/59049",
"1280/729",
"16/9",
"50/27",
"15/8",
"243/128",
"12800/6561",
"160/81",
"2/1"
]
},
{
"id": "deka_6144",
"desc": "Dekatesserany (2x2x2 chord cube) porwell (6144/6125) 2.5.7 convex closure",
"stepCount": "20",
"steps": [
"1071875/1048576",
"8575/8192",
"4375/4096",
"35/32",
"37515625/33554432",
"1225/1024",
"5/4",
"42875/32768",
"175/128",
"256/175",
"6125/4096",
"49/32",
"25/16",
"8/5",
"214375/131072",
"875/512",
"7/4",
"30625/16384",
"245/128",
"2/1"
]
},
{
"id": "deka_65625",
"desc": "Dekatesserany (2x2x2 chord cube) horwell (65625/65536) 5-limit convex closure",
"stepCount": "39",
"steps": [
"128/125",
"16384/15625",
"16/15",
"140625/131072",
"2048/1875",
"1125/1024",
"262144/234375",
"9/8",
"32768/28125",
"75/64",
"4194304/3515625",
"6/5",
"5/4",
"32/25",
"4096/3125",
"512/375",
"5625/4096",
"65536/46875",
"45/32",
"8192/5625",
"375/256",
"1048576/703125",
"3/2",
"134217728/87890625",
"192/125",
"25/16",
"8/5",
"1024/625",
"128/75",
"28125/16384",
"16384/9375",
"225/128",
"2097152/1171875",
"1875/1024",
"262144/140625",
"15/8",
"33554432/17578125",
"48/25",
"2/1"
]
},
{
"id": "dekany_agni",
"desc": "Dekany agni {385/384, 1375/1372} oblique transversal convex closure",
"stepCount": "16",
"steps": [
"25/2",
"4/375",
"2/15",
"5/3",
"75/2",
"4/125",
"2/5",
"5",
"125/2",
"4/75",
"2/3",
"25/3",
"15",
"8/1125",
"4/25",
"2/1"
]
},
{
"id": "dekany_apollo",
"desc": "Dekany apollo {100/99, 225/224} 5-limit convex closure",
"stepCount": "16",
"steps": [
"25/24",
"125/108",
"75/64",
"5/4",
"125/96",
"25/18",
"375/256",
"25/16",
"625/384",
"5/3",
"125/72",
"225/128",
"50/27",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "dekany_guanyin",
"desc": "Dekany guanyin {176/175, 540/539} oblique transversal convex closure",
"stepCount": "18",
"steps": [
"625/8",
"75/8",
"390625/64",
"2/5",
"125/4",
"15/4",
"78125/32",
"9375/32",
"25/2",
"3/2",
"15625/16",
"1875/16",
"125/3",
"5",
"3/5",
"3125/8",
"375/8",
"2/1"
]
},
{
"id": "dekany_indra",
"desc": "Dekany indra {540/539, 1375/1372} oblique transversal convex closure",
"stepCount": "19",
"steps": [
"15/4",
"3/10",
"9/100",
"9/1250",
"27/12500",
"125/2",
"5",
"243/15625000",
"3/2",
"3/25",
"9/20",
"9/250",
"9/3125",
"27/2500",
"27/31250",
"250/3",
"81/312500",
"25",
"2/1"
]
},
{
"id": "dekany_jove",
"desc": "Dekany jove {243/242, 441/440} oblique transversal convex closure",
"stepCount": "19",
"steps": [
"25/2",
"45/2",
"81/2",
"2025/4",
"5/3",
"3/1",
"75/2",
"135/2",
"243/2",
"5/1",
"125/2",
"9/1",
"225/2",
"405/2",
"25/3",
"15/1",
"27/1",
"675/2",
"2/1"
]
},
{
"id": "dekany_laka",
"desc": "Dekany laka {5120/5103, 540/539} 5-limit convex closure",
"stepCount": "29",
"steps": [
"531441/524288",
"135/128",
"2187/2048",
"10/9",
"9/8",
"4782969/4194304",
"2560/2187",
"19683/16384",
"5/4",
"81/64",
"320/243",
"177147/131072",
"14348907/10485760",
"45/32",
"729/512",
"3200/2187",
"40/27",
"3/2",
"1594323/1048576",
"6561/4096",
"5/3",
"27/16",
"1280/729",
"59049/32768",
"4782969/2621440",
"15/8",
"243/128",
"160/81",
"2/1"
]
},
{
"id": "dekany_laka_205",
"desc": "Dekany laka convex closure of the 2)5 Dekany 1.3.5.7.11 (1.3 tonic), 205-tET tuning",
"stepCount": "29",
"steps": [
"29.26829",
"93.65854",
"117.07317",
"181.46341",
"204.87805",
"234.14634",
"269.26829",
"321.95122",
"386.34146",
"409.75610",
"474.14634",
"526.82927",
"550.24390",
"591.21951",
"614.63415",
"655.60976",
"679.02439",
"702.43902",
"731.70732",
"819.51220",
"883.90244",
"907.31707",
"971.70732",
"1024.39024",
"1047.80488",
"1088.78049",
"1112.19512",
"1176.58537",
"2/1"
]
},
{
"id": "dekany_marvel",
"desc": "Dekany marvel {225/224, 385/384} 5-limit convex closure",
"stepCount": "15",
"steps": [
"16/15",
"256/225",
"75/64",
"5/4",
"4/3",
"512/375",
"375/256",
"25/16",
"8/5",
"5/3",
"128/75",
"225/128",
"2048/1125",
"15/8",
"2/1"
]
},
{
"id": "dekany_minerva",
"desc": "Dekany minerva {99/98, 176/175} 5-limit convex closure",
"stepCount": "15",
"steps": [
"1125/1024",
"9375/8192",
"75/64",
"5/4",
"5625/4096",
"375/256",
"25/16",
"421875/262144",
"5/3",
"28125/16384",
"225/128",
"1875/1024",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "dekany_pele",
"desc": "Dekany pele {441/440, 896/891} 5-limit convex closure",
"stepCount": "24",
"steps": [
"1638400/1594323",
"20480/19683",
"10/9",
"204800/177147",
"2560/2187",
"52428800/43046721",
"5/4",
"25600/19683",
"320/243",
"6553600/4782969",
"81920/59049",
"3200/2187",
"40/27",
"819200/531441",
"10240/6561",
"209715200/129140163",
"5/3",
"102400/59049",
"1280/729",
"26214400/14348907",
"327680/177147",
"12800/6561",
"160/81",
"2/1"
]
},
{
"id": "dekany_portent",
"desc": "Dekany portent {1029/1024, 385/384} 2.5.7 convex closure",
"stepCount": "17",
"steps": [
"256/245",
"35/32",
"8/7",
"2401/2048",
"2048/1715",
"5/4",
"64/49",
"343/256",
"16384/12005",
"12005/8192",
"49/32",
"8/5",
"1715/1024",
"7/4",
"64/35",
"245/128",
"2/1"
]
},
{
"id": "dekany_prodigy",
"desc": "Dekany prodigy {225/224, 441/440} 5-limit convex closure",
"stepCount": "20",
"steps": [
"1125/1024",
"151875/131072",
"75/64",
"10125/8192",
"5/4",
"675/512",
"91125/65536",
"45/32",
"375/256",
"50625/32768",
"25/16",
"6834375/4194304",
"3375/2048",
"5/3",
"455625/262144",
"225/128",
"30375/16384",
"15/8",
"2025/1024",
"2/1"
]
},
{
"id": "dekany_sensamagic",
"desc": "Dekany sensamagic {245/243, 385/384} oblique transversal convex closure",
"stepCount": "19",
"steps": [
"4/15",
"9/8",
"40/9",
"3/10",
"75/4",
"5",
"4/3",
"16/45",
"45/8",
"3/2",
"2/5",
"8/75",
"25",
"20/3",
"9/20",
"16/9",
"64/135",
"15/2",
"2/1"
]
},
{
"id": "dekany_spectacle",
"desc": "Dekany spectacle {225/224, 243/242} oblique transversal convex closure",
"stepCount": "24",
"steps": [
"5/12",
"3645/16",
"6075/64",
"81/2",
"135/8",
"225/32",
"3",
"5/4",
"18225/64",
"243/2",
"405/8",
"675/32",
"1125/128",
"9",
"15/4",
"25/16",
"54675/64",
"5/18",
"1215/8",
"2025/32",
"27",
"45/4",
"75/16",
"2/1"
]
},
{
"id": "dekany_thrush",
"desc": "Dekany thrush {126/125, 176/175} 5-limit convex closure",
"stepCount": "16",
"steps": [
"25/24",
"625/576",
"15625/13824",
"125/108",
"5/4",
"125/96",
"3125/2304",
"25/18",
"625/432",
"15625/10368",
"390625/248832",
"5/3",
"125/72",
"3125/1728",
"78125/41472",
"2/1"
]
},
{
"id": "dekany_union",
"desc": "Union of 2)5 and 3)5 1.3.5.7.9 dekanies, or 3)6 1.3.5.5.7.9",
"stepCount": "14",
"steps": [
"21/20",
"9/8",
"7/6",
"5/4",
"21/16",
"7/5",
"35/24",
"3/2",
"63/40",
"5/3",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "dekany_zeus",
"desc": "Dekany zeus {121/120, 176/175} oblique transversal convex closure",
"stepCount": "11",
"steps": [
"5/1",
"3/250",
"1000/9",
"3/50",
"3/10",
"20/3",
"100/3",
"2/25",
"500/3",
"2/5",
"2/1"
]
},
{
"id": "dekany_cs_marv",
"desc": "dekany-cs in marvel tempering, POTE tuning",
"stepCount": "12",
"steps": [
"49.37898",
"116.07099",
"200.77735",
"267.46935",
"316.84833",
"468.24670",
"548.99031",
"700.38867",
"816.45966",
"967.85803",
"1048.60163",
"2/1"
]
},
{
"id": "dekany_cs",
"desc": "CPS ({1,3,7,9,11}, 2) union {77/72, 77/64}. Grady-Narushima",
"stepCount": "12",
"steps": [
"33/32",
"77/72",
"9/8",
"7/6",
"77/64",
"21/16",
"11/8",
"3/2",
"77/48",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "dekany",
"desc": "2)5 Dekany 1.3.5.7.11 (1.3 tonic)",
"stepCount": "10",
"steps": [
"55/48",
"7/6",
"5/4",
"11/8",
"35/24",
"77/48",
"5/3",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "dekany_2",
"desc": "3)5 Dekany 1.3.5.7.9 (1.3.5.7.9 tonic)",
"stepCount": "10",
"steps": [
"16/15",
"8/7",
"6/5",
"4/3",
"48/35",
"32/21",
"8/5",
"12/7",
"16/9",
"2/1"
]
},
{
"id": "dekany_3",
"desc": "2)5 Dekany 1.3.5.7.9 and 3)5 Dekany 1 1/3 1/5 1/7 1/9",
"stepCount": "10",
"steps": [
"9/8",
"7/6",
"5/4",
"21/16",
"35/24",
"3/2",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "dekany_4",
"desc": "2)5 Dekany 1.7.13.19.29 (1.7 tonic)",
"stepCount": "10",
"steps": [
"29/28",
"247/224",
"19/16",
"551/448",
"19/14",
"13/8",
"377/224",
"29/16",
"13/7",
"2/1"
]
},
{
"id": "dekanymarvwoo",
"desc": "Convex closure of the 2)5 Cps({1,3,5,7,11}, 2)5 dekany in marvel; marvel woo tuning",
"stepCount": "15",
"steps": [
"49.41539",
"151.28207",
"267.51234",
"316.92773",
"383.74261",
"433.15800",
"468.20980",
"549.38827",
"584.44007",
"700.67034",
"816.90061",
"933.13088",
"968.18268",
"1084.41295",
"1200.64322"
]
},
{
"id": "dent_19_otti",
"desc": "Tom Dent's 19otti scale",
"stepCount": "12",
"steps": [
"135/128",
"573/512",
"19/16",
"2565/2048",
"171/128",
"45/32",
"383/256",
"2431/1536",
"3429/2048",
"57/32",
"15/8",
"2/1"
]
},
{
"id": "dent_berger",
"desc": "Tom Dent's 19berger scale",
"stepCount": "12",
"steps": [
"256/243",
"151/135",
"19/16",
"304/243",
"4864/3645",
"2215/1576",
"2423/1620",
"155648/98415",
"271/162",
"8417/4728",
"15/8",
"2/1"
]
},
{
"id": "dent_mean_7",
"desc": "Tom Dent's 7-limit irregular meantone",
"stepCount": "12",
"steps": [
"1875/1792",
"28/25",
"1875/1568",
"5/4",
"75/56",
"7/5",
"3/2",
"196/125",
"375/224",
"224/125",
"15/8",
"2/1"
]
},
{
"id": "dent_yn_rwt",
"desc": "Tom Dent's Young-Neidhardt well-temperament (rationalized by George Secor)",
"stepCount": "12",
"steps": [
"560/531",
"2643/2360",
"70/59",
"74/59",
"315/236",
"1329/944",
"883/590",
"280/177",
"890/531",
"105/59",
"887/472",
"2/1"
]
},
{
"id": "dent",
"desc": "Tom Dent, well temperament with A=421 Hz and integer Hz beat rates from A",
"stepCount": "12",
"steps": [
"531/502",
"563/502",
"597/502",
"315/251",
"335/251",
"354/251",
"376/251",
"398/251",
"421/251",
"447/251",
"472/251",
"2/1"
]
},
{
"id": "dent_2",
"desc": "Tom Dent, well-temperament, 2/32 and 5/32 comma, TL 3 & 5-09-2005",
"stepCount": "12",
"steps": [
"96.21115",
"197.18929",
"298.16743",
"394.37857",
"499.38914",
"595.60029",
"698.59464",
"796.82200",
"895.78393",
"998.77828",
"1094.98943",
"2/1"
]
},
{
"id": "dent_3",
"desc": "Tom Dent, Bach harpsichord \"sine wave\"temperament, TL 10-10-2005",
"stepCount": "12",
"steps": [
"95.00000",
"197.00000",
"299.00000",
"394.00000",
"500.00000",
"594.00000",
"699.00000",
"797.00000",
"895.00000",
"1000.00000",
"1094.00000",
"2/1"
]
},
{
"id": "dent_4",
"desc": "Tom Dent, modified meantone with appr. to 7/5, 13/11, 14/11, 19/15, 19/16. TL 30-01-2009",
"stepCount": "12",
"steps": [
"86.00000",
"195.00000",
"296.00000",
"389.00000",
"503.00000",
"584.00000",
"698.00000",
"791.00000",
"892.00000",
"1001.00000",
"1087.00000",
"2/1"
]
},
{
"id": "deporcy",
"desc": "A 15-note chord-based detempering of 7-limit porcupine",
"stepCount": "15",
"steps": [
"25/24",
"35/32",
"8/7",
"6/5",
"5/4",
"4/3",
"48/35",
"35/24",
"3/2",
"8/5",
"5/3",
"7/4",
"64/35",
"48/25",
"2/1"
]
},
{
"id": "diab_17_a",
"desc": "[25, 125, 175, 2401, 12005] breed diamond",
"stepCount": "17",
"steps": [
"2560/2401",
"343/320",
"8/7",
"400/343",
"2401/2000",
"5/4",
"3200/2401",
"7/5",
"10/7",
"2401/1600",
"8/5",
"4000/2401",
"343/200",
"7/4",
"640/343",
"2401/1280",
"2/1"
]
},
{
"id": "diab_17_bb",
"desc": "[25, 125, 175, 2401, 16807] breed diamond",
"stepCount": "17",
"steps": [
"84.33333",
"231.33333",
"266.66667",
"315.66667",
"386.33333",
"470.66667",
"498.00000",
"582.33333",
"617.66667",
"702.00000",
"729.33333",
"813.66667",
"884.33333",
"933.33333",
"968.66667",
"1115.66667",
"2/1"
]
},
{
"id": "diab_17_cb",
"desc": "[25, 35, 125, 175, 2401] breed diamond, 3600-tET tempered",
"stepCount": "17",
"steps": [
"119.66667",
"196.00000",
"231.33333",
"266.66667",
"315.66667",
"386.33333",
"498.00000",
"582.33333",
"617.66667",
"702.00000",
"813.66667",
"884.33333",
"933.33333",
"968.66667",
"1004.00000",
"1080.33333",
"2/1"
]
},
{
"id": "diab_17_db",
"desc": "[25, 125, 175, 245, 2401] breed diamond, 3600-tET tempered",
"stepCount": "17",
"steps": [
"35.33333",
"231.33333",
"266.66667",
"315.66667",
"351.00000",
"386.33333",
"498.00000",
"582.33333",
"617.66667",
"702.00000",
"813.66667",
"849.00000",
"884.33333",
"933.33333",
"968.66667",
"1164.66667",
"2/1"
]
},
{
"id": "diab_19_72",
"desc": "diab19a in 72-tET",
"stepCount": "19",
"steps": [
"33.33333",
"116.66667",
"233.33333",
"266.66667",
"316.66667",
"350.00000",
"383.33333",
"500.00000",
"583.33333",
"616.66667",
"700.00000",
"816.66667",
"850.00000",
"883.33333",
"933.33333",
"966.66667",
"1083.33333",
"1166.66667",
"2/1"
]
},
{
"id": "diab_19_612",
"desc": "diab19a in 612-tET",
"stepCount": "19",
"steps": [
"35.29412",
"119.60784",
"231.37255",
"266.66667",
"315.68628",
"350.98039",
"386.27451",
"498.03922",
"582.35294",
"617.64706",
"701.96078",
"813.72549",
"849.01961",
"884.31372",
"933.33333",
"968.62745",
"1080.39216",
"1164.70588",
"2/1"
]
},
{
"id": "diab_19_a",
"desc": "19-tone 7-limit JI scale",
"stepCount": "19",
"steps": [
"50/49",
"15/14",
"8/7",
"7/6",
"6/5",
"49/40",
"5/4",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"80/49",
"5/3",
"12/7",
"7/4",
"28/15",
"49/25",
"2/1"
]
},
{
"id": "diab_19_ab",
"desc": "[25, 125, 175, 245, 1715, 2401] breed diamond, 3600-tET tempered",
"stepCount": "19",
"steps": [
"35.33333",
"119.66667",
"231.33333",
"266.66667",
"315.66667",
"351.00000",
"386.33333",
"498.00000",
"582.33333",
"617.66667",
"702.00000",
"813.66667",
"849.00000",
"884.33333",
"933.33333",
"968.66667",
"1080.33333",
"1164.66667",
"2/1"
]
},
{
"id": "diablack",
"desc": "Unique 256/245&2048/2025 Fokker block",
"stepCount": "10",
"steps": [
"16/15",
"9/8",
"6/5",
"81/64",
"64/45",
"3/2",
"8/5",
"27/16",
"9/5",
"2/1"
]
},
{
"id": "diabree",
"desc": "detempered convex closure of 11-limit diamond in {243/242, 441/440} temperament plane",
"stepCount": "39",
"steps": [
"45/44",
"21/20",
"15/14",
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"14/11",
"9/7",
"21/16",
"4/3",
"15/11",
"11/8",
"7/5",
"10/7",
"16/11",
"22/15",
"3/2",
"32/21",
"14/9",
"11/7",
"8/5",
"18/11",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"28/15",
"21/11",
"49/25",
"2/1"
]
},
{
"id": "diachrome_1",
"desc": "First 25/24&2048/2025 scale",
"stepCount": "10",
"steps": [
"16/15",
"9/8",
"6/5",
"32/25",
"45/32",
"3/2",
"8/5",
"27/16",
"9/5",
"2/1"
]
},
{
"id": "diaconv_225",
"desc": "convex closure of 7-limit diamond with respect to 225/224",
"stepCount": "15",
"steps": [
"15/14",
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "diaconv_1029",
"desc": "convex closure of 7-limit diamond with respect to 1029/1024",
"stepCount": "19",
"steps": [
"21/20",
"35/32",
"8/7",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"32/21",
"8/5",
"5/3",
"12/7",
"7/4",
"64/35",
"40/21",
"2/1"
]
},
{
"id": "diaconv_2401",
"desc": "convex closure of 7-limit diamond with respect to 2401/2400",
"stepCount": "17",
"steps": [
"49/48",
"8/7",
"7/6",
"6/5",
"49/40",
"5/4",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"49/30",
"5/3",
"12/7",
"7/4",
"49/25",
"2/1"
]
},
{
"id": "diaconv_2401_t",
"desc": "convex closure of 7-limit diamond with respect to 2401/2400, 3600-tET",
"stepCount": "17",
"steps": [
"35.33333",
"231.33333",
"266.66667",
"315.66667",
"351.00000",
"386.33333",
"498.00000",
"582.33333",
"617.66667",
"702.00000",
"813.66667",
"849.00000",
"884.33333",
"933.33333",
"968.66667",
"1164.66667",
"2/1"
]
},
{
"id": "diaconv_3136",
"desc": "convex closure of 7-limit diamond with respect to 3136/3125",
"stepCount": "23",
"steps": [
"25/24",
"15/14",
"28/25",
"8/7",
"7/6",
"6/5",
"5/4",
"32/25",
"4/3",
"75/56",
"7/5",
"10/7",
"112/75",
"3/2",
"25/16",
"8/5",
"5/3",
"12/7",
"7/4",
"25/14",
"28/15",
"48/25",
"2/1"
]
},
{
"id": "diaconv_4375",
"desc": "convex closure of 7-limit diamond with respect to 4375/4374",
"stepCount": "25",
"steps": [
"36/35",
"27/25",
"10/9",
"8/7",
"7/6",
"6/5",
"100/81",
"5/4",
"35/27",
"4/3",
"25/18",
"7/5",
"10/7",
"36/25",
"3/2",
"54/35",
"8/5",
"81/50",
"5/3",
"12/7",
"7/4",
"9/5",
"50/27",
"35/18",
"2/1"
]
},
{
"id": "diaconv_5120",
"desc": "convex closure of 7-limit diamond with respect to 5120/5103",
"stepCount": "29",
"steps": [
"64/63",
"21/20",
"10/9",
"9/8",
"8/7",
"7/6",
"32/27",
"6/5",
"5/4",
"80/63",
"21/16",
"4/3",
"27/20",
"7/5",
"10/7",
"40/27",
"3/2",
"32/21",
"63/40",
"8/5",
"5/3",
"27/16",
"12/7",
"7/4",
"16/9",
"9/5",
"40/21",
"63/32",
"2/1"
]
},
{
"id": "diaconv_6144",
"desc": "convex closure of 7-limit diamond with respect to 6144/6125",
"stepCount": "19",
"steps": [
"35/32",
"8/7",
"7/6",
"6/5",
"5/4",
"32/25",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"25/16",
"8/5",
"5/3",
"12/7",
"7/4",
"64/35",
"2/1"
]
},
{
"id": "diacycle_13",
"desc": "Diacycle on 20/13, 13/10; there are also nodes at 3/2, 4/3; 13/9, 18/13",
"stepCount": "23",
"steps": [
"40/39",
"20/19",
"40/37",
"10/9",
"8/7",
"20/17",
"40/33",
"5/4",
"40/31",
"4/3",
"40/29",
"10/7",
"40/27",
"20/13",
"30/19",
"60/37",
"5/3",
"12/7",
"30/17",
"20/11",
"15/8",
"60/31",
"2/1"
]
},
{
"id": "diaddim_1",
"desc": "First 2048/2025&2048/1875 scale",
"stepCount": "14",
"steps": [
"135/128",
"9/8",
"6/5",
"32/25",
"675/512",
"512/375",
"45/32",
"3/2",
"8/5",
"128/75",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "dialim_1",
"desc": "First 27/25&2048/2025 scale",
"stepCount": "14",
"steps": [
"16/15",
"9/8",
"6/5",
"32/25",
"4/3",
"27/20",
"45/32",
"3/2",
"8/5",
"27/16",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "diam_19",
"desc": "Optimized 13-limit from diamond9plus",
"stepCount": "19",
"steps": [
"182.1261",
"204.0654",
"231.1980",
"266.9967",
"315.5588",
"383.3099",
"435.7345",
"497.2228",
"582.3425",
"617.6575",
"702.7772",
"764.2655",
"816.6901",
"884.4412",
"933.0033",
"968.8020",
"995.9346",
"1017.8739",
"2/1"
]
},
{
"id": "diamin_7_72",
"desc": "diamin7 in 72-tET",
"stepCount": "18",
"steps": [
"116.666667",
"183.333333",
"266.666667",
"233.333333",
"316.666667",
"383.333333",
"500.000000",
"516.666667",
"583.333333",
"616.666667",
"700.000000",
"816.666667",
"883.333333",
"966.666667",
"933.333333",
"1016.666667",
"1083.333333",
"2/1"
]
},
{
"id": "diamin_7",
"desc": "permutation epimorphic scale with 7-limit diamond, Hahn and TM reduced <18 29 42 50|",
"stepCount": "18",
"steps": [
"16/15",
"10/9",
"7/6",
"8/7",
"6/5",
"5/4",
"4/3",
"27/20",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"7/4",
"12/7",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "diamin_7_marv",
"desc": "1/4 kleismic tempered diamin7",
"stepCount": "18",
"steps": [
"115.58705",
"184.33159",
"268.79879",
"8/7",
"6/5",
"384.38583",
"499.97288",
"515.69553",
"584.44007",
"615.55993",
"700.02712",
"815.61417",
"5/3",
"7/4",
"931.20121",
"1015.66841",
"1084.41295",
"2/1"
]
},
{
"id": "diamisty",
"desc": "Diamisty scale 2048/2025 and 67108864/66430125",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"1215/1024",
"512/405",
"4/3",
"64/45",
"3/2",
"405/256",
"54675/32768",
"32768/18225",
"256/135",
"2/1"
]
},
{
"id": "diamond_chess",
"desc": "9-limit chessboard pattern diamond. OdC",
"stepCount": "11",
"steps": [
"8/7",
"6/5",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"5/3",
"7/4",
"2/1"
]
},
{
"id": "diamond_chess_11",
"desc": "11-limit chessboard pattern diamond. OdC",
"stepCount": "17",
"steps": [
"11/10",
"8/7",
"6/5",
"11/9",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"16/11",
"3/2",
"14/9",
"18/11",
"5/3",
"7/4",
"20/11",
"2/1"
]
},
{
"id": "diamond_dup",
"desc": "Two 7-limit diamonds 3/2 apart",
"stepCount": "20",
"steps": [
"21/20",
"15/14",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "diamond_mod",
"desc": "13-tone Octave Modular Diamond, based on Archytas's Enharmonic",
"stepCount": "13",
"steps": [
"36/35",
"28/27",
"16/15",
"5/4",
"9/7",
"4/3",
"3/2",
"14/9",
"8/5",
"15/8",
"27/14",
"35/18",
"2/1"
]
},
{
"id": "diamond_tetr",
"desc": "Tetrachord Modular Diamond based on Archytas's Enharmonic",
"stepCount": "8",
"steps": ["28/27", "16/15", "5/4", "9/7", "35/27", "4/3", "48/35", "2/1"]
},
{
"id": "diamond_7_126",
"desc": "7-limit diamond starling (126/125) 5-limit convex closure",
"stepCount": "15",
"steps": [
"25/24",
"144/125",
"125/108",
"6/5",
"5/4",
"4/3",
"25/18",
"36/25",
"3/2",
"8/5",
"5/3",
"216/125",
"125/72",
"48/25",
"2/1"
]
},
{
"id": "diamond_7_225",
"desc": "7-limit diamond marvel (225/224) 5-limit convex closure",
"stepCount": "15",
"steps": [
"16/15",
"256/225",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"64/45",
"3/2",
"8/5",
"5/3",
"128/75",
"225/128",
"15/8",
"2/1"
]
},
{
"id": "diamond_7_13",
"desc": "7 9 11 13 diamond",
"stepCount": "13",
"steps": [
"14/13",
"13/11",
"11/9",
"14/11",
"9/7",
"18/13",
"13/9",
"14/9",
"11/7",
"18/11",
"22/13",
"13/7",
"2/1"
]
},
{
"id": "diamond_7",
"desc": "7-limit diamond, also double-tie circular mirroring of 4:5:6:7 with common pivot",
"stepCount": "13",
"steps": [
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "diamond_9_875",
"desc": "9-limit diamond keemic (875/864) 5-limit convex closure",
"stepCount": "27",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"144/125",
"125/108",
"6/5",
"5/4",
"32/25",
"125/96",
"4/3",
"864/625",
"25/18",
"36/25",
"625/432",
"3/2",
"192/125",
"25/16",
"8/5",
"5/3",
"216/125",
"125/72",
"16/9",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "diamond_9",
"desc": "9-limit tonality diamond",
"stepCount": "19",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"2/1"
]
},
{
"id": "diamond_9_block",
"desc": "Weak Fokker block one note different from the 9-limit diamond",
"stepCount": "19",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"27/14",
"2/1"
]
},
{
"id": "diamond_9_keemic",
"desc": "Keemic (875/864) tempering of 9-limit diamond, POTE tuning",
"stepCount": "19",
"steps": [
"176.72185",
"203.74653",
"235.78536",
"262.34137",
"321.40488",
"380.46839",
"439.53189",
"498.12673",
"583.74625",
"616.25375",
"701.87327",
"760.46811",
"819.53161",
"878.59512",
"937.65863",
"964.21464",
"996.25347",
"1023.27815",
"2/1"
]
},
{
"id": "diamond_9_plus",
"desc": "9-limit tonality diamond extended with two secors",
"stepCount": "21",
"steps": [
"115.587",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"1084.413",
"2/1"
]
},
{
"id": "diamond_11_a",
"desc": "11-limit Diamond (partch_29.scl) with added 16/15 & 15/8, Zoomoozophone tuning: 1/1 = 392 Hz",
"stepCount": "31",
"steps": [
"16/15",
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"14/11",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"16/11",
"3/2",
"14/9",
"11/7",
"8/5",
"18/11",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"15/8",
"2/1"
]
},
{
"id": "diamond_11_ak",
"desc": "microtempered version of diamond11a, Dave Keenan TL 11-1-2000, 225/224&385/384",
"stepCount": "31",
"steps": [
"115.79629",
"151.99206",
"11/10",
"10/9",
"201.20000",
"231.60409",
"267.79591",
"316.99629",
"11/9",
"383.60371",
"419.78796",
"432.80410",
"499.40000",
"548.60794",
"584.79219",
"615.20781",
"651.39206",
"700.60000",
"767.19590",
"780.21204",
"816.39629",
"18/11",
"883.00371",
"932.20409",
"968.39591",
"998.80000",
"9/5",
"20/11",
"1048.00794",
"1084.20371",
"2/1"
]
},
{
"id": "diamond_11_map",
"desc": "11-limit diamond on a 'centreless' map",
"stepCount": "72",
"steps": [
"7/6",
"4/3",
"3/2",
"5/3",
"11/6",
"2/1",
"7/3",
"8/3",
"3/1",
"10/3",
"11/3",
"12/11",
"14/11",
"16/11",
"18/11",
"20/11",
"2/1",
"24/11",
"28/11",
"32/11",
"36/11",
"40/11",
"4/1",
"6/5",
"7/5",
"8/5",
"9/5",
"2/1",
"11/5",
"12/5",
"14/5",
"16/5",
"18/5",
"4/1",
"22/5",
"4/3",
"14/9",
"16/9",
"2/1",
"20/9",
"22/9",
"8/3",
"28/9",
"32/9",
"4/1",
"40/9",
"44/9",
"3/2",
"7/4",
"2/1",
"9/4",
"5/2",
"11/4",
"3/1",
"7/2",
"4/1",
"9/2",
"5/1",
"11/2",
"12/7",
"2/1",
"16/7",
"18/7",
"20/7",
"22/7",
"24/7",
"4/1",
"32/7",
"36/7",
"40/7",
"44/7",
"4/1"
]
},
{
"id": "diamond_11_strange",
"desc": "Lesfip scale, 11-limit diamond, 10 cents tolerance",
"stepCount": "16",
"steps": [
"116.94577",
"177.73850",
"266.17058",
"322.76186",
"381.86836",
"498.63344",
"557.73994",
"614.33123",
"702.76331",
"763.55603",
"880.50180",
"936.15732",
"996.30671",
"1084.19509",
"1144.34448",
"2/1"
]
},
{
"id": "diamond_11_tr",
"desc": "11-limit triangular diamond lattice with 64/63 intervals removed",
"stepCount": "15",
"steps": [
"9/8",
"7/6",
"6/5",
"5/4",
"4/3",
"11/8",
"7/5",
"10/7",
"16/11",
"3/2",
"8/5",
"5/3",
"12/7",
"16/9",
"2/1"
]
},
{
"id": "diamond_15",
"desc": "15-limit diamond + 2nd ratios. See Novaro, 1927, Sistema Natural...",
"stepCount": "59",
"steps": [
"33/32",
"16/15",
"15/14",
"14/13",
"13/12",
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"15/13",
"7/6",
"13/11",
"32/27",
"6/5",
"39/32",
"11/9",
"16/13",
"5/4",
"14/11",
"9/7",
"13/10",
"21/16",
"4/3",
"15/11",
"11/8",
"18/13",
"7/5",
"45/32",
"64/45",
"10/7",
"13/9",
"16/11",
"22/15",
"3/2",
"32/21",
"20/13",
"14/9",
"11/7",
"8/5",
"13/8",
"18/11",
"64/39",
"5/3",
"27/16",
"22/13",
"12/7",
"26/15",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"24/13",
"13/7",
"28/15",
"15/8",
"64/33",
"2/1"
]
},
{
"id": "diamond_17",
"desc": "17-limit diamond",
"stepCount": "43",
"steps": [
"17/16",
"14/13",
"13/12",
"12/11",
"11/10",
"8/7",
"7/6",
"20/17",
"13/11",
"6/5",
"17/14",
"16/13",
"5/4",
"14/11",
"22/17",
"13/10",
"17/13",
"4/3",
"11/8",
"7/5",
"24/17",
"17/12",
"10/7",
"16/11",
"3/2",
"26/17",
"20/13",
"17/11",
"11/7",
"8/5",
"13/8",
"28/17",
"5/3",
"22/13",
"17/10",
"12/7",
"7/4",
"20/11",
"11/6",
"24/13",
"13/7",
"32/17",
"2/1"
]
},
{
"id": "diamond_17_a",
"desc": "17-limit, +9 diamond",
"stepCount": "55",
"steps": [
"18/17",
"17/16",
"14/13",
"13/12",
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"20/17",
"13/11",
"6/5",
"17/14",
"11/9",
"16/13",
"5/4",
"14/11",
"9/7",
"22/17",
"13/10",
"17/13",
"4/3",
"11/8",
"18/13",
"7/5",
"24/17",
"17/12",
"10/7",
"13/9",
"16/11",
"3/2",
"26/17",
"20/13",
"17/11",
"14/9",
"11/7",
"8/5",
"13/8",
"18/11",
"28/17",
"5/3",
"22/13",
"17/10",
"12/7",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"24/13",
"13/7",
"32/17",
"17/9",
"2/1"
]
},
{
"id": "diamond_17_b",
"desc": "17-limit, +9 +15 diamond, Denny Genovese, 3/2=384 Hz",
"stepCount": "65",
"steps": [
"18/17",
"17/16",
"16/15",
"15/14",
"14/13",
"13/12",
"12/11",
"11/10",
"10/9",
"9/8",
"17/15",
"8/7",
"15/13",
"7/6",
"20/17",
"13/11",
"6/5",
"17/14",
"11/9",
"16/13",
"5/4",
"14/11",
"9/7",
"22/17",
"13/10",
"17/13",
"4/3",
"15/11",
"11/8",
"18/13",
"7/5",
"24/17",
"17/12",
"10/7",
"13/9",
"16/11",
"22/15",
"3/2",
"26/17",
"20/13",
"17/11",
"14/9",
"11/7",
"8/5",
"13/8",
"18/11",
"28/17",
"5/3",
"22/13",
"17/10",
"12/7",
"26/15",
"7/4",
"30/17",
"16/9",
"9/5",
"20/11",
"11/6",
"24/13",
"13/7",
"28/15",
"15/8",
"32/17",
"17/9",
"2/1"
]
},
{
"id": "diamond_19",
"desc": "19-limit diamond",
"stepCount": "57",
"steps": [
"20/19",
"17/16",
"14/13",
"13/12",
"12/11",
"11/10",
"19/17",
"8/7",
"22/19",
"7/6",
"20/17",
"13/11",
"19/16",
"6/5",
"17/14",
"16/13",
"5/4",
"24/19",
"14/11",
"22/17",
"13/10",
"17/13",
"4/3",
"19/14",
"26/19",
"11/8",
"7/5",
"24/17",
"17/12",
"10/7",
"16/11",
"19/13",
"28/19",
"3/2",
"26/17",
"20/13",
"17/11",
"11/7",
"19/12",
"8/5",
"13/8",
"28/17",
"5/3",
"32/19",
"22/13",
"17/10",
"12/7",
"19/11",
"7/4",
"34/19",
"20/11",
"11/6",
"24/13",
"13/7",
"32/17",
"19/10",
"2/1"
]
},
{
"id": "diamond_27",
"desc": "Diamond 21 23 25 27, Christopher Vaisvil",
"stepCount": "13",
"steps": [
"27/25",
"25/23",
"23/21",
"27/23",
"25/21",
"9/7",
"14/9",
"42/25",
"46/27",
"42/23",
"46/25",
"50/27",
"2/1"
]
},
{
"id": "diamondupblock",
"desc": "Weak Fokker block with val <20 31 46 59|",
"stepCount": "20",
"steps": [
"16/15",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "diaphonic_7",
"desc": "7-tone Diaphonic Cycle, disjunctive form on 4/3 and 3/2",
"stepCount": "7",
"steps": ["12/11", "6/5", "4/3", "16/11", "8/5", "16/9", "2/1"]
},
{
"id": "diaphonic_10",
"desc": "10-tone Diaphonic Cycle",
"stepCount": "10",
"steps": [
"18/17",
"9/8",
"6/5",
"9/7",
"18/13",
"3/2",
"8/5",
"12/7",
"24/13",
"2/1"
]
},
{
"id": "diaphonic_12",
"desc": "12-tone Diaphonic Cycle, conjunctive form on 3/2 and 4/3",
"stepCount": "12",
"steps": [
"21/20",
"21/19",
"7/6",
"21/17",
"21/16",
"7/5",
"3/2",
"30/19",
"5/3",
"30/17",
"15/8",
"2/1"
]
},
{
"id": "diaphonic_12_a",
"desc": "2nd 12-tone Diaphonic Cycle, conjunctive form on 10/7 and 7/5",
"stepCount": "12",
"steps": [
"21/20",
"21/19",
"7/6",
"21/17",
"21/16",
"7/5",
"28/19",
"14/9",
"28/17",
"7/4",
"28/15",
"2/1"
]
},
{
"id": "diat_chrom",
"desc": "Diatonic- Chromatic, on the border between the chromatic and diatonic genera",
"stepCount": "7",
"steps": ["15/14", "15/13", "4/3", "3/2", "45/28", "45/26", "2/1"]
},
{
"id": "diat_dies_2",
"desc": "Dorian Diatonic, 2 part Diesis",
"stepCount": "7",
"steps": [
"33.33333",
"300.00000",
"500.00000",
"700.00000",
"733.33333",
"1000.00000",
"2/1"
]
},
{
"id": "diat_dies_5",
"desc": "Dorian Diatonic, 5 part Diesis",
"stepCount": "7",
"steps": [
"83.33333",
"300.00000",
"500.00000",
"700.00000",
"783.33333",
"1000.00000",
"2/1"
]
},
{
"id": "diat_enh",
"desc": "Diat. + Enharm. Diesis, Dorian Mode",
"stepCount": "7",
"steps": [
"50.00000",
"300.00000",
"500.00000",
"700.00000",
"750.00000",
"1000.00000",
"2/1"
]
},
{
"id": "diat_enh_2",
"desc": "Diat. + Enharm. Diesis, Dorian Mode 3 + 12 + 15 parts",
"stepCount": "7",
"steps": [
"50.00000",
"250.00000",
"500.00000",
"700.00000",
"750.00000",
"950.00000",
"2/1"
]
},
{
"id": "diat_enh_3",
"desc": "Diat. + Enharm. Diesis, Dorian Mode, 15 + 3 + 12 parts",
"stepCount": "7",
"steps": [
"250.00000",
"300.00000",
"500.00000",
"700.00000",
"950.00000",
"1000.00000",
"2/1"
]
},
{
"id": "diat_enh_4",
"desc": "Diat. + Enharm. Diesis, Dorian Mode, 15 + 12 + 3 parts",
"stepCount": "7",
"steps": [
"250.00000",
"450.00000",
"500.00000",
"700.00000",
"950.00000",
"1150.00000",
"2/1"
]
},
{
"id": "diat_enh_5",
"desc": "Dorian Mode, 12 + 15 + 3 parts",
"stepCount": "7",
"steps": [
"200.00000",
"450.00000",
"500.00000",
"700.00000",
"900.00000",
"1150.00000",
"2/1"
]
},
{
"id": "diat_enh_6",
"desc": "Dorian Mode, 12 + 3 + 15 parts",
"stepCount": "7",
"steps": [
"200.00000",
"250.00000",
"500.00000",
"700.00000",
"900.00000",
"950.00000",
"2/1"
]
},
{
"id": "diat_eq",
"desc": "Equal Diatonic, Islamic form, similar to 11/10 x 11/10 x 400/363",
"stepCount": "7",
"steps": [
"166.66667",
"333.33333",
"500.00000",
"700.00000",
"866.66667",
"1033.33333",
"2/1"
]
},
{
"id": "diat_eq_2",
"desc": "Equal Diatonic, 11/10 x 400/363 x 11/10",
"stepCount": "7",
"steps": ["11/10", "40/33", "4/3", "3/2", "33/20", "20/11", "2/1"]
},
{
"id": "diat_hemchrom",
"desc": "Diat. + Hem. Chrom. Diesis, Another genus of Aristoxenos, Dorian Mode",
"stepCount": "7",
"steps": [
"75.00000",
"300.00000",
"500.00000",
"700.00000",
"775.00000",
"1000.00000",
"2/1"
]
},
{
"id": "diat_smal",
"desc": "\"Smallest number\"diatonic scale",
"stepCount": "7",
"steps": ["8/7", "5/4", "4/3", "3/2", "5/3", "7/4", "2/1"]
},
{
"id": "diat_sofchrom",
"desc": "Diat. + Soft Chrom. Diesis, Another genus of Aristoxenos, Dorian Mode",
"stepCount": "7",
"steps": [
"66.66667",
"300.00000",
"500.00000",
"700.00000",
"766.66667",
"1000.00000",
"2/1"
]
},
{
"id": "diat_soft",
"desc": "Soft Diatonic genus 5 + 10 + 15 parts",
"stepCount": "7",
"steps": [
"83.33333",
"250.00000",
"500.00000",
"700.00000",
"783.33333",
"950.00000",
"2/1"
]
},
{
"id": "diat_soft_2",
"desc": "Soft Diatonic genus with equally divided Pyknon; Dorian Mode",
"stepCount": "7",
"steps": [
"125.00000",
"250.00000",
"500.00000",
"700.00000",
"825.00000",
"950.00000",
"2/1"
]
},
{
"id": "diat_soft_3",
"desc": "New Soft Diatonic genus with equally divided Pyknon; Dorian Mode; 1:1 pyknon",
"stepCount": "7",
"steps": [
"125.00000",
"375.00000",
"500.00000",
"700.00000",
"825.00000",
"1075.00000",
"2/1"
]
},
{
"id": "diat_soft_4",
"desc": "New Soft Diatonic genus with equally divided Pyknon; Dorian Mode; 1:1 pyknon",
"stepCount": "7",
"steps": [
"250.00000",
"375.00000",
"500.00000",
"700.00000",
"950.00000",
"1075.00000",
"2/1"
]
},
{
"id": "diat_13",
"desc": "This genus is from K.S's diatonic Hypodorian harmonia",
"stepCount": "7",
"steps": ["16/15", "16/13", "4/3", "3/2", "8/5", "24/13", "2/1"]
},
{
"id": "diat_15_inv",
"desc": "Inverted Tonos-15 Harmonia, a harmonic series from 15 from 30.",
"stepCount": "8",
"steps": ["16/15", "6/5", "4/3", "7/5", "22/15", "8/5", "26/15", "2/1"]
},
{
"id": "diat_15",
"desc": "Tonos-15 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": ["15/13", "5/4", "15/11", "10/7", "3/2", "5/3", "15/8", "2/1"]
},
{
"id": "diat_17",
"desc": "Tonos-17 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": [
"17/15",
"17/13",
"17/12",
"34/23",
"17/11",
"17/10",
"17/9",
"2/1"
]
},
{
"id": "diat_19",
"desc": "Tonos-19 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": [
"19/18",
"19/16",
"19/14",
"38/27",
"19/13",
"19/12",
"19/11",
"2/1"
]
},
{
"id": "diat_21_inv",
"desc": "Inverted Tonos-21 Harmonia, a harmonic series from 21 from 42.",
"stepCount": "8",
"steps": ["8/7", "26/21", "4/3", "10/7", "32/21", "12/7", "38/21", "2/1"]
},
{
"id": "diat_21",
"desc": "Tonos-21 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": ["21/19", "7/6", "21/16", "7/5", "3/2", "21/13", "7/4", "2/1"]
},
{
"id": "diat_23",
"desc": "Tonos-23 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": [
"23/21",
"23/20",
"23/18",
"23/17",
"23/16",
"23/14",
"23/13",
"2/1"
]
},
{
"id": "diat_25",
"desc": "Tonos-25 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": [
"25/22",
"5/4",
"25/18",
"25/17",
"25/16",
"25/14",
"25/13",
"2/1"
]
},
{
"id": "diat_27_inv",
"desc": "Inverted Tonos-27 Harmonia, a harmonic series from 27 from 54",
"stepCount": "8",
"steps": ["28/27", "32/27", "4/3", "13/9", "40/27", "14/9", "16/9", "2/1"]
},
{
"id": "diat_27",
"desc": "Tonos-27 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": ["9/8", "9/7", "27/20", "27/19", "3/2", "27/16", "27/14", "2/1"]
},
{
"id": "diat_29",
"desc": "Tonos-29 Diatonic and its own trite synemmenon Bb",
"stepCount": "8",
"steps": [
"29/26",
"29/24",
"29/22",
"29/21",
"29/20",
"29/18",
"29/16",
"2/1"
]
},
{
"id": "diat_31",
"desc": "Tonos-31 Diatonic. The disjunctive and conjunctive diatonic forms are the same",
"stepCount": "8",
"steps": [
"31/28",
"31/26",
"31/24",
"31/23",
"31/22",
"31/20",
"31/18",
"2/1"
]
},
{
"id": "diat_33",
"desc": "Tonos-33 Diatonic. The conjunctive form is 23 (Bb instead of B) 20 18 33/2",
"stepCount": "8",
"steps": ["11/10", "11/9", "11/8", "33/23", "3/2", "33/20", "11/6", "2/1"]
},
{
"id": "didy_chrom",
"desc": "Didymus Chromatic",
"stepCount": "7",
"steps": ["16/15", "10/9", "4/3", "3/2", "8/5", "5/3", "2/1"]
},
{
"id": "didy_chrom_1",
"desc": "Permuted Didymus Chromatic",
"stepCount": "7",
"steps": ["16/15", "32/25", "4/3", "3/2", "8/5", "48/25", "2/1"]
},
{
"id": "didy_chrom_2",
"desc": "Didymos's Chromatic, 6/5 x 25/24 x 16/15",
"stepCount": "7",
"steps": ["6/5", "5/4", "4/3", "3/2", "9/5", "15/8", "2/1"]
},
{
"id": "didy_chrom_3",
"desc": "Didymos's Chromatic, 25/24 x 16/15 x 6/5",
"stepCount": "7",
"steps": ["25/24", "10/9", "4/3", "3/2", "25/16", "5/3", "2/1"]
},
{
"id": "didy_diat",
"desc": "Didymus Diatonic",
"stepCount": "7",
"steps": ["16/15", "32/27", "4/3", "3/2", "8/5", "16/9", "2/1"]
},
{
"id": "didy_enh",
"desc": "Dorian mode of Didymos's Enharmonic",
"stepCount": "7",
"steps": ["32/31", "16/15", "4/3", "3/2", "48/31", "8/5", "2/1"]
},
{
"id": "didy_enh_2",
"desc": "Permuted Didymus Enharmonic",
"stepCount": "7",
"steps": ["256/243", "16/15", "4/3", "3/2", "128/81", "8/5", "2/1"]
},
{
"id": "didymus_19_sync",
"desc": "Didymus[19] hobbit (81/80) in synchronized tuning ! 3-2x, 5-x, 7-2x, where x is the smaller root of 16x^4 - 96x^3 + 216x^2 - 200x + 1",
"stepCount": "19",
"steps": [
"41.37646",
"119.28478",
"192.28609",
"233.66254",
"311.57087",
"384.57217",
"462.48050",
"503.85696",
"545.23341",
"654.76659",
"696.14304",
"737.51950",
"815.42783",
"888.42913",
"966.33746",
"1007.71391",
"1080.71522",
"1158.62354",
"2/1"
]
},
{
"id": "diesic_m",
"desc": "Minimal Diesic temperament, g=176.021, 5-limit",
"stepCount": "7",
"steps": [
"176.02067",
"352.04134",
"528.06201",
"704.08268",
"880.10335",
"1056.12402",
"2/1"
]
},
{
"id": "diesic_t",
"desc": "Tiny Diesic temperament, g=443.017, 5-limit",
"stepCount": "19",
"steps": [
"73.18474",
"129.05038",
"202.23513",
"258.10077",
"331.28551",
"387.15115",
"443.01679",
"516.20154",
"572.06718",
"645.25192",
"701.11756",
"774.30230",
"830.16795",
"886.03359",
"959.21833",
"1015.08397",
"1088.26871",
"1144.13436",
"2/1"
]
},
{
"id": "diff_19_9_4",
"desc": "Scale derived from (19,9,4) Type Q cyclic difference set, 19-tET",
"stepCount": "10",
"steps": [
"63.15789",
"252.63158",
"315.78947",
"378.94737",
"442.10526",
"568.42105",
"694.73684",
"1010.52632",
"1073.68421",
"2/1"
]
},
{
"id": "diff_31_72",
"desc": "Diff31, 11/9, 4/3, 7/5, 3/2, 7/4, 9/5 difference diamond, tempered to 72-tET",
"stepCount": "31",
"steps": [
"50.00000",
"83.33333",
"116.66667",
"150.00000",
"200.00000",
"233.33333",
"266.66667",
"316.66667",
"350.00000",
"383.33333",
"433.33333",
"466.66667",
"516.66667",
"533.33333",
"583.33333",
"616.66667",
"666.66667",
"683.33333",
"733.33333",
"766.66667",
"816.66667",
"850.00000",
"883.33333",
"933.33333",
"966.66667",
"1000.00000",
"1050.00000",
"1083.33333",
"1116.66667",
"1150.00000",
"2/1"
]
},
{
"id": "diff_31_h_8",
"desc": "(31, 15, 7) type H8 cyclic difference set, 31-tET",
"stepCount": "16",
"steps": [
"38.70968",
"77.41935",
"116.12903",
"154.83871",
"232.25806",
"309.67742",
"464.51613",
"580.64516",
"619.35484",
"658.06452",
"890.32258",
"929.03226",
"1045.16129",
"1122.58065",
"1161.29032",
"2/1"
]
},
{
"id": "diff_31_q",
"desc": "(31, 15, 7) type Q cyclic difference set, 31-tET",
"stepCount": "16",
"steps": [
"38.70968",
"77.41935",
"154.83871",
"193.54839",
"270.96774",
"309.67742",
"348.38710",
"387.09677",
"541.93548",
"619.35484",
"696.77419",
"735.48387",
"774.19355",
"967.74194",
"1083.87097",
"2/1"
]
},
{
"id": "diminished",
"desc": "Diminished temperament, g=94.134357 period=300.0, 7-limit",
"stepCount": "20",
"steps": [
"76.53743",
"94.13436",
"188.26871",
"282.40307",
"300.00000",
"376.53743",
"394.13436",
"488.26871",
"582.40307",
"600.00000",
"676.53743",
"694.13436",
"788.26871",
"882.40307",
"900.00000",
"976.53743",
"994.13436",
"1088.26871",
"1182.40307",
"2/1"
]
},
{
"id": "dimteta",
"desc": "A heptatonic form on the 9/7",
"stepCount": "7",
"steps": ["27/25", "27/23", "9/7", "14/9", "42/25", "42/23", "2/1"]
},
{
"id": "dimtetb",
"desc": "A pentatonic form on the 9/7",
"stepCount": "5",
"steps": ["9/8", "9/7", "14/9", "7/4", "2/1"]
},
{
"id": "dint",
"desc": "Breed reduction of 43 note scale of all tetrads sharing interval with 7-limit diamond",
"stepCount": "41",
"steps": [
"49/48",
"36/35",
"25/24",
"21/20",
"16/15",
"15/14",
"35/32",
"10/9",
"28/25",
"8/7",
"7/6",
"25/21",
"6/5",
"49/40",
"5/4",
"9/7",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"14/9",
"8/5",
"49/30",
"5/3",
"42/25",
"12/7",
"7/4",
"25/14",
"9/5",
"64/35",
"28/15",
"15/8",
"40/21",
"48/25",
"35/18",
"49/25",
"2/1"
]
},
{
"id": "div_fifth_1",
"desc": "Divided Fifth #1, From Schlesinger, see Chapter 8, p. 160",
"stepCount": "5",
"steps": ["24/23", "12/11", "4/3", "3/2", "2/1"]
},
{
"id": "div_fifth_2",
"desc": "Divided Fifth #2, From Schlesinger, see Chapter 8, p. 160",
"stepCount": "5",
"steps": ["16/15", "8/7", "4/3", "3/2", "2/1"]
},
{
"id": "div_fifth_3",
"desc": "Divided Fifth #3, From Schlesinger, see Chapter 8, p. 160",
"stepCount": "5",
"steps": ["28/27", "7/6", "4/3", "3/2", "2/1"]
},
{
"id": "div_fifth_4",
"desc": "Divided Fifth #4, From Schlesinger, see Chapter 8, p. 160",
"stepCount": "5",
"steps": ["21/20", "7/6", "21/16", "3/2", "2/1"]
},
{
"id": "div_fifth_5",
"desc": "Divided Fifth #5, From Schlesinger, see Chapter 8, p. 160",
"stepCount": "5",
"steps": ["11/10", "11/9", "11/8", "11/7", "2/1"]
},
{
"id": "divine_9",
"desc": "Gert Kramer�s Divine 9 tuning, 5-limit with one 7-limit interval (2011), 1/1=253.125 Hz",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"15625/12288",
"27/20",
"64/45",
"3/2",
"8/5",
"27/16",
"9/5",
"4375/2304",
"2/1"
]
},
{
"id": "dkring_1",
"desc": "Double-tie circular mirroring of 4:5:6:7",
"stepCount": "12",
"steps": [
"21/20",
"7/6",
"6/5",
"49/40",
"5/4",
"7/5",
"3/2",
"42/25",
"12/7",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "dkring_2",
"desc": "Double-tie circular mirroring of 3:5:7:9",
"stepCount": "12",
"steps": [
"21/20",
"7/6",
"63/50",
"9/7",
"27/20",
"7/5",
"3/2",
"14/9",
"49/30",
"5/3",
"9/5",
"2/1"
]
},
{
"id": "dkring_3",
"desc": "Double-tie circular mirroring of 6:7:8:9",
"stepCount": "12",
"steps": [
"9/8",
"8/7",
"7/6",
"9/7",
"4/3",
"72/49",
"3/2",
"32/21",
"12/7",
"16/9",
"27/14",
"2/1"
]
},
{
"id": "dkring_4",
"desc": "Double-tie circular mirroring of 7:8:9:10",
"stepCount": "12",
"steps": [
"10/9",
"9/8",
"8/7",
"5/4",
"9/7",
"45/32",
"10/7",
"81/56",
"45/28",
"25/14",
"9/5",
"2/1"
]
},
{
"id": "dodeceny",
"desc": "Degenerate eikosany 3)6 from 1.3.5.9.15.45 tonic 1.3.15",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"5/3",
"27/16",
"15/8",
"2/1"
]
},
{
"id": "domdimpajinjschis",
"desc": "Dominant-diminished-pajara-injera-schism wakalix",
"stepCount": "12",
"steps": [
"21/20",
"8/7",
"6/5",
"9/7",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"28/15",
"2/1"
]
},
{
"id": "donar_46",
"desc": "Donar[46] hobbit in 3390-tET, commas 4375/4374, 3025/3024 and 4225/4224",
"stepCount": "46",
"steps": [
"26.54867",
"48.84956",
"75.39823",
"106.90265",
"133.45133",
"160.00000",
"182.30088",
"208.84956",
"235.39823",
"257.69912",
"284.24779",
"315.75221",
"342.30088",
"364.60177",
"391.15044",
"417.69912",
"444.24779",
"466.54867",
"493.09735",
"524.60177",
"551.15044",
"573.45133",
"600.00000",
"626.54867",
"648.84956",
"675.39823",
"706.90265",
"733.45133",
"760.00000",
"782.30088",
"808.84956",
"835.39823",
"857.69912",
"884.24779",
"915.75221",
"942.30088",
"964.60177",
"991.15044",
"1017.69912",
"1044.24779",
"1066.54867",
"1093.09735",
"1124.60177",
"1151.15044",
"1173.45133",
"2/1"
]
},
{
"id": "dorian_chrom",
"desc": "Dorian Chromatic Tonos",
"stepCount": "24",
"steps": [
"16/15",
"8/7",
"32/27",
"64/53",
"16/13",
"4/3",
"16/11",
"32/21",
"64/41",
"8/5",
"16/9",
"2/1",
"32/15",
"16/7",
"64/27",
"128/53",
"32/13",
"8/3",
"32/11",
"64/21",
"128/41",
"16/5",
"32/9",
"4/1"
]
},
{
"id": "dorian_chrom_2",
"desc": "Schlesinger's Dorian Harmonia in the chromatic genus",
"stepCount": "7",
"steps": ["22/21", "11/10", "11/8", "11/7", "44/27", "22/13", "2/1"]
},
{
"id": "dorian_chrominv",
"desc": "A harmonic form of Schlesinger's Chromatic Dorian inverted",
"stepCount": "7",
"steps": ["24/23", "12/11", "14/11", "16/11", "17/11", "18/11", "2/1"]
},
{
"id": "dorian_diat",
"desc": "Dorian Diatonic Tonos",
"stepCount": "24",
"steps": [
"16/15",
"8/7",
"16/13",
"32/25",
"4/3",
"32/23",
"16/11",
"8/5",
"32/19",
"16/9",
"32/17",
"2/1",
"32/15",
"16/7",
"32/13",
"64/25",
"8/3",
"64/23",
"32/11",
"16/5",
"64/19",
"32/9",
"64/17",
"4/1"
]
},
{
"id": "dorian_diat_2",
"desc": "Schlesinger's Dorian Harmonia, a subharmonic series through 13 from 22",
"stepCount": "8",
"steps": ["11/10", "11/9", "11/8", "22/15", "11/7", "22/13", "11/6", "2/1"]
},
{
"id": "dorian_diat_2_inv",
"desc": "Inverted Schlesinger's Dorian Harmonia, a harmonic series from 11 from 22",
"stepCount": "8",
"steps": [
"12/11",
"13/11",
"14/11",
"15/11",
"16/11",
"18/11",
"20/11",
"2/1"
]
},
{
"id": "dorian_diatcon",
"desc": "A Dorian Diatonic with its own trite synemmenon replacing paramese",
"stepCount": "7",
"steps": ["11/10", "11/9", "11/8", "22/15", "11/7", "11/6", "2/1"]
},
{
"id": "dorian_diatred_11",
"desc": "Dorian mode of a diatonic genus with reduplicated 11/10",
"stepCount": "7",
"steps": ["11/10", "121/100", "4/3", "3/2", "33/20", "363/200", "2/1"]
},
{
"id": "dorian_enh",
"desc": "Dorian Enharmonic Tonos",
"stepCount": "24",
"steps": [
"16/15",
"8/7",
"64/55",
"128/109",
"32/27",
"4/3",
"16/11",
"64/43",
"128/85",
"32/21",
"16/9",
"2/1",
"32/15",
"16/7",
"128/55",
"256/109",
"64/27",
"8/3",
"32/11",
"128/43",
"256/85",
"64/21",
"32/9",
"4/1"
]
},
{
"id": "dorian_enh_2",
"desc": "Schlesinger's Dorian Harmonia in the enharmonic genus",
"stepCount": "7",
"steps": ["44/43", "22/21", "11/8", "11/7", "44/27", "22/13", "2/1"]
},
{
"id": "dorian_en_hinv",
"desc": "A harmonic form of Schlesinger's Dorian enharmonic inverted",
"stepCount": "7",
"steps": ["48/47", "24/23", "14/11", "16/11", "3/2", "17/11", "2/1"]
},
{
"id": "dorian_pent",
"desc": "Schlesinger's Dorian Harmonia in the pentachromatic genus",
"stepCount": "7",
"steps": ["55/53", "11/10", "11/8", "11/7", "55/34", "22/13", "2/1"]
},
{
"id": "dorian_pis",
"desc": "Diatonic Perfect Immutable System in the Dorian Tonos, a non-rep. 16 tone gamut",
"stepCount": "15",
"steps": [
"8/7",
"16/13",
"4/3",
"16/11",
"8/5",
"16/9",
"2/1",
"32/15",
"16/7",
"32/13",
"8/3",
"32/11",
"16/5",
"32/9",
"4/1"
]
},
{
"id": "dorian_schl",
"desc": "Schlesinger's Dorian Piano Tuning (Sub 22)",
"stepCount": "12",
"steps": [
"22/21",
"11/10",
"22/19",
"11/9",
"22/17",
"11/8",
"22/15",
"11/7",
"22/13",
"44/25",
"11/6",
"2/1"
]
},
{
"id": "dorian_tri_1",
"desc": "Schlesinger's Dorian Harmonia in the first trichromatic genus",
"stepCount": "7",
"steps": ["33/32", "33/31", "11/8", "11/7", "66/41", "33/20", "2/1"]
},
{
"id": "dorian_tri_2",
"desc": "Schlesinger's Dorian Harmonia in the second trichromatic genus",
"stepCount": "7",
"steps": ["33/32", "11/10", "11/8", "11/7", "66/41", "22/13", "2/1"]
},
{
"id": "doty_14",
"desc": "David Doty and Dale Soules, 7-limit just tuning of Other Music�s American gamelan",
"stepCount": "14",
"steps": [
"15/14",
"9/8",
"7/6",
"5/4",
"9/7",
"4/3",
"7/5",
"3/2",
"14/9",
"5/3",
"7/4",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "doublediadie",
"desc": "13-limit 8 cents tolerance",
"stepCount": "23",
"steps": [
"33.74084",
"117.02639",
"200.31193",
"234.05278",
"267.01514",
"349.85431",
"383.90973",
"466.95579",
"500.29239",
"550.41659",
"584.09479",
"616.67632",
"700.35457",
"733.69820",
"817.37646",
"849.95798",
"883.63619",
"933.76038",
"967.09699",
"1050.14305",
"1084.19847",
"1167.03764",
"2/1"
]
},
{
"id": "douwes",
"desc": "Claas Douwes recommendation of 24/23 and 15/14 steps for clavichord (1699)",
"stepCount": "12",
"steps": [
"24/23",
"180/161",
"1350/1127",
"386.24692",
"505.68973",
"579.37039",
"698.81319",
"772.49385",
"1127/675",
"161/90",
"28/15",
"2/1"
]
},
{
"id": "dow_high",
"desc": "Highest octave of Dowlands lute tuning, strings 5,6. 1/1=G (1610)",
"stepCount": "14",
"steps": [
"18/17",
"33/31",
"9/8",
"33/28",
"297/248",
"264/211",
"81/64",
"297/224",
"4/3",
"24/17",
"3/2",
"99/62",
"27/16",
"99/56"
]
},
{
"id": "dow_lmh",
"desc": "All three octaves of Dowland's lute tuning",
"stepCount": "55",
"steps": [
"33/31",
"9/8",
"33/28",
"264/211",
"4/3",
"24/17",
"44/31",
"3/2",
"11/7",
"99/62",
"352/211",
"27/16",
"99/56",
"16/9",
"32/17",
"176/93",
"2/1",
"44/21",
"66/31",
"1408/633",
"9/4",
"33/14",
"64/27",
"297/124",
"128/51",
"81/32",
"297/112",
"8/3",
"594/211",
"88/31",
"3/1",
"22/7",
"54/17",
"99/31",
"27/8",
"99/28",
"891/248",
"792/211",
"243/64",
"891/224",
"4/1",
"72/17",
"132/31",
"9/2",
"33/7",
"297/62",
"1056/211",
"81/16",
"297/56",
"16/3",
"96/17",
"6/1",
"198/31",
"27/4",
"99/14"
]
},
{
"id": "dow_low",
"desc": "Lowest octave of Dowlands lute tuning, strings 1,2,3. 1/1=G. (1610)",
"stepCount": "17",
"steps": [
"33/31",
"9/8",
"33/28",
"264/211",
"4/3",
"24/17",
"44/31",
"3/2",
"11/7",
"99/62",
"352/211",
"27/16",
"99/56",
"16/9",
"32/17",
"176/93",
"2/1"
]
},
{
"id": "dow_middle",
"desc": "Middle octave of Dowlands lute tuning, strings 3,4,5. 1/1=G (1610)",
"stepCount": "24",
"steps": [
"22/21",
"33/31",
"704/633",
"9/8",
"33/28",
"32/27",
"297/248",
"64/51",
"81/64",
"297/224",
"4/3",
"297/211",
"44/31",
"3/2",
"11/7",
"27/17",
"99/62",
"27/16",
"99/56",
"891/496",
"396/211",
"243/128",
"891/448",
"2/1"
]
},
{
"id": "dowland_12",
"desc": "subset of Dowland's lute tuning, lowest octave",
"stepCount": "12",
"steps": [
"33/31",
"9/8",
"33/28",
"264/211",
"4/3",
"24/17",
"3/2",
"99/62",
"27/16",
"99/56",
"32/17",
"2/1"
]
},
{
"id": "druri",
"desc": "Scale of druri dana of Siwoli, south Nias, Jaap Kunst",
"stepCount": "4",
"steps": ["153.00000", "386.00000", "539.00000", "2/1"]
},
{
"id": "dudon_3_limit_with_429",
"desc": "cycle of 10 pure fourths (4/3) from D ending in 429/256",
"stepCount": "12",
"steps": [
"256/243",
"9/8",
"32/27",
"8192/6561",
"4/3",
"1024/729",
"3/2",
"128/81",
"429/256",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "dudon_12_of_19_ht",
"desc": "12 of 19-tones harmonic temperament, from 27 to 35",
"stepCount": "12",
"steps": [
"187/180",
"67/60",
"6/5",
"56/45",
"241/180",
"25/18",
"269/180",
"14/9",
"5/3",
"161/90",
"28/15",
"2/1"
]
},
{
"id": "dudon_19_l_rocky_hwt",
"desc": "19-limit well-temperament, C to B achieving eq-b of bluesy DEG-type chords (2005)",
"stepCount": "12",
"steps": [
"256/243 ! C#",
"272/243 ! D",
"32/27 ! Eb",
"304/243 ! E",
"4/3 ! F",
"1024/729 ! F#",
"364/243 ! G",
"128/81 ! G#",
"1216/729 ! A",
"16/9 ! Bb",
"4096/2187 ! B",
"2/1"
]
},
{
"id": "dudon_a",
"desc": "Dudon Tetrachord A",
"stepCount": "7",
"steps": ["59/54", "11/9", "4/3", "3/2", "59/36", "11/6", "2/1"]
},
{
"id": "dudon_afshari",
"desc": "Avaz-e-Afshari -c JI interpretation",
"stepCount": "12",
"steps": [
"13/12",
"9/8",
"39/32",
"11/9",
"4/3",
"97/72",
"3/2",
"105/64",
"119/72",
"16/9",
"57/32",
"2/1"
]
},
{
"id": "dudon_aka",
"desc": "Cylf-scale (Baka sequence- pentatonic Slendro plus pure fifths)",
"stepCount": "12",
"steps": [
"112/111",
"212/185",
"128/111",
"244/185",
"736/555",
"4/3",
"56/37",
"846/555",
"64/37",
"976/555",
"368/185",
"2/1"
]
},
{
"id": "dudon_aksand",
"desc": "Fractal Aksaka - c sequence (x^2 - x = 1/4), 16:20:24:29:35, plus 163",
"stepCount": "12",
"steps": [
"2/1",
"29/24",
"29/12",
"4/3",
"8/3",
"35/24",
"35/12",
"5/3",
"10/3",
"163/96",
"163/48",
"2/1"
]
},
{
"id": "dudon_aluna",
"desc": "Chromatic scale based on F25, with turkish 31/25 segahs and many different thirds",
"stepCount": "12",
"steps": [
"107/100",
"28/25",
"239/200",
"31/25",
"267/200",
"71/50",
"3/2",
"8/5",
"167/100",
"89/50",
"93/50",
"2/1"
]
},
{
"id": "dudon_amlak",
"desc": "Amlak recurrent sequence (x^2 = x + 1/3), as a matrix for Ethiopian scales",
"stepCount": "12",
"steps": [
"1/1",
"45/38",
"19/16",
"91/76",
"107/76",
"27/19",
"455/304",
"3/2",
"30/19",
"575/304",
"36/19",
"2/1"
]
},
{
"id": "dudon_appalachian",
"desc": "Synchronous beating quasi-1/4 syntonic comma meantone temperament",
"stepCount": "12",
"steps": [
"4025/3852",
"3230/2889",
"128/107",
"5/4",
"1288/963",
"8075/5778",
"160/107",
"25/16",
"1610/963",
"5168/2889",
"200/107",
"2/1"
]
},
{
"id": "dudon_are_are_tapping",
"desc": "'Are'are tapping bamboo tubes as collected by Hugo Zemp in 1977, JI interpretation",
"stepCount": "12",
"steps": [
"2/1",
"51/44",
"51/22",
"29/22",
"29/11",
"65/44",
"65/22",
"13/8",
"13/4",
"20/11",
"40/11",
"2/1"
]
},
{
"id": "dudon_are_are_women_1",
"desc": "'Are'are women songs as collected by Hugo Zemp in 1977, JI interpretation (2009)",
"stepCount": "12",
"steps": [
"29/26",
"107/96",
"79/64",
"119/96",
"4/3",
"43/32",
"287/192",
"3/2",
"5/3",
"355/192",
"89/48",
"2/1"
]
},
{
"id": "dudon_are_are_women_2",
"desc": "'Are'are women songs as collected by Hugo Zemp in 1977, JI interpretation (Dudon 2009)",
"stepCount": "12",
"steps": [
"10/9",
"161/144",
"89/72",
"179/144",
"4/3",
"385/288",
"3/2",
"119/72",
"5/3",
"89/48",
"67/36",
"2/1"
]
},
{
"id": "dudon_armadillo",
"desc": "Triple equal-beating sequence from C to B, optimal major chords on white keys",
"stepCount": "12",
"steps": [
"8361/7936",
"555/496",
"75249/63488",
"621/496",
"84655/63488",
"2787/1984",
"371/248",
"25083/15872",
"3321/1984",
"112873/63488",
"929/496",
"2/1"
]
},
{
"id": "dudon_atlantis",
"desc": "Triple equal-beating of minor triads + septimal sevenths meantone sequence",
"stepCount": "12",
"steps": [
"327/314",
"1403/1256",
"188/157",
"12547/10048",
"210/157",
"3497/2512",
"469/314",
"1955/1256",
"4191/2512",
"281/157",
"37399/20096",
"2/1"
]
},
{
"id": "dudon_aulos",
"desc": "Double clarinet -c version of Ptolemy's Diatonon Homalon",
"stepCount": "12",
"steps": [
"12/11",
"35/32",
"6/5",
"53/44",
"4/3",
"1/1",
"3/2",
"1/1",
"18/11",
"9/5",
"317/176",
"2/1"
]
},
{
"id": "dudon_b",
"desc": "Dudon Tetrachord B",
"stepCount": "7",
"steps": ["13/12", "59/48", "4/3", "3/2", "13/8", "59/32", "2/1"]
},
{
"id": "dudon_baka",
"desc": "Baka typical semifourth pentatonic, can also be accepted as a circular Slendro",
"stepCount": "12",
"steps": [
"8/7",
"668/581",
"768/581",
"768/581",
"110/83",
"880/581",
"880/581",
"144/83",
"144/83",
"1152/581",
"1160/581",
"2/1"
]
},
{
"id": "dudon_bala_ribbon",
"desc": "Parizekmic scale based on a double Bala sequence",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"13/10",
"4/3",
"83/60",
"3/2",
"8/5",
"26/15",
"9/5",
"39/20",
"2/1"
]
},
{
"id": "dudon_bala_ribbon_19",
"desc": "Parizekmic scale based on a double Bala sequence",
"stepCount": "19",
"steps": [
"203/192",
"13/12",
"9/8",
"443/384",
"39/32",
"5/4",
"125/96",
"4/3",
"45/32",
"277/192",
"3/2",
"203/128",
"13/8",
"5/3",
"83/48",
"117/64",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "dudon_bala_ribbon_24",
"desc": "Parizekmic scale based on a double Bala sequence",
"stepCount": "24",
"steps": [
"197/192",
"203/192",
"13/12",
"9/8",
"443/384",
"227/192",
"39/32",
"5/4",
"125/96",
"4/3",
"131/96",
"45/32",
"277/192",
"3/2",
"197/128",
"203/128",
"13/8",
"5/3",
"83/48",
"341/192",
"117/64",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "dudon_balafon_semifo",
"desc": "Burkinabe typical semifourth pentatonic balafon feast scale",
"stepCount": "12",
"steps": [
"135/104",
"26/23",
"104/69",
"207/160",
"13/10",
"45/26",
"104/69",
"2/1",
"69/40",
"26/15",
"52/23",
"2/1"
]
},
{
"id": "dudon_balasept_above",
"desc": "5.7.13.15 tuning based on a single Balasept sequence",
"stepCount": "12",
"steps": [
"517/480",
"277/240",
"597/480",
"13/10",
"4/3",
"689/480",
"3/2",
"53/32",
"26/15",
"28/15",
"39/20",
"2/1"
]
},
{
"id": "dudon_balasept_under",
"desc": "5.7.13.15.21 tuning based on a single Balasept sequence",
"stepCount": "12",
"steps": [
"21/20",
"277/240",
"97/80",
"13/10",
"4/3",
"7/5",
"3/2",
"97/60",
"26/15",
"28/15",
"39/20",
"2/1"
]
},
{
"id": "dudon_bali_balaeb_14",
"desc": "Bali-Bala[14] (676/675 tempering), equal-beating version",
"stepCount": "14",
"steps": [
"43.261584366",
"205.3907325072",
"248.6523168732",
"291.9139012392",
"454.0430493804",
"497.3046337464",
"659.4337818876",
"702.6953662536",
"745.9569506196",
"908.0860987608",
"951.3476831268",
"994.6092674928",
"1156.738415634",
"2/1"
]
},
{
"id": "dudon_bambara",
"desc": "Typical pentatonic balafon ceremonial tuning from Mali or Burkina Faso",
"stepCount": "12",
"steps": [
"1/1",
"1448/1273",
"1448/1273",
"1688/1273",
"1688/1273",
"1688/1273",
"1920/1273",
"1920/1273",
"2184/1273",
"2184/1273",
"2/1",
"2/1"
]
},
{
"id": "dudon_bayati_in_d",
"desc": "Bayati (or Husayni) maqam in D",
"stepCount": "12",
"steps": [
"256/255",
"96/85",
"104/85",
"21/17",
"114/85",
"23/17",
"128/85",
"513/340",
"144/85",
"156/85",
"469/255",
"2/1"
]
},
{
"id": "dudon_baziguzuk",
"desc": "8 9 11 12 13 defective Mohajira (Dudon 1985)",
"stepCount": "12",
"steps": [
"1/1",
"13/12",
"4/3",
"13/12",
"4/3",
"11/6",
"3/2",
"11/6",
"4/3",
"11/6",
"3/2",
"2/1"
]
},
{
"id": "dudon_bhairav",
"desc": "Bhairav thaat raga, based on 17th harmonic",
"stepCount": "12",
"steps": [
"17/16",
"16/15",
"5/4",
"301/240",
"4/3",
"1/1",
"3/2",
"51/32",
"307/192",
"179/96",
"15/8",
"2/1"
]
},
{
"id": "dudon_bhairavi",
"desc": "Bhairavi thaat raga, by Dudon (2004)",
"stepCount": "12",
"steps": [
"17/16",
"19/17",
"19/16",
"304/255",
"4/3",
"17/12",
"3/2",
"19/12",
"1216/765",
"57/32",
"152/85",
"2/1"
]
},
{
"id": "dudon_bhatiyar",
"desc": "Early morning North indian raga, a modelisation based on Amlak 57",
"stepCount": "12",
"steps": [
"20/19",
"271/256",
"5/4",
"24/19",
"4/3",
"80/57",
"3/2",
"57/34",
"32/19",
"107/57",
"36/19",
"2/1"
]
},
{
"id": "dudon_bhavapriya",
"desc": "Bhavapriya (South indian, prati madhyama mela # 44) or Bhavani (North indian)",
"stepCount": "12",
"steps": [
"17/16",
"273/256",
"19/16",
"307/256",
"45/32",
"361/256",
"3/2",
"51/32",
"205/128",
"16/9",
"57/32",
"2/1"
]
},
{
"id": "dudon_brazil",
"desc": "Triple equal-beating 1/5 syntonic comma meantone, limited to 8 tones",
"stepCount": "12",
"steps": [
"405/404",
"1809/1616",
"5/4",
"64801/51712",
"135/101",
"2321289/1654784",
"1209/808",
"10155/6464",
"10827/6464",
"6045/3232",
"387843/206848",
"2/1"
]
},
{
"id": "dudon_burma",
"desc": "Burmese typical diatonic scale, compatible with modes Pule, Thanyu, Autpyin",
"stepCount": "12",
"steps": [
"1216/1161",
"48/43",
"464/387",
"1448/1161",
"518/387",
"536/387",
"1735/1161",
"1792/1161",
"1936/1161",
"2080/1161",
"80/43",
"2/1"
]
},
{
"id": "dudon_buzurg",
"desc": "Decaphonic system inspired by medieval Persian mode Buzurg (Safi al-Din), Dudon 1997",
"stepCount": "12",
"steps": [
"14/13",
"13/12",
"8/7",
"26/21",
"55/42",
"39/28",
"3/2",
"21/13",
"13/8",
"12/7",
"13/7",
"2/1"
]
},
{
"id": "dudon_byzantine",
"desc": "Byzantine scale, JI interpretation and -c extrapolation of turkish Hijaz in C",
"stepCount": "12",
"steps": [
"69/64",
"13/12",
"239/192",
"5/4",
"85/64",
"4/3",
"3/2",
"155/96",
"13/8",
"85/48",
"16/9",
"2/1"
]
},
{
"id": "dudon_c_1",
"desc": "Differentially coherent scale in interval class 1",
"stepCount": "7",
"steps": ["19/16", "5/4", "81/64", "3/2", "101/64", "15/8", "2/1"]
},
{
"id": "dudon_c_12",
"desc": "Differentially coherent scale in interval class 1 and 2",
"stepCount": "7",
"steps": ["37/32", "5/4", "21/16", "3/2", "13/8", "29/16", "2/1"]
},
{
"id": "dudon_chandrakaus",
"desc": "Chandrakaus from Bb on black keys plus other version from D on white keys",
"stepCount": "12",
"steps": [
"1/1",
"19/18",
"10/9",
"91/72",
"91/72",
"95/72",
"101/72",
"113/72",
"19/12",
"5/3",
"5/3",
"2/1"
]
},
{
"id": "dudon_chiffonie",
"desc": "Hurdy-Gurdy variation on fractal Gazelle (Rebab tuning)",
"stepCount": "12",
"steps": [
"1/1",
"161/144",
"11/9",
"5/4",
"43/32",
"65/48",
"3/2",
"865/576",
"5/3",
"131/72",
"29/16",
"2/1"
]
},
{
"id": "dudon_chromatic_subh",
"desc": "Chromatic subharmonic scale using smallest possible numbers",
"stepCount": "12",
"steps": [
"16/15",
"17/15",
"6/5",
"19/15",
"4/3",
"43/30",
"3/2",
"8/5",
"17/10",
"9/5",
"19/10",
"2/1"
]
},
{
"id": "dudon_coherent_shrutis",
"desc": "12 of the 22 shrutis (cycle of fifths from A to D), differentially coherent with C or 2C",
"stepCount": "12",
"steps": [
"19/18",
"9/8",
"19/16",
"5/4",
"4/3",
"45/32",
"3/2",
"19/12",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "dudon_cometslendro_1",
"desc": "Five septimal tone comets (quasi auto-coherent intervals) in one octave",
"stepCount": "12",
"steps": [
"280/279",
"320/279",
"427/372",
"322/279",
"491/372",
"370/279",
"47/31",
"424/279",
"323/186",
"485/279",
"488/279",
"2/1"
]
},
{
"id": "dudon_cometslendro_2",
"desc": "Five septimal tone comets (quasi auto-coherent intervals) in one octave",
"stepCount": "12",
"steps": [
"4117/3600",
"517/450",
"473/360",
"95/72",
"33/25",
"679/450",
"10913/7200",
"26/15",
"1567/900",
"448/225",
"448/225",
"2/1"
]
},
{
"id": "dudon_comptine_h_3",
"desc": "1/4 pyth. comma meantone sequence between G and B, completed by 8 pure fifths",
"stepCount": "12",
"steps": [
"2225/2112",
"592/528",
"20025/16896",
"1323/1056",
"4/3",
"29667/21120",
"3/2",
"6675/4224",
"885/528",
"60075/33792",
"9889/5280",
"2/1"
]
},
{
"id": "dudon_comptine",
"desc": "1/4 pyth. comma meantone sequence between C and E, completed by 8 pure fifths",
"stepCount": "12",
"steps": [
"256/243",
"21995/19683",
"32/27",
"8192/6561",
"4/3",
"1024/729",
"9808/6561",
"128/81",
"10960/6561",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "dudon_country_blues",
"desc": "Differentially-coherent 12 tones country blues scale",
"stepCount": "12",
"steps": [
"101/96",
"9/8",
"29/24",
"5/4",
"4/3",
"67/48",
"3/2",
"19/12",
"5/3",
"43/24",
"15/8",
"2/1"
]
},
{
"id": "dudon_countrysongs",
"desc": "CDEG chords and all transpositions equal-beating meantone sequence",
"stepCount": "12",
"steps": [
"7413/7072",
"495/442",
"264/221",
"4429/3536",
"591/442",
"9925/7072",
"1323/884",
"11097/7072",
"2961/1768",
"395/221",
"6633/3536",
"2/1"
]
},
{
"id": "dudon_crying_commas",
"desc": "Pentatonic differentiallly-coherent scale with crying commas",
"stepCount": "12",
"steps": [
"9/8",
"217/192",
"437/384",
"55/48",
"4/3",
"3/2",
"3/2",
"5/3",
"323/192",
"163/96",
"55/32",
"2/1"
]
},
{
"id": "dudon_darbari",
"desc": "Darbari Kanada (midnight raga)",
"stepCount": "12",
"steps": [
"1/1",
"9/8",
"19/16",
"115/96",
"4/3",
"9/8",
"3/2",
"19/12",
"115/72",
"57/32",
"115/64",
"2/1"
]
},
{
"id": "dudon_diat",
"desc": "Dudon Neutral Diatonic",
"stepCount": "7",
"steps": ["9/8", "27/22", "59/44", "3/2", "18/11", "81/44", "2/1"]
},
{
"id": "dudon_diatess",
"desc": "Sequence of 11 Diatess fifths from Eb (75)",
"stepCount": "12",
"steps": [
"16549/15984",
"1114/999",
"400/333",
"4969/3996",
"446/333",
"1385/999",
"1492/999",
"8237/5328",
"1109/666",
"1792/999",
"1855/999",
"2/1"
]
},
{
"id": "dudon_didymus",
"desc": "Greek-genre scale rich in commas",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"6/5",
"56/45",
"7/5",
"45/32",
"3/2",
"8/5",
"5/3",
"9/5",
"28/15",
"2/1"
]
},
{
"id": "dudon_egyptian_rast",
"desc": "Egyptian style Rast -c modelisation",
"stepCount": "12",
"steps": [
"107/96",
"9/8",
"11/9",
"59/48",
"4/3",
"1/1",
"3/2",
"5/3",
"121/72",
"11/6",
"133/72",
"2/1"
]
},
{
"id": "dudon_evan_thai",
"desc": "Evan differentially-coherent double Thai heptaphone",
"stepCount": "12",
"steps": [
"14107/14080",
"243/220",
"6235/5632",
"537/440",
"74/55",
"2373/1760",
"327/220",
"5243/3520",
"289/176",
"23171/14080",
"3193/1760",
"2/1"
]
},
{
"id": "dudon_flamenca",
"desc": "Flamenco chromatic scale around the 17th harmonic, in A (= guitar), Dudon 2005",
"stepCount": "12",
"steps": [
"160/153",
"512/459",
"32/27",
"64/51",
"4/3",
"1216/867",
"76/51",
"80/51",
"256/153",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "dudon_fong",
"desc": "Differentially-coherent Thai scale, with double seventh note",
"stepCount": "12",
"steps": [
"97/88",
"97/88",
"107/88",
"107/88",
"59/44",
"65/44",
"1041/704",
"287/176",
"18/11",
"633/352",
"639/352",
"2/1"
]
},
{
"id": "dudon_gayakapriya",
"desc": "South indian raga with Ethiopian flavors, interpreted through a 19-limit Amlak sequence",
"stepCount": "12",
"steps": [
"1/1",
"9/8",
"19/16",
"115/96",
"5/4",
"3/2",
"3/2",
"19/12",
"51/32",
"15/8",
"361/192",
"2/1"
]
},
{
"id": "dudon_gnawa_pelog",
"desc": "Differentially-coherent model of a Gnawa scale, with Pelog variations",
"stepCount": "12",
"steps": [
"141/140",
"39/35",
"157/140",
"191/140",
"48/35",
"48/35",
"52/35",
"52/35",
"3/2",
"64/35",
"64/35",
"2/1"
]
},
{
"id": "dudon_golden_h_7_eb",
"desc": "12 of 19/31/50 etc... Golden meantone harmonic 7-c and eq-b version",
"stepCount": "12",
"steps": [
"44603/42752",
"2987/2672",
"200/167",
"3337/2672",
"447/334",
"29839/21376",
"999/668",
"33339/21376",
"4465/2672",
"299/167",
"2495/1336",
"2/1"
]
},
{
"id": "dudon_gulu_nem",
"desc": "5 tones Pelog from a sequence of very low \"Gulu-nem\"fifths (about 5/9 of an octave)",
"stepCount": "12",
"steps": [
"1/1",
"1393/1284",
"1393/1284",
"2015/1712",
"2015/1712",
"2015/1712",
"473/321",
"473/321",
"4105/2568",
"4105/2568",
"4105/2568",
"2/1"
]
},
{
"id": "dudon_harm_minor",
"desc": "So-called \"harmonic\"minor scale, also raga Kiravani, one of Dudon's versions",
"stepCount": "12",
"steps": [
"143/128",
"9/8",
"19/16",
"6/5",
"4/3",
"429/320",
"3/2",
"8/5",
"57/32",
"9/5",
"301/160",
"2/1"
]
},
{
"id": "dudon_harry",
"desc": "Hommage to Harry Partch, 20th century just intonation pioneer (1901-1974)",
"stepCount": "12",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"21/16",
"4/3",
"40/27",
"3/2",
"32/21",
"14/9",
"7/4",
"2/1"
]
},
{
"id": "dudon_hawaiian",
"desc": "Equal-beating lapsteel-style Major 6th chords (C:E:G:A:C:E) meantone sequence",
"stepCount": "12",
"steps": [
"1418440/1360773",
"168926/151197",
"60354/50399",
"566204/453591",
"67431/50399",
"1897784/1360773",
"75338/50399",
"2120315/1360773",
"84172/50399",
"90219/50399",
"846376/453591",
"2/1"
]
},
{
"id": "dudon_hijazira",
"desc": "Hijazira = Hijaz-Mohajira",
"stepCount": "7",
"steps": ["13/12", "5/4", "4/3", "3/2", "13/8", "11/6", "2/1"]
},
{
"id": "dudon_hiroyoshi",
"desc": "Japanese koto most famous mode, also Ethiopian minor scale, etc.",
"stepCount": "12",
"steps": [
"107/152",
"3/4",
"5/4",
"143/114",
"45/32",
"429/304",
"3/2",
"1/1",
"5/4",
"15/8",
"143/76",
"2/1"
]
},
{
"id": "dudon_homayun",
"desc": "Homayun in G",
"stepCount": "12",
"steps": [
"1/1",
"9/8",
"9/8",
"39/32",
"85/64",
"85/64",
"3/2",
"3/2",
"13/8",
"13/8",
"119/64",
"2/1"
]
},
{
"id": "dudon_hoomi",
"desc": "Hoomi singing scale in F/F# (on black keys), or in C or G, CFGAC^equal-beating sequence",
"stepCount": "12",
"steps": [
"1/1",
"857/766",
"857/766",
"480/383",
"512/383",
"512/383",
"573/383",
"573/383",
"1283/766",
"1283/766",
"718/383",
"2/1"
]
},
{
"id": "dudon_ifbis",
"desc": "Ifbis -c recurrent sequence: x^5 - x^3 = 1 (not traditional)",
"stepCount": "12",
"steps": [
"61/56",
"8/7",
"17/14",
"9/7",
"75/56",
"10/7",
"3/2",
"11/7",
"93/56",
"7/4",
"13/7",
"2/1"
]
},
{
"id": "dudon_iph_arax",
"desc": "Iph-Arax heptatone",
"stepCount": "6",
"steps": [
"93.88582",
"366.90974",
"466.18060",
"560.06655",
"833.09030",
"926.97633"
]
},
{
"id": "dudon_isrep",
"desc": "Fractal Isrep -c recurrent sequence, x^2 = 8x - 8 from F=64",
"stepCount": "12",
"steps": [
"2/1",
"75/64",
"75/32",
"1/1",
"11/8",
"11/4",
"3/2",
"3/1",
"13/8",
"13/4",
"75/64",
"2/1"
]
},
{
"id": "dudon_jamlak",
"desc": "Cycle of fifths developped around a 19-limit Amlak sequence",
"stepCount": "12",
"steps": [
"321/320",
"9/8",
"381/320",
"101/80",
"107/80",
"57/40",
"3/2",
"127/80",
"539/320",
"571/320",
"19/10",
"2/1"
]
},
{
"id": "dudon_jazz",
"desc": "Jazz in 7 tones",
"stepCount": "12",
"steps": [
"1/1",
"301/256",
"19/16",
"4/3",
"171/128",
"361/256",
"767/512",
"3/2",
"5/3",
"455/256",
"57/32",
"2/1"
]
},
{
"id": "dudon_jobim",
"desc": "Triple equal-beating 1/5 syntonic comma meantone, full 12 tones scale",
"stepCount": "12",
"steps": [
"13893147/13238272",
"1809/1616",
"246989/206848",
"64801/51712",
"135/101",
"2321289/1654784",
"1209/808",
"10155/6464",
"10827/6464",
"184251/103424",
"387843/206848",
"2/1"
]
},
{
"id": "dudon_jog",
"desc": "Jog with (ascent only) additional 15/8",
"stepCount": "12",
"steps": [
"1/1",
"19/16",
"6/5",
"5/4",
"4/3",
"43/32",
"3/2",
"3/2",
"16/9",
"43/24",
"15/8",
"2/1"
]
},
{
"id": "dudon_joged_bumbung",
"desc": "Typical Balinese grantang and tingklik (bamboo xylophones) slendro tuning",
"stepCount": "12",
"steps": [
"1/1",
"1448/1273",
"8/7",
"1688/1273",
"1688/1273",
"4/3",
"3/2",
"1920/1273",
"12/7",
"2184/1273",
"2/1",
"2/1"
]
},
{
"id": "dudon_kalyana",
"desc": "Kalyana thaat raga, harmonics 3-5-17-19-43 version by Dudon 2004",
"stepCount": "12",
"steps": [
"19/17",
"172/153",
"5/4",
"64/51",
"45/32",
"24/17",
"3/2",
"256/153",
"57/34",
"15/8",
"32/17",
"2/1"
]
},
{
"id": "dudon_kanakangi",
"desc": "Raga Kanakangi (Karnatic music, suddha madhyama mela # 1)",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"9/8",
"4/3",
"4/3",
"3/2",
"3/2",
"19/12",
"5/3",
"5/3",
"2/1",
"2/1"
]
},
{
"id": "dudon_kellner_eb",
"desc": "JI version of Anton Kellner 1/5 Pyth.c well-temperament, based on Skisni algorithm",
"stepCount": "12",
"steps": [
"256/243",
"272/243",
"32/27",
"2738/2187",
"4/3",
"1024/729",
"3272/2187",
"128/81",
"3664/2187",
"16/9",
"1369/729",
"2/1"
]
},
{
"id": "dudon_kidarvani",
"desc": "Kidarvani, combination tuning of ragas Kirvani and Darbari",
"stepCount": "10",
"steps": [
"9/8",
"19/16",
"6/5",
"4/3",
"3/2",
"8/5",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "dudon_kirvanti",
"desc": "Raga Kirvanti (known also as Hungarian Gypsy scale)",
"stepCount": "12",
"steps": [
"1/1",
"9/8",
"19/16",
"6/5",
"64/45",
"57/40",
"3/2",
"51/32",
"8/5",
"15/8",
"303/160",
"2/1"
]
},
{
"id": "dudon_kora_snd",
"desc": "Kora tuning in the Mandinka semi-neutral diatonic style",
"stepCount": "12",
"steps": [
"129/104",
"29/26",
"35/26",
"129/104",
"35/26",
"43/26",
"3/2",
"24/13",
"345/208",
"2/1",
"24/13",
"2/1"
]
},
{
"id": "dudon_kora_chimere",
"desc": "Kora diatonic, slightly neutral",
"stepCount": "12",
"steps": [
"635/382",
"425/382",
"2/1",
"945/764",
"256/191",
"945/382",
"285/191",
"512/191",
"635/382",
"1415/764",
"570/191",
"2/1"
]
},
{
"id": "dudon_kumoyoshi_19_l",
"desc": "Japanese famous mode, -c 17+19th harmonics interpretation",
"stepCount": "12",
"steps": [
"3/2",
"19/18",
"17/16",
"1/1",
"4/3",
"17/8",
"3/2",
"2/1",
"19/12",
"51/32",
"1/1",
"2/1"
]
},
{
"id": "dudon_lakota",
"desc": "Comma variations add to the richness of differential tones",
"stepCount": "12",
"steps": [
"1/1",
"19/16",
"6/5",
"29/24",
"4/3",
"107/80",
"3/2",
"1/1",
"5/3",
"57/32",
"9/5",
"2/1"
]
},
{
"id": "dudon_liane",
"desc": "Class 1 differentially coherent interleaved intervals, hexatonic scale",
"stepCount": "12",
"steps": [
"6273/6272",
"55/49",
"9/8",
"121/98",
"969/784",
"10/7",
"561/392",
"11/7",
"11/7",
"89/49",
"51/28",
"2/1"
]
},
{
"id": "dudon_lucie",
"desc": "Sequence of 11 fractal Lucie fifths (exactly 695,5023126 c.) from Eb",
"stepCount": "12",
"steps": [
"1477/1424",
"1789/1602",
"320/267",
"111/89",
"1072/801",
"1489/1068",
"133/89",
"2229/1424",
"297/178",
"4304/2403",
"663/356",
"2/1"
]
},
{
"id": "dudon_madhuvanti",
"desc": "Madhuvanti (also called Ambika), late evening raga",
"stepCount": "12",
"steps": [
"1/1",
"9/8",
"19/16",
"6/5",
"45/32",
"91/64",
"3/2",
"429/256",
"27/16",
"15/8",
"483/256",
"2/1"
]
},
{
"id": "dudon_mahur",
"desc": "Persian Dastgah Mahur",
"stepCount": "12",
"steps": [
"143/128",
"9/8",
"5/4",
"1287/1024",
"4/3",
"171/128",
"3/2",
"5/3",
"429/256",
"57/32",
"15/8",
"2/1"
]
},
{
"id": "dudon_mandinka",
"desc": "Guinean Balafon circular tuning, neutral diatonic -c interpretation",
"stepCount": "12",
"steps": [
"1/1",
"581/524",
"581/524",
"161/131",
"176/131",
"176/131",
"195/131",
"195/131",
"865/524",
"865/524",
"240/131",
"2/1"
]
},
{
"id": "dudon_marovany",
"desc": "Typical Malagasy scale, neutral diatonic, multiways -c and eq-b",
"stepCount": "12",
"steps": [
"783/704",
"3141/2816",
"2/1",
"871/704",
"59/44",
"871/352",
"525/352",
"1053/704",
"73/44",
"10393/5632",
"5197/2816",
"2/1"
]
},
{
"id": "dudon_marva",
"desc": "Raga Marva, differential-coherent version, modelized by Jacques Dudon",
"stepCount": "12",
"steps": [
"20/19",
"17/16",
"5/4",
"24/19",
"1/1",
"45/32",
"27/19",
"5/3",
"32/19",
"15/8",
"36/19",
"2/1"
]
},
{
"id": "dudon_meancaline",
"desc": "12 of 19-tones quasi-equal HT with coherent semifourths on black keys",
"stepCount": "12",
"steps": [
"1420/1371",
"7648/6855",
"8224/6855",
"2844/2285",
"9178/6855",
"3168/2285",
"2048/1371",
"10606/6855",
"3808/2285",
"4096/2285",
"12736/6855",
"2/1"
]
},
{
"id": "dudon_melkis_3_f",
"desc": "Sequence of 6 Melkis fourths from G, then 3 pure fourths between C# and E",
"stepCount": "12",
"steps": [
"540/511",
"573/511",
"2427/2044",
"640/511",
"2727/2044",
"720/511",
"766/511",
"1619/1022",
"856/511",
"2079/1168",
"960/511",
"2/1"
]
},
{
"id": "dudon_melkis",
"desc": "Sequence of 11 Melkis fourths (499.11472 c.) from D",
"stepCount": "12",
"steps": [
"30739/29088",
"3064/2727",
"3238/2727",
"36499/29088",
"539/404",
"15379/10908",
"4088/2727",
"160/101",
"584345/349056",
"1618/909",
"10259/5454",
"2/1"
]
},
{
"id": "dudon_meso_iph_7",
"desc": "Neutral diatonic variation based on two Iph fractal series",
"stepCount": "7",
"steps": [
"3072/2783",
"3440/2783",
"3712/2783",
"4168/2783",
"4608/2783",
"224/121",
"2/1"
]
},
{
"id": "dudon_meso_iph_12",
"desc": "Partial Meso-Iph fifth transposition of two Iph fractal series (2010)",
"stepCount": "12",
"steps": [
"3008/2783",
"3072/2783",
"3184/2783",
"3440/2783",
"3712/2783",
"3936/2783",
"4168/2783",
"4608/2783",
"4864/2783",
"4960/2783",
"224/121",
"2/1"
]
},
{
"id": "dudon_michemine",
"desc": "Triple equal-beating of all minor triads meantone sequence",
"stepCount": "12",
"steps": [
"333711/321536",
"1403/1256",
"188/157",
"12547/10048",
"210/157",
"112283/80384",
"469/314",
"1006387/643072",
"4191/2512",
"281/157",
"37399/20096",
"2/1"
]
},
{
"id": "dudon_moha_baya",
"desc": "Mohajira + Bayati (Dudon) 3 + 4 + 3 Mohajira and 3 + 3 + 4 Bayati tetrachords",
"stepCount": "7",
"steps": [
"150.00000",
"350.00000",
"500.00000",
"700.00000",
"850.00000",
"1000.00000",
"2/1"
]
},
{
"id": "dudon_mohajira_r",
"desc": "Jacques Dudon, JI Mohajira, Lumi�res audibles",
"stepCount": "7",
"steps": ["13/12", "59/48", "4/3", "3/2", "13/8", "11/6", "2/1"]
},
{
"id": "dudon_mohajira",
"desc": "Dudon's Mohajira, neutral diatonic. g^5-g^4=1/2",
"stepCount": "7",
"steps": [
"153.26216",
"348.91261",
"502.17478",
"697.82522",
"851.08739",
"1046.73784",
"2/1"
]
},
{
"id": "dudon_mohajira_117",
"desc": "Jacques Dudon Mohajira, 1/1 vol.2 no.1, p. 11, with 3/2 (117:78)",
"stepCount": "7",
"steps": ["44/39", "16/13", "4/3", "3/2", "64/39", "24/13", "2/1"]
},
{
"id": "dudon_mougi",
"desc": "Tsigan-style raga, based on the 19/16 minor third -c properties",
"stepCount": "12",
"steps": [
"9/8",
"361/320",
"19/16",
"115/96",
"361/256",
"57/40",
"3/2",
"57/32",
"115/64",
"361/192",
"19/10",
"2/1"
]
},
{
"id": "dudon_mounos",
"desc": "Mounos extended fifths -c sequence, quasi-septimal minor diatonic scale",
"stepCount": "12",
"steps": [
"9/8",
"1647/1448",
"211/181",
"4/3",
"240/181",
"3/2",
"273/181",
"27/16",
"9937/5792",
"1273/724",
"16/9",
"2/1"
]
},
{
"id": "dudon_nan_kouan",
"desc": "Nan-Kouan (medieval chinese ballade) scale interpretation",
"stepCount": "12",
"steps": [
"19/17",
"172/153",
"5/4",
"321/256",
"64/51",
"11/8",
"3/2",
"107/64",
"256/153",
"57/34",
"11/6",
"2/1"
]
},
{
"id": "dudon_napolitan",
"desc": "Napolitan scale, class-1 differential coherence ; whole tone scale by omitting C",
"stepCount": "12",
"steps": [
"17/16",
"205/192",
"455/384",
"19/16",
"4/3",
"171/128",
"3/2",
"3/2",
"5/3",
"15/8",
"241/128",
"2/1"
]
},
{
"id": "dudon_natte",
"desc": "Sequence of 7 consecutive tones of a Natte series from 28 to 151",
"stepCount": "12",
"steps": [
"86/57",
"65/57",
"98/57",
"74/57",
"151/114",
"2/1",
"86/57",
"65/57",
"98/57",
"74/57",
"112/57",
"2/1"
]
},
{
"id": "dudon_nung_phan_1",
"desc": "7 tones from a sequence of Nung-Phan very low fifths (in theory 679.5604542 c.)",
"stepCount": "12",
"steps": [
"2/1",
"57/52",
"57/26",
"125/104",
"275/208",
"275/104",
"77/52",
"77/26",
"13/8",
"13/4",
"185/104",
"2/1"
]
},
{
"id": "dudon_nung_phan_2",
"desc": "7 tones from a Nung-Phan sequence (very low fifths, in theory 679.5604542 c.)",
"stepCount": "12",
"steps": [
"3/2",
"169/150",
"5/3",
"37/30",
"27/20",
"2/1",
"3/2",
"169/75",
"5/3",
"37/15",
"11/6",
"2/1"
]
},
{
"id": "dudon_okna_hwt",
"desc": "Harmonic well-temperament for mongolian lute",
"stepCount": "12",
"steps": [
"135/128",
"1149/1024",
"19/16",
"321/256",
"171/128",
"45/32",
"3/2",
"405/256",
"429/256",
"7293/4096",
"15/8",
"2/1"
]
},
{
"id": "dudon_over_under_ht",
"desc": "Cycle of fifths, one half above 3/2, the other below (meantone)",
"stepCount": "12",
"steps": [
"33/32",
"215/192",
"75/64",
"239/192",
"4/3",
"131/96",
"287/192",
"149/96",
"5/3",
"85/48",
"179/96",
"2/1"
]
},
{
"id": "dudon_pelog_35",
"desc": "JI -c Pelog with 5, 13, 35 and complements",
"stepCount": "12",
"steps": [
"256/349",
"384/349",
"280/349",
"512/349",
"1/1",
"350/349",
"416/349",
"385/349",
"512/349",
"416/349",
"560/349",
"2/1"
]
},
{
"id": "dudon_pelog_59",
"desc": "JI -c Pelog with 5, 11, 59 and complements",
"stepCount": "12",
"steps": [
"321/256",
"11/8",
"5/4",
"645/512",
"11/8",
"3/2",
"385/256",
"119/64",
"255/128",
"59/32",
"119/64",
"2/1"
]
},
{
"id": "dudon_pelog_ambi",
"desc": "Differential-coherent 5 notes Pelog, ambiguous tonic between C & E",
"stepCount": "12",
"steps": [
"575/384",
"43/32",
"59/48",
"119/96",
"4/3",
"43/32",
"575/384",
"469/384",
"1/1",
"11/6",
"59/32",
"2/1"
]
},
{
"id": "dudon_phi_13",
"desc": "Division of phi giving close approximations to ratios with Fibonacci denominators",
"stepCount": "13",
"steps": [
"93.88597",
"149.46359",
"235.77436",
"317.98569",
"366.90970",
"443.25400",
"488.80753",
"560.06655",
"628.50809",
"669.49310",
"733.81941",
"795.84097",
"833.09030"
]
},
{
"id": "dudon_phidiama",
"desc": "Two Phidiama series, used in \"Appel\", x^2=3x-1",
"stepCount": "8",
"steps": ["9/8", "55/48", "21/16", "4/3", "3/2", "55/32", "7/4", "2/1"]
},
{
"id": "dudon_piphat_min",
"desc": "Gazelle-Naggar -c series + comma 953-960, minor mode",
"stepCount": "12",
"steps": [
"1/1",
"176/161",
"176/161",
"176/161",
"865/644",
"865/644",
"953/644",
"240/161",
"262/161",
"263/161",
"264/161",
"2/1"
]
},
{
"id": "dudon_piphat",
"desc": "Gazelle-Naggar -c series + comma 953-960, major mode",
"stepCount": "12",
"steps": [
"1/1",
"953/865",
"192/173",
"1048/865",
"1052/865",
"1029/692",
"1288/865",
"1288/865",
"1408/865",
"1408/865",
"1408/865",
"2/1"
]
},
{
"id": "dudon_purvi",
"desc": "Purvi Thaat Raga",
"stepCount": "12",
"steps": [
"101/96",
"19/18",
"5/4",
"121/96",
"45/32",
"17/12",
"3/2",
"101/64",
"19/12",
"15/8",
"91/48",
"2/1"
]
},
{
"id": "dudon_quechua",
"desc": "Gazelle-Naggar -c series + comma 953-960, F.11 mode",
"stepCount": "12",
"steps": [
"1/1",
"1/1",
"865/704",
"865/704",
"953/704",
"15/11",
"131/88",
"263/176",
"3/2",
"161/88",
"161/88",
"2/1"
]
},
{
"id": "dudon_raph",
"desc": "Raph recurrent sequence, series Phi17 & Phi93",
"stepCount": "12",
"steps": [
"31/30",
"191/180",
"131/120",
"19/15",
"59/45",
"27/20",
"25/18",
"73/45",
"5/3",
"103/60",
"53/30",
"2/1"
]
},
{
"id": "dudon_rast_matrix",
"desc": "Wusta-Zalzal Arijaom sequence with Rast on white keys and other maqamat",
"stepCount": "12",
"steps": [
"171/157",
"176/157",
"192/157",
"387/314",
"419/314",
"216/157",
"236/157",
"258/157",
"264/157",
"1129/628",
"288/157",
"2/1"
]
},
{
"id": "dudon_rast_iph_39",
"desc": "Neutral diatonic composed of Rast and Iph tetrachords, based on F and 3F series",
"stepCount": "7",
"steps": ["233/208", "16/13", "4/3", "233/156", "64/39", "24/13", "2/1"]
},
{
"id": "dudon_rast_iph_63",
"desc": "Neutral diatonic composed of Rast and Iph tetrachords, based on F and 3F series",
"stepCount": "7",
"steps": ["377/336", "26/21", "4/3", "377/252", "104/63", "233/126", "2/1"]
},
{
"id": "dudon_rast_mohajira",
"desc": "Rast + Mohajira -c quartertones set",
"stepCount": "12",
"steps": [
"107/96",
"9/8",
"11/9",
"59/48",
"4/3",
"11/8",
"3/2",
"5/3",
"27/16",
"11/6",
"59/32",
"2/1"
]
},
{
"id": "dudon_rebab",
"desc": "Gazelle, x^5 = 8x^4 - 32, -c series + comma 953-960, Dudon 2009",
"stepCount": "12",
"steps": [
"1/1",
"1048/953",
"1052/953",
"5145/3812",
"1288/953",
"1288/953",
"1408/953",
"1419/953",
"1420/953",
"1730/953",
"1730/953",
"2/1"
]
},
{
"id": "dudon_s_n_buzurg",
"desc": "Decaphonic system inspired by medieval Persian mode Buzurg (Safi al-Din)",
"stepCount": "12",
"steps": [
"14/13",
"13/12",
"8/7",
"26/21",
"55/42",
"39/28",
"3/2",
"21/13",
"13/8",
"12/7",
"13/7",
"2/1"
]
},
{
"id": "dudon_saba_c",
"desc": "Differentially coherent version of Maqam Saba",
"stepCount": "12",
"steps": [
"259/240",
"87/80",
"19/16",
"6/5",
"19/15",
"179/120",
"3/2",
"8/5",
"129/80",
"71/40",
"9/5",
"2/1"
]
},
{
"id": "dudon_sapaan",
"desc": "7 tones from a sequence of Sapaan very low fifths (in theory 680.015678 c.)",
"stepCount": "12",
"steps": [
"1/1",
"337/300",
"337/300",
"277/225",
"304/225",
"304/225",
"1333/900",
"1333/900",
"374/225",
"374/225",
"82/45",
"2/1"
]
},
{
"id": "dudon_saqqara",
"desc": "Scale of a ney flute (n� 69815) from ancient Egypt found in Saqqara",
"stepCount": "12",
"steps": [
"212/211",
"475/422",
"259/211",
"260/211",
"571/422",
"318/211",
"320/211",
"342/211",
"344/211",
"382/211",
"384/211",
"2/1"
]
},
{
"id": "dudon_satara",
"desc": "Rajasthani double flute drone-c tuning amusement",
"stepCount": "12",
"steps": [
"3/4",
"9/8",
"3/4",
"5/4",
"43/32",
"3/4",
"3/2",
"3/4",
"27/16",
"3/4",
"15/8",
"2/1"
]
},
{
"id": "dudon_saung_gauk",
"desc": "Typical diatonic heptaphone played on the saung gauk (burmese harp)",
"stepCount": "12",
"steps": [
"1/1",
"3463/3114",
"3463/3114",
"623881/504468",
"232/173",
"232/173",
"258/173",
"258/173",
"23240/14013",
"23240/14013",
"232600/126117",
"2/1"
]
},
{
"id": "dudon_segah_subh",
"desc": "Inversed Dudon Neutral Diatonic (mediants of major and minor)",
"stepCount": "12",
"steps": [
"1/1",
"66/59",
"11/9",
"11/9",
"4/3",
"4/3",
"3/2",
"3/2",
"44/27",
"11/6",
"11/6",
"2/1"
]
},
{
"id": "dudon_segah",
"desc": "Dastgah Segah, JI interpretation",
"stepCount": "12",
"steps": [
"285/256",
"9/8",
"38/31",
"157/128",
"4/3",
"343/256",
"3/2",
"13/8",
"157/96",
"56/31",
"29/16",
"2/1"
]
},
{
"id": "dudon_septimal_2",
"desc": "Slendro formed by five 8/7 separated by two commas, Dudon (2009)",
"stepCount": "12",
"steps": [
"264/233",
"266/233",
"304/233",
"304/233",
"308/233",
"352/233",
"352/233",
"400/233",
"402/233",
"460/233",
"464/233",
"2/1"
]
},
{
"id": "dudon_septimal_3",
"desc": "Five 8/7 or close approximations separated by three commas, Dudon (2009)",
"stepCount": "12",
"steps": [
"413/361",
"416/361",
"472/361",
"472/361",
"476/361",
"544/361",
"549/361",
"624/361",
"33/19",
"712/361",
"716/361",
"2/1"
]
},
{
"id": "dudon_shaku",
"desc": "Japanese Shakuhachi scale, -c interpretation",
"stepCount": "12",
"steps": [
"1/1",
"2431/2304",
"19/18",
"17/16",
"85/64",
"4/3",
"2303/1536",
"3/2",
"127/72",
"113/64",
"16/9",
"2/1"
]
},
{
"id": "dudon_shri_rag",
"desc": "Sunset indian raga (Purvi Thaat), as modeled from a 19-limit Amlak sequence",
"stepCount": "12",
"steps": [
"20/19",
"161/152",
"191/152",
"24/19",
"107/76",
"27/19",
"3/2",
"30/19",
"19/12",
"575/304",
"36/19",
"2/1"
]
},
{
"id": "dudon_shur",
"desc": "Shur Dastgah -c version, modelisation by Dudon (1990)",
"stepCount": "12",
"steps": [
"13/12",
"59/54",
"32/27",
"65/54",
"4/3",
"1/1",
"3/2",
"13/8",
"44/27",
"16/9",
"97/54",
"2/1"
]
},
{
"id": "dudon_siam_97",
"desc": "Black keys = 5 quasi-edo ; White keys = 7 quasi-edo (Dudon 1997)",
"stepCount": "12",
"steps": [
"49/48",
"53/48",
"169/144",
"39/32",
"3101/2304",
"97/72",
"107/72",
"223/144",
"105/64",
"16/9",
"29/16",
"2/1"
]
},
{
"id": "dudon_simdek",
"desc": "Heptatonic scale from a sequence of Simdek very low fifths (in theory 676,48557456 c.)",
"stepCount": "12",
"steps": [
"769/621",
"704/621",
"280/207",
"769/621",
"280/207",
"1040/621",
"34/23",
"1136/621",
"1040/621",
"2/1",
"1136/621",
"2/1"
]
},
{
"id": "dudon_sireine_f",
"desc": "Sequence of 11 Sireine fifths (exactly 691.2348426 c.) from F",
"stepCount": "12",
"steps": [
"10503/10304",
"1431/1288",
"23157/20608",
"3179/2576",
"216/161",
"63/46",
"240/161",
"7807/5152",
"2133/1288",
"34191/20608",
"4737/2576",
"2/1"
]
},
{
"id": "dudon_skisni_hwt",
"desc": "Triple equal-beating sequence from C to B, optimal major chords on white keys",
"stepCount": "12",
"steps": [
"256/243",
"573/512",
"32/27",
"641/512",
"4/3",
"1024/729",
"383/256",
"128/81",
"857/512",
"16/9",
"959/512",
"2/1"
]
},
{
"id": "dudon_skisni",
"desc": "Triple equal-beating sequence of 11 quasi-1/5 Pythagorean comma meantone fifths",
"stepCount": "12",
"steps": [
"3480/3321",
"3716/3321",
"3968/3321",
"4158/3321",
"4440/3321",
"9305/6642",
"4968/3321",
"5206/3321",
"5559/3321",
"5936/3321",
"6220/3321",
"2/1"
]
},
{
"id": "dudon_slendra",
"desc": "Cylf-scale (Baka pentatonic Slendro plus pure fifths)",
"stepCount": "12",
"steps": [
"112/111",
"212/185",
"644/555",
"244/185",
"736/555",
"4/3",
"56/37",
"846/555",
"322/185",
"976/555",
"368/185",
"2/1"
]
},
{
"id": "dudon_slendro_m_mean",
"desc": "Wilson meantone from Bb to F# extended in a Slendro M on black keys",
"stepCount": "12",
"steps": [
"2689/2576",
"359/322",
"55/46",
"803/644",
"215/161",
"32/23",
"481/322",
"36/23",
"537/322",
"288/161",
"1199/644",
"2/1"
]
},
{
"id": "dudon_slendro_matrix",
"desc": "Ten tones for many 7-limit slendros from Lou Harrison, of the five types N, M, A, S, J",
"stepCount": "12",
"steps": [
"1/1",
"8/7",
"8/7",
"64/49",
"21/16",
"4/3",
"3/2",
"32/21",
"12/7",
"256/147",
"7/4",
"2/1"
]
},
{
"id": "dudon_smallest_numbers",
"desc": "Chromatic scale achieved with smallest possible numbers",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"43/32",
"45/32",
"3/2",
"51/32",
"27/16",
"57/32",
"15/8",
"2/1"
]
},
{
"id": "dudon_soria",
"desc": "12 from a 17-notes cycle, equal-beating extended fifths (705.5685 c.) sequence",
"stepCount": "12",
"steps": [
"481/445",
"4011/3560",
"2067/1780",
"1133/890",
"9503/7120",
"128/89",
"533/356",
"723/445",
"754/445",
"1233/712",
"1703/890",
"2/1"
]
},
{
"id": "dudon_soria_12",
"desc": "12 from a 17-notes cycle, equal-beating extended fifths (705.5685 c.) sequence",
"stepCount": "12",
"steps": [
"959/886",
"15995/14176",
"8345/7088",
"2259/1772",
"37727/28352",
"638/443",
"5319/3544",
"2883/1772",
"1503/886",
"12443/7088",
"6791/3544",
"2/1"
]
},
{
"id": "dudon_sumer",
"desc": "Neutral diatonic soft Rast scale with Ishku -c variations",
"stepCount": "12",
"steps": [
"79/72",
"10/9",
"11/9",
"89/72",
"4/3",
"49/36",
"3/2",
"119/72",
"5/3",
"131/72",
"11/6",
"2/1"
]
},
{
"id": "dudon_synch_12",
"desc": "Synchronous-beating alternative to 12-tET, cycle of fourths beats from C:F = 1 2 1 1 2 4 3 6 8 8 8 32",
"stepCount": "12",
"steps": [
"373/352",
"395/352",
"419/352",
"887/704",
"235/176",
"249/176",
"527/352",
"559/352",
"37/22",
"157/88",
"1329/704",
"2/1"
]
},
{
"id": "dudon_tango",
"desc": "Fractal Melkis lowest numbers HWT fifths sequence, from D",
"stepCount": "12",
"steps": [
"203/192",
"9/8",
"19/16",
"241/192",
"4/3",
"361/256",
"3/2",
"19/12",
"643/384",
"57/32",
"361/192",
"2/1"
]
},
{
"id": "dudon_thai",
"desc": "Dudon, coherent Thai heptatonic scale, 1/1 vol.11 no.2, 2003",
"stepCount": "7",
"steps": [
"11266/10225",
"12414/10225",
"13696/10225",
"60417/40900",
"16656/10225",
"18368/10225",
"2/1"
]
},
{
"id": "dudon_thai_2",
"desc": "Slightly better version, 3.685 cents deviation",
"stepCount": "7",
"steps": [
"120/109",
"131/109",
"1157/872",
"1277/872",
"176/109",
"12675/6976",
"2/1"
]
},
{
"id": "dudon_thai_3",
"desc": "Dudon, Thai scale with two 704/703 = 2.46 c. deviations and simpler numbers",
"stepCount": "7",
"steps": [
"107/96",
"59/48",
"65/48",
"193/128",
"319/192",
"703/384",
"2/1"
]
},
{
"id": "dudon_tibet",
"desc": "Differentially coherent minor pentatonic",
"stepCount": "12",
"steps": [
"1/1",
"38/31",
"157/128",
"4/3",
"166/124",
"167/124",
"3/2",
"3/2",
"3/2",
"56/31",
"29/16",
"2/1"
]
},
{
"id": "dudon_tielenka",
"desc": "Tielenka (Romanian harmonic flute) scale JI imitation, Dudon (2009)",
"stepCount": "12",
"steps": [
"1/1",
"162/143",
"1341/1144",
"5/4",
"2/1",
"18/13",
"3/2",
"18/11",
"7/4",
"252/143",
"270/143",
"2/1"
]
},
{
"id": "dudon_timbila",
"desc": "Bala tuning whole tone intervals -c heptaphone",
"stepCount": "12",
"steps": [
"1/1",
"107/97",
"107/97",
"118/97",
"130/97",
"1041/776",
"287/194",
"144/97",
"639/388",
"639/388",
"176/97",
"2/1"
]
},
{
"id": "dudon_tit_fleur",
"desc": "Differentially coherent semi-neutral diatonic, small numbers",
"stepCount": "12",
"steps": [
"43/39",
"29/26",
"16/13",
"129/104",
"4/3",
"58/39",
"3/2",
"64/39",
"43/26",
"11/6",
"24/13",
"2/1"
]
},
{
"id": "dudon_todi",
"desc": "Morning Thaat raga (with G = Todi ; without G = Gujari Todi)",
"stepCount": "12",
"steps": [
"20/19",
"161/152",
"45/38",
"19/16",
"215/152",
"27/19",
"3/2",
"30/19",
"1935/1216",
"2297/1216",
"36/19",
"2/1"
]
},
{
"id": "dudon_tsaharuk_24",
"desc": "Rational version of Tsaharuk linear temperament",
"stepCount": "24",
"steps": [
"28/27",
"59/56",
"35/32",
"9/8",
"7/6",
"32/27",
"59/48",
"5/4",
"35/27",
"4/3",
"112/81",
"59/42",
"35/24",
"3/2",
"14/9",
"128/81",
"59/36",
"27/16",
"7/4",
"16/9",
"59/32",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "dudon_valiha",
"desc": "Typical Malagasy scale, neutral diatonic, equal-beating on minor triads",
"stepCount": "12",
"steps": [
"1/1",
"1431/1288",
"1431/1288",
"3179/2576",
"216/161",
"216/161",
"240/161",
"240/161",
"2133/1288",
"34191/20608",
"4737/2576",
"2/1"
]
},
{
"id": "dudon_werckmeister_3_eb",
"desc": "Harmonic equal-beating version of the famous well-temperament (2006)",
"stepCount": "12",
"steps": [
"256/243",
"21995/19683",
"32/27",
"2740/2187",
"4/3",
"1024/729",
"9808/6561",
"128/81",
"10960/6561",
"16/9",
"1370/729",
"2/1"
]
},
{
"id": "dudon_x_slen_31",
"desc": "X-slen fractal temperament, sequence of 420 to 1600",
"stepCount": "31",
"steps": [
"41/40",
"1171/1120",
"15/14",
"153/140",
"251/224",
"8/7",
"41/35",
"1339/1120",
"49/40",
"5/4",
"41/32",
"209/160",
"75/56",
"153/112",
"7/5",
"10/7",
"41/28",
"3/2",
"857/560",
"439/280",
"8/5",
"459/280",
"937/560",
"12/7",
"7/4",
"251/140",
"64/35",
"15/8",
"153/80",
"549/280",
"2/1"
]
},
{
"id": "dudon_zinith",
"desc": "Dudon's \"Zinith\"generator, (sqrt(3)+1)/2, TL 30-03-2009",
"stepCount": "20",
"steps": [
"59.83059",
"120.03765",
"179.86823",
"239.69882",
"299.90588",
"359.73647",
"419.94353",
"479.77411",
"539.98118",
"599.81176",
"660.01882",
"719.84941",
"780.05647",
"839.88706",
"899.71764",
"959.92470",
"1019.75529",
"1079.96235",
"1139.79294",
"2/1"
]
},
{
"id": "dudon_ziraat",
"desc": "Dudon's \"Zira'at\"generator, sqrt(3)+2, TL 30-03-2009",
"stepCount": "10",
"steps": [
"119.66117",
"239.69882",
"359.73647",
"479.77411",
"599.81176",
"719.84941",
"839.88706",
"959.92470",
"1079.96235",
"2/1"
]
},
{
"id": "dudon_zurna",
"desc": "Quartertone scale with tonic transposition on a turkish segah of 159/128",
"stepCount": "12",
"steps": [
"3/2",
"172/159",
"128/159",
"64/53",
"66/53",
"70/53",
"238/159",
"256/159",
"86/53",
"278/159",
"280/159",
"2/1"
]
},
{
"id": "duncan",
"desc": "Dudley Duncan's Superparticular Scale",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "duoden_12",
"desc": "Almost equal 12-tone subset of Duodenarium",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"1215/1024",
"512/405",
"4/3",
"64/45",
"3/2",
"405/256",
"2048/1215",
"3645/2048",
"256/135",
"2/1"
]
},
{
"id": "duodenarium",
"desc": "Ellis's Duodenarium : genus [3^12 5^8]",
"stepCount": "117",
"steps": [
"2048/2025",
"81/80",
"128/125",
"250/243",
"16875/16384",
"648/625",
"25/24",
"273375/262144",
"256/243",
"135/128",
"16/15",
"2187/2048",
"32768/30375",
"27/25",
"625/576",
"2048/1875",
"2187/2000",
"1125/1024",
"10/9",
"18225/16384",
"9/8",
"256/225",
"729/640",
"144/125",
"125/108",
"151875/131072",
"729/625",
"75/64",
"32/27",
"1215/1024",
"6/5",
"4096/3375",
"243/200",
"625/512",
"768/625",
"100/81",
"10125/8192",
"5/4",
"512/405",
"81/64",
"32/25",
"625/486",
"65536/50625",
"162/125",
"125/96",
"1366875/1048576",
"320/243",
"675/512",
"4/3",
"10935/8192",
"8192/6075",
"27/20",
"512/375",
"2187/1600",
"5625/4096",
"864/625",
"25/18",
"91125/65536",
"45/32",
"64/45",
"729/512",
"36/25",
"625/432",
"8192/5625",
"729/500",
"375/256",
"40/27",
"6075/4096",
"3/2",
"1024/675",
"243/160",
"192/125",
"125/81",
"50625/32768",
"972/625",
"25/16",
"128/81",
"405/256",
"8/5",
"16384/10125",
"81/50",
"625/384",
"1024/625",
"400/243",
"3375/2048",
"5/3",
"54675/32768",
"2048/1215",
"27/16",
"128/75",
"2187/1280",
"262144/151875",
"216/125",
"125/72",
"455625/262144",
"2187/1250",
"225/128",
"16/9",
"3645/2048",
"9/5",
"2048/1125",
"729/400",
"1875/1024",
"1152/625",
"50/27",
"30375/16384",
"15/8",
"256/135",
"243/128",
"48/25",
"625/324",
"32768/16875",
"243/125",
"125/64",
"160/81",
"2025/1024",
"2/1"
]
},
{
"id": "duodene_double",
"desc": "Ellis's Duodene union 11/9 times the duodene in 240-tET",
"stepCount": "24",
"steps": [
"35.00000",
"115.00000",
"165.00000",
"200.00000",
"235.00000",
"315.00000",
"350.00000",
"385.00000",
"465.00000",
"500.00000",
"550.00000",
"585.00000",
"665.00000",
"700.00000",
"735.00000",
"815.00000",
"850.00000",
"885.00000",
"935.00000",
"1015.00000",
"1050.00000",
"1085.00000",
"1165.00000",
"2/1"
]
},
{
"id": "duodene_min",
"desc": "Minor Duodene",
"stepCount": "12",
"steps": [
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"27/20",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "duodene_r_45",
"desc": "Ellis's Duodene rotated -45 degrees",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"32/25",
"27/20",
"36/25",
"192/125",
"25/16",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "duodene_r_45",
"desc": "Ellis's Duodene rotated 45 degrees",
"stepCount": "12",
"steps": [
"135/128",
"16/15",
"9/8",
"6/5",
"32/25",
"375/256",
"25/16",
"5/3",
"225/128",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "duodene_skew",
"desc": "Rotated 6/5x3/2 duodene",
"stepCount": "12",
"steps": [
"27/25",
"10/9",
"6/5",
"5/4",
"4/3",
"36/25",
"3/2",
"8/5",
"5/3",
"9/5",
"48/25",
"2/1"
]
},
{
"id": "duodene_t",
"desc": "Duodene with equal tempered fifths",
"stepCount": "12",
"steps": [
"113.68629",
"200.00000",
"313.68629",
"5/4",
"500.00000",
"586.31371",
"700.00000",
"8/5",
"886.31371",
"1013.68629",
"1086.31371",
"2/1"
]
},
{
"id": "duodene_w",
"desc": "Ellis duodene well-tuned to fifth=(7168/11)^(1/16) third=(11/7)^(1/2), G.W. Smith",
"stepCount": "12",
"steps": [
"107.65973",
"202.18850",
"309.84823",
"391.24602",
"498.90575",
"593.43451",
"701.09425",
"808.75398",
"890.15177",
"1010.94248",
"1092.34027",
"2/1"
]
},
{
"id": "duodene",
"desc": "Ellis's Duodene : genus [33355]",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "duodene_3_11_9",
"desc": "3-11/9 Duodene",
"stepCount": "12",
"steps": [
"12/11",
"9/8",
"11/9",
"27/22",
"4/3",
"11/8",
"3/2",
"44/27",
"18/11",
"11/6",
"81/44",
"2/1"
]
},
{
"id": "duodene_6_7_9",
"desc": "6-7-9 Duodene",
"stepCount": "12",
"steps": [
"9/8",
"8/7",
"7/6",
"9/7",
"21/16",
"4/3",
"3/2",
"14/9",
"12/7",
"7/4",
"27/14",
"2/1"
]
},
{
"id": "duodene_14_18_21",
"desc": "14-18-21 Duodene",
"stepCount": "12",
"steps": [
"28/27",
"9/8",
"7/6",
"9/7",
"4/3",
"81/56",
"3/2",
"14/9",
"12/7",
"7/4",
"27/14",
"2/1"
]
},
{
"id": "duohex",
"desc": "Scale with two hexanies, inverse mode of hahn_7.scl",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"6/5",
"5/4",
"9/7",
"10/7",
"3/2",
"45/28",
"12/7",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "duohexmarvwoo",
"desc": "Marvel woo version of duohex, a scale with two hexanies",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"6/5",
"5/4",
"9/7",
"10/7",
"3/2",
"45/28",
"12/7",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "dwarf_11_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf(<11 17 26|)",
"stepCount": "11",
"steps": [
"115.587047",
"315.641287",
"384.385833",
"499.972880",
"515.695527",
"700.027120",
"815.614167",
"884.358713",
"1015.668407",
"1084.412953",
"2/1"
]
},
{
"id": "dwarf_12_7",
"desc": "Dwarf(<12 19 28 34|) five major triads, four minor triads two otonal pentads",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"9/5",
"28/15",
"2/1"
]
},
{
"id": "dwarf_12_11",
"desc": "Dwarf(<12 19 28 34 42|) two otonal hexads",
"stepCount": "12",
"steps": [
"16/15",
"11/10",
"6/5",
"5/4",
"4/3",
"7/5",
"22/15",
"8/5",
"5/3",
"9/5",
"28/15",
"2/1"
]
},
{
"id": "dwarf_12_11_marvwoo",
"desc": "Marvel woo version of Dwarf(<12 19 28 34 42|)",
"stepCount": "12",
"steps": [
"116.23027",
"165.64566",
"316.92773",
"383.74261",
"499.97288",
"584.44007",
"665.61854",
"816.90061",
"883.71549",
"1017.59808",
"1084.41295",
"1200.64322"
]
},
{
"id": "dwarf_12_marv",
"desc": "Marvelous dwarf: 1/4 kleismic tempered duodene",
"stepCount": "12",
"steps": [
"131.309694",
"200.054240",
"315.641287",
"431.228334",
"515.695527",
"631.282574",
"700.027120",
"815.614167",
"900.081360",
"1015.668407",
"1131.255454",
"2/1"
]
},
{
"id": "dwarf_13_7_d",
"desc": "Dwarf(<13 21 30 37|)",
"stepCount": "13",
"steps": [
"15/14",
"8/7",
"7/6",
"5/4",
"4/3",
"10/7",
"3/2",
"32/21",
"5/3",
"12/7",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "dwarf_13_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf(<13 20 30|)",
"stepCount": "13",
"steps": [
"200.054240",
"268.798786",
"315.641287",
"384.385833",
"431.228334",
"631.282574",
"700.027120",
"768.771666",
"815.614167",
"1015.668407",
"1084.412953",
"1131.255454",
"2/1"
]
},
{
"id": "dwarf_14_block",
"desc": "Weak Fokker block tweaked from Dwarf(<14 23 36 40|)",
"stepCount": "14",
"steps": [
"8/7",
"7/6",
"6/5",
"4/3",
"7/5",
"3/2",
"14/9",
"8/5",
"49/30",
"5/3",
"12/7",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "dwarf_14_c_7_hecate",
"desc": "7-limit Dwarf(14c) in hecate tempering, 166-tET tuning",
"stepCount": "14",
"steps": [
"65.06024",
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"231.32530",
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"498.79518",
"701.20482",
"730.12048",
"881.92771",
"903.61446",
"932.53012",
"1113.25301",
"1134.93976",
"2/1"
]
},
{
"id": "dwarf_14_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf(<14 22 33})",
"stepCount": "14",
"steps": [
"200.054240",
"315.641287",
"384.385833",
"431.228334",
"584.440073",
"631.282574",
"700.027120",
"768.771666",
"815.614167",
"1015.668407",
"1084.412953",
"1131.255454",
"1153.157499",
"2/1"
]
},
{
"id": "dwarf_15_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<15 24 35|) subset rosatimarv",
"stepCount": "15",
"steps": [
"115.587047",
"184.331593",
"200.054240",
"315.641287",
"384.385833",
"499.972880",
"584.440073",
"615.559927",
"700.027120",
"815.614167",
"884.358713",
"999.945760",
"1015.668407",
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"2/1"
]
},
{
"id": "dwarf_15_marvwoo",
"desc": "Marvelous dwarf: dwarf(<15 24 35|) in [10/3 7/2 11] marvel woo tuning",
"stepCount": "15",
"steps": [
"116.23027",
"183.04515",
"200.69746",
"316.92773",
"383.74261",
"499.97288",
"584.44007",
"616.20315",
"700.67034",
"816.90061",
"883.71549",
"999.94576",
"1017.59808",
"1084.41295",
"1200.64322"
]
},
{
"id": "dwarf_16_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf(<16 25 37|)",
"stepCount": "16",
"steps": [
"15.722647",
"68.744546",
"115.587047",
"184.331593",
"315.641287",
"384.385833",
"499.972880",
"515.695527",
"568.717426",
"615.559927",
"768.771666",
"815.614167",
"884.358713",
"999.945760",
"1015.668407",
"2/1"
]
},
{
"id": "dwarf_17_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf(<17 27 40|)",
"stepCount": "17",
"steps": [
"68.744546",
"115.587047",
"184.331593",
"268.798786",
"315.641287",
"384.385833",
"499.972880",
"568.717426",
"615.559927",
"700.027120",
"768.771666",
"815.614167",
"884.358713",
"953.103259",
"999.945760",
"1084.412953",
"2/1"
]
},
{
"id": "dwarf_17_marveq",
"desc": "Semimarvelous dwarf: equal beating dwarf(<17 27 40|)",
"stepCount": "17",
"steps": [
"70.247930173690388400",
"115.13195688812420070",
"185.37988706181458910",
"269.90670087373119520",
"314.79072758816500750",
"385.03865776185539590",
"500.17061464997959660",
"570.41854482366998500",
"615.30257153810379730",
"699.82938535002040340",
"770.07731552371079180",
"814.96134223814460410",
"885.20927241183499250",
"955.45720258552538090",
"1000.3412292999591932",
"1084.8680431118757993",
"2/1"
]
},
{
"id": "dwarf_17_marvwoo",
"desc": "Semimarvelous dwarf: dwarf(<17 27 40|) in [10/3 7/2 11] marvel woo tuning",
"stepCount": "17",
"steps": [
"66.81488",
"116.23027",
"183.04515",
"267.51234",
"316.92773",
"383.74261",
"499.97288",
"566.78776",
"616.20315",
"700.67034",
"767.48522",
"816.90061",
"883.71549",
"950.53037",
"999.94576",
"1084.41295",
"1200.64322"
]
},
{
"id": "dwarf_18_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<18 29 42|)",
"stepCount": "18",
"steps": [
"15.722647",
"115.587047",
"131.309694",
"200.054240",
"315.641287",
"400.108480",
"431.228334",
"499.972880",
"515.695527",
"631.282574",
"700.027120",
"815.614167",
"831.336814",
"900.081360",
"931.201214",
"1015.668407",
"1131.255454",
"2/1"
]
},
{
"id": "dwarf_19_43",
"desc": "Dwarf scale for 43-limit patent val of 19-tET",
"stepCount": "19",
"steps": [
"33/32",
"17/16",
"9/8",
"37/32",
"19/16",
"5/4",
"21/16",
"43/32",
"11/8",
"23/16",
"3/2",
"25/16",
"13/8",
"27/16",
"7/4",
"29/16",
"15/8",
"31/16",
"2/1"
]
},
{
"id": "dwarf_19_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<19 30 44|) = inverse wilson1",
"stepCount": "19",
"steps": [
"68.74455",
"115.58705",
"200.05424",
"268.79879",
"6/5",
"384.38583",
"431.22833",
"499.97288",
"584.44007",
"36/25",
"700.02712",
"768.77167",
"815.61417",
"5/3",
"931.20121",
"1015.66841",
"1084.41295",
"1131.25545",
"2/1"
]
},
{
"id": "dwarf_20_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<20 32 47|) = genus(3^4 5^3)",
"stepCount": "20",
"steps": [
"68.744546",
"184.331593",
"253.076139",
"299.918640",
"368.663186",
"384.385833",
"453.130379",
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"568.717426",
"684.304473",
"753.049019",
"768.771666",
"799.891520",
"884.358713",
"953.103259",
"999.945760",
"1068.690306",
"1153.157499",
"1184.277353",
"2/1"
]
},
{
"id": "dwarf_21_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<21 33 49|)",
"stepCount": "21",
"steps": [
"68.744546",
"184.331593",
"200.054240",
"268.798786",
"299.918640",
"368.663186",
"384.385833",
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"568.717426",
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"684.304473",
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"768.771666",
"799.891520",
"884.358713",
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"1068.690306",
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"2/1"
]
},
{
"id": "dwarf_22_marv",
"desc": "Semimarvelous dwarf: 1/4 kleismic dwarf22_5 and dwarf22_7",
"stepCount": "22",
"steps": [
"68.744546",
"115.587047",
"131.309694",
"200.054240",
"268.798786",
"315.641287",
"384.385833",
"431.228334",
"499.972880",
"515.695527",
"584.440073",
"631.282574",
"700.027120",
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"2/1"
]
},
{
"id": "dwarf_25_marv",
"desc": "Marvelous dwarf: 1/4 kleismic dwarf(<25 40 58|) = genus(3^4 5^4)",
"stepCount": "25",
"steps": [
"68.74455",
"115.58705",
"184.33159",
"253.07614",
"268.79879",
"299.91864",
"315.64129",
"384.38583",
"453.13038",
"499.97288",
"568.71743",
"615.55993",
"653.18462",
"684.30447",
"700.02712",
"768.77167",
"815.61417",
"884.35871",
"953.10326",
"999.94576",
"1068.69031",
"1084.41295",
"1115.53281",
"1153.15750",
"2/1"
]
},
{
"id": "dwarf_27_7_tempered",
"desc": "Irregularly tempered dwarf(<27 43 63 76|)",
"stepCount": "27",
"steps": [
"8.50411",
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"94.02735",
"155.44995",
"204.62445",
"239.75461",
"275.21962",
"300.57603",
"386.44020",
"410.42948",
"471.11121",
"506.30767",
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"591.15701",
"616.87618",
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"857.59196",
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"969.00623",
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"1088.74607",
"1113.63615",
"2/1"
]
},
{
"id": "dwarf_31_11",
"desc": "Dwarf(<31 49 72 87 107|)",
"stepCount": "31",
"steps": [
"36/35",
"22/21",
"16/15",
"11/10",
"9/8",
"8/7",
"7/6",
"6/5",
"128/105",
"44/35",
"9/7",
"55/42",
"4/3",
"48/35",
"7/5",
"10/7",
"22/15",
"3/2",
"32/21",
"11/7",
"8/5",
"49/30",
"176/105",
"12/7",
"7/4",
"9/5",
"64/35",
"28/15",
"40/21",
"55/28",
"2/1"
]
},
{
"id": "dwarf_271_bp",
"desc": "Tritave dwarf(<171 271 397 480|)",
"stepCount": "271",
"steps": [
"1600000/1594323",
"245/243",
"179200/177147",
"20000/19683",
"43904000/43046721",
"2240/2187",
"250/243",
"548800/531441",
"28/27",
"20480/19683",
"6860/6561",
"5017600/4782969",
"256/243",
"62500/59049",
"62720/59049",
"7000/6561",
"5120000/4782969",
"784/729",
"573440/531441",
"64000/59049",
"15625000/14348907",
"7168/6561",
"800/729",
"1756160/1594323",
"196000/177147",
"10/9",
"21952/19683",
"2450/2187",
"1792000/1594323",
"200000/177147",
"200704/177147",
"22400/19683",
"2500/2187",
"5488000/4782969",
"280/243",
"204800/177147",
"68600/59049",
"50176000/43046721",
"2560/2187",
"625000/531441",
"627200/531441",
"32/27",
"51200000/43046721",
"7840/6561",
"875/729",
"640000/531441",
"98/81",
"71680/59049",
"8000/6561",
"1953125/1594323",
"896/729",
"100/81",
"219520/177147",
"24500/19683",
"8192/6561",
"2744/2187",
"2007040/1594323",
"224000/177147",
"25000/19683",
"25088/19683",
"2800/2187",
"2048000/1594323",
"686000/531441",
"35/27",
"25600/19683",
"8575/6561",
"6272000/4782969",
"320/243",
"78125/59049",
"78400/59049",
"4/3",
"6400000/4782969",
"980/729",
"716800/531441",
"80000/59049",
"19531250/14348907",
"8960/6561",
"1000/729",
"2195200/1594323",
"112/81",
"81920/59049",
"27440/19683",
"20070400/14348907",
"1024/729",
"343/243",
"250880/177147",
"28000/19683",
"3125/2187",
"3136/2187",
"350/243",
"256000/177147",
"85750/59049",
"28672/19683",
"3200/2187",
"781250/531441",
"784000/531441",
"40/27",
"87808/59049",
"9800/6561",
"7168000/4782969",
"800000/531441",
"802816/531441",
"89600/59049",
"10000/6561",
"21952000/14348907",
"1120/729",
"125/81",
"274400/177147",
"14/9",
"10240/6561",
"3430/2187",
"2508800/1594323",
"128/81",
"31250/19683",
"31360/19683",
"3500/2187",
"2560000/1594323",
"392/243",
"286720/177147",
"32000/19683",
"7812500/4782969",
"3584/2187",
"400/243",
"878080/531441",
"98000/59049",
"5/3",
"10976/6561",
"1225/729",
"896000/531441",
"100000/59049",
"100352/59049",
"11200/6561",
"1250/729",
"2744000/1594323",
"140/81",
"102400/59049",
"34300/19683",
"25088000/14348907",
"1280/729",
"312500/177147",
"313600/177147",
"16/9",
"25600000/14348907",
"3920/2187",
"2867200/1594323",
"320000/177147",
"49/27",
"35840/19683",
"4000/2187",
"8780800/4782969",
"448/243",
"50/27",
"109760/59049",
"12250/6561",
"4096/2187",
"1372/729",
"1003520/531441",
"112000/59049",
"12500/6561",
"12544/6561",
"1400/729",
"1024000/531441",
"343000/177147",
"114688/59049",
"12800/6561",
"3125000/1594323",
"3136000/1594323",
"160/81",
"351232/177147",
"39200/19683",
"2/1",
"3200000/1594323",
"490/243",
"358400/177147",
"40000/19683",
"9765625/4782969",
"4480/2187",
"500/243",
"1097600/531441",
"56/27",
"40960/19683",
"13720/6561",
"10035200/4782969",
"512/243",
"125000/59049",
"125440/59049",
"14000/6561",
"10240000/4782969",
"1568/729",
"175/81",
"128000/59049",
"42875/19683",
"14336/6561",
"1600/729",
"390625/177147",
"392000/177147",
"20/9",
"43904/19683",
"4900/2187",
"3584000/1594323",
"400000/177147",
"401408/177147",
"44800/19683",
"5000/2187",
"10976000/4782969",
"560/243",
"409600/177147",
"137200/59049",
"7/3",
"5120/2187",
"1715/729",
"1254400/531441",
"64/27",
"15625/6561",
"15680/6561",
"1750/729",
"1280000/531441",
"196/81",
"143360/59049",
"16000/6561",
"3906250/1594323",
"1792/729",
"200/81",
"439040/177147",
"49000/19683",
"16384/6561",
"5488/2187",
"4014080/1594323",
"448000/177147",
"50000/19683",
"50176/19683",
"5600/2187",
"625/243",
"1372000/531441",
"70/27",
"51200/19683",
"17150/6561",
"12544000/4782969",
"640/243",
"156250/59049",
"156800/59049",
"8/3",
"12800000/4782969",
"1960/729",
"1433600/531441",
"160000/59049",
"39062500/14348907",
"17920/6561",
"2000/729",
"4390400/1594323",
"224/81",
"25/9",
"54880/19683",
"6125/2187",
"2048/729",
"686/243",
"501760/177147",
"56000/19683",
"6250/2187",
"6272/2187",
"700/243",
"512000/177147",
"171500/59049",
"57344/19683",
"6400/2187",
"1562500/531441",
"1568000/531441",
"80/27",
"175616/59049",
"19600/6561",
"3/1"
]
},
{
"id": "dwarf_72277",
"desc": "7-limit Dwarf(22) tempered in 77-tET",
"stepCount": "22",
"steps": [
"15.58442",
"77.92208",
"124.67532",
"187.01299",
"280.51948",
"311.68831",
"389.61039",
"420.77922",
"467.53247",
"514.28571",
"576.62338",
"623.37662",
"701.29870",
"779.22078",
"810.38961",
"825.97403",
"888.31169",
"966.23377",
"1012.98701",
"1090.90909",
"1122.07792",
"2/1"
]
},
{
"id": "dwart_14_block",
"desc": "Weak Fokker block tweaked from Dwarf(<14 23 36 40|)",
"stepCount": "14",
"steps": [
"8/7",
"7/6",
"6/5",
"4/3",
"7/5",
"3/2",
"14/9",
"8/5",
"49/30",
"5/3",
"12/7",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "dyadic_53_tone_9_div",
"desc": "Philolaos tone-9-division 8:9=72:73:74:75:76:77:78:79:80:81",
"stepCount": "53",
"steps": [
"1039/1024",
"1053/1024",
"2133/2048",
"135/128",
"547/512",
"1109/1024",
"4495/4096",
"569/512",
"9/8",
"73/64",
"37/32",
"75/64",
"19/16",
"77/64",
"39/32",
"79/64",
"5/4",
"81/64",
"657/512",
"333/256",
"675/512",
"683/512",
"693/512",
"351/256",
"711/512",
"45/32",
"729/512",
"2957/2048",
"2997/2048",
"759/512",
"3/2",
"779/512",
"1579/1024",
"25/16",
"405/256",
"821/512",
"13/8",
"3371/2048",
"1707/1024",
"27/16",
"219/128",
"111/64",
"225/128",
"1823/1024",
"231/128",
"117/64",
"237/128",
"15/8",
"243/128",
"495/256",
"999/512",
"253/128",
"2/1"
]
},
{
"id": "efg_333",
"desc": "Genus primum [333]",
"stepCount": "4",
"steps": ["9/8", "4/3", "3/2", "2/1"]
},
{
"id": "efg_335",
"desc": "Genus secundum [335]",
"stepCount": "6",
"steps": ["5/4", "4/3", "3/2", "5/3", "15/8", "2/1"]
},
{
"id": "efg_337",
"desc": "Genus quintum [337]",
"stepCount": "6",
"steps": ["9/8", "21/16", "3/2", "7/4", "63/32", "2/1"]
},
{
"id": "efg_355",
"desc": "Genus tertium [355]",
"stepCount": "6",
"steps": ["6/5", "5/4", "3/2", "8/5", "15/8", "2/1"]
},
{
"id": "efg_357",
"desc": "Genus sextum [357] & 7-limit Octony, see ch.6 p.118",
"stepCount": "8",
"steps": ["35/32", "5/4", "21/16", "3/2", "105/64", "7/4", "15/8", "2/1"]
},
{
"id": "efg_377",
"desc": "Genus octavum [377]",
"stepCount": "6",
"steps": ["147/128", "21/16", "3/2", "49/32", "7/4", "2/1"]
},
{
"id": "efg_555",
"desc": "Genus quartum [555]",
"stepCount": "4",
"steps": ["5/4", "25/16", "125/64", "2/1"]
},
{
"id": "efg_557",
"desc": "Genus septimum [557]",
"stepCount": "6",
"steps": ["35/32", "5/4", "7/5", "8/5", "7/4", "2/1"]
},
{
"id": "efg_577",
"desc": "Genus nonum [577]",
"stepCount": "6",
"steps": ["35/32", "5/4", "49/32", "7/4", "245/128", "2/1"]
},
{
"id": "efg_777",
"desc": "Genus decimum [777]",
"stepCount": "4",
"steps": ["343/256", "49/32", "7/4", "2/1"]
},
{
"id": "efg_3335",
"desc": "Genus diatonicum veterum correctum [3335]",
"stepCount": "8",
"steps": ["10/9", "5/4", "4/3", "3/2", "5/3", "16/9", "15/8", "2/1"]
},
{
"id": "efg_3337",
"desc": "Genus [3337]",
"stepCount": "8",
"steps": ["9/8", "7/6", "21/16", "4/3", "3/2", "7/4", "63/32", "2/1"]
},
{
"id": "efg_3355",
"desc": "Genus chromaticum veterum correctum [3355]",
"stepCount": "9",
"steps": ["16/15", "6/5", "5/4", "4/3", "3/2", "8/5", "5/3", "15/8", "2/1"]
},
{
"id": "efg_3357",
"desc": "Genus enharmonicum vocale [3357]",
"stepCount": "12",
"steps": [
"35/32",
"7/6",
"5/4",
"21/16",
"4/3",
"35/24",
"3/2",
"105/64",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "efg_3377",
"desc": "Genus [3377]",
"stepCount": "9",
"steps": [
"8/7",
"7/6",
"21/16",
"4/3",
"3/2",
"32/21",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "efg_3555",
"desc": "Genus enharmonicum veterum correctum [3555]",
"stepCount": "8",
"steps": [
"75/64",
"5/4",
"375/256",
"3/2",
"25/16",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "efg_3557",
"desc": "Genus enharmonicum instrumentale [3557]",
"stepCount": "12",
"steps": [
"21/20",
"35/32",
"6/5",
"5/4",
"21/16",
"7/5",
"3/2",
"8/5",
"105/64",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "efg_3577",
"desc": "Genus [3577]",
"stepCount": "12",
"steps": [
"15/14",
"35/32",
"8/7",
"5/4",
"21/16",
"10/7",
"3/2",
"105/64",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "efg_3711",
"desc": "Genus [3 7 11]",
"stepCount": "8",
"steps": ["12/11", "14/11", "21/16", "16/11", "3/2", "7/4", "21/11", "2/1"]
},
{
"id": "efg_3777",
"desc": "Genus [3777]",
"stepCount": "8",
"steps": [
"1029/1024",
"147/128",
"21/16",
"343/256",
"3/2",
"49/32",
"7/4",
"2/1"
]
},
{
"id": "efg_5557",
"desc": "Genus [5557]",
"stepCount": "8",
"steps": [
"35/32",
"5/4",
"175/128",
"25/16",
"875/512",
"7/4",
"125/64",
"2/1"
]
},
{
"id": "efg_5577",
"desc": "Genus [5577]",
"stepCount": "9",
"steps": [
"28/25",
"49/40",
"32/25",
"7/5",
"49/32",
"8/5",
"7/4",
"49/25",
"2/1"
]
},
{
"id": "efg_5777",
"desc": "Genus [5777]",
"stepCount": "8",
"steps": ["35/32", "8/7", "5/4", "10/7", "49/32", "7/4", "245/128", "2/1"]
},
{
"id": "efg_33335",
"desc": "Genus [33335], Dwarf(<10 16 23|), also blackchrome1",
"stepCount": "10",
"steps": [
"135/128",
"9/8",
"5/4",
"4/3",
"45/32",
"3/2",
"5/3",
"27/16",
"15/8",
"2/1"
]
},
{
"id": "efg_33337",
"desc": "Genus [33337]",
"stepCount": "10",
"steps": [
"9/8",
"7/6",
"21/16",
"4/3",
"189/128",
"3/2",
"27/16",
"7/4",
"63/32",
"2/1"
]
},
{
"id": "efg_33355",
"desc": "Genus diatonico-chromaticum hodiernum correctum [33355]",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"32/27",
"5/4",
"4/3",
"25/18",
"40/27",
"25/16",
"5/3",
"16/9",
"50/27",
"2/1"
]
},
{
"id": "efg_33357",
"desc": "Genus diatonico-enharmonicum [33357]",
"stepCount": "16",
"steps": [
"21/20",
"16/15",
"7/6",
"6/5",
"56/45",
"21/16",
"4/3",
"7/5",
"64/45",
"3/2",
"14/9",
"8/5",
"7/4",
"16/9",
"28/15",
"2/1"
]
},
{
"id": "efg_33377",
"desc": "Genus [33377] Bi-enharmonicum simplex",
"stepCount": "12",
"steps": [
"9/8",
"8/7",
"7/6",
"9/7",
"21/16",
"4/3",
"3/2",
"32/21",
"12/7",
"7/4",
"63/32",
"2/1"
]
},
{
"id": "efg_33555",
"desc": "Genus bichromaticum [33555]",
"stepCount": "12",
"steps": [
"9/8",
"75/64",
"6/5",
"5/4",
"45/32",
"3/2",
"25/16",
"8/5",
"225/128",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "efg_33555_marvwoo",
"desc": "Genus [33555] in marvel temperament, woo tuning",
"stepCount": "12",
"steps": [
"66.81488",
"116.23027",
"267.51234",
"316.92773",
"383.74261",
"499.97288",
"700.67034",
"767.48522",
"816.90061",
"883.71549",
"1084.41295",
"1200.64322"
]
},
{
"id": "efg_33557",
"desc": "Genus chromatico-enharmonicum [33557]",
"stepCount": "18",
"steps": [
"21/20",
"16/15",
"35/32",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"35/24",
"3/2",
"8/5",
"105/64",
"5/3",
"7/4",
"28/15",
"15/8",
"2/1"
]
},
{
"id": "efg_33577",
"desc": "Genus [33577]",
"stepCount": "18",
"steps": [
"15/14",
"35/32",
"8/7",
"7/6",
"5/4",
"21/16",
"4/3",
"10/7",
"35/24",
"3/2",
"32/21",
"105/64",
"5/3",
"12/7",
"7/4",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "efg_33777",
"desc": "Genus [33777]",
"stepCount": "12",
"steps": [
"49/48",
"8/7",
"147/128",
"7/6",
"21/16",
"4/3",
"3/2",
"32/21",
"49/32",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "efg_33777_a",
"desc": "Genus [33777] with 1029/1024 discarded which vanishes in 31-tET",
"stepCount": "10",
"steps": [
"49/48",
"8/7",
"7/6",
"21/16",
"4/3",
"3/2",
"32/21",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "efg_35555",
"desc": "Genus [35555]",
"stepCount": "10",
"steps": [
"75/64",
"6/5",
"5/4",
"32/25",
"3/2",
"25/16",
"8/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "efg_35557",
"desc": "Genus [35557]",
"stepCount": "16",
"steps": [
"525/512",
"21/20",
"35/32",
"75/64",
"6/5",
"5/4",
"21/16",
"175/128",
"7/5",
"3/2",
"25/16",
"8/5",
"105/64",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "efg_35577",
"desc": "Genus [35577]",
"stepCount": "18",
"steps": [
"21/20",
"15/14",
"35/32",
"8/7",
"6/5",
"5/4",
"21/16",
"48/35",
"7/5",
"10/7",
"3/2",
"8/5",
"105/64",
"12/7",
"7/4",
"64/35",
"15/8",
"2/1"
]
},
{
"id": "efg_35711",
"desc": "Genus [3 5 7 11]",
"stepCount": "16",
"steps": [
"33/32",
"35/32",
"1155/1024",
"77/64",
"5/4",
"165/128",
"21/16",
"11/8",
"3/2",
"385/256",
"105/64",
"55/32",
"7/4",
"231/128",
"15/8",
"2/1"
]
},
{
"id": "efg_35777",
"desc": "Genus [35777]",
"stepCount": "16",
"steps": [
"15/14",
"35/32",
"8/7",
"147/128",
"5/4",
"21/16",
"10/7",
"735/512",
"3/2",
"49/32",
"105/64",
"12/7",
"7/4",
"15/8",
"245/128",
"2/1"
]
},
{
"id": "efg_35777_a",
"desc": "Genus [35777] with comma discarded which disappears in 31-tET",
"stepCount": "14",
"steps": [
"15/14",
"35/32",
"8/7",
"5/4",
"21/16",
"10/7",
"3/2",
"49/32",
"105/64",
"12/7",
"7/4",
"15/8",
"245/128",
"2/1"
]
},
{
"id": "efg_37711",
"desc": "Genus [3 7 7 11]",
"stepCount": "12",
"steps": [
"49/48",
"49/44",
"7/6",
"14/11",
"4/3",
"16/11",
"49/33",
"49/32",
"56/33",
"7/4",
"64/33",
"2/1"
]
},
{
"id": "efg_37777",
"desc": "Genus [37777]",
"stepCount": "10",
"steps": [
"1029/1024",
"8/7",
"147/128",
"21/16",
"343/256",
"3/2",
"49/32",
"12/7",
"7/4",
"2/1"
]
},
{
"id": "efg_37777_a",
"desc": "Genus [37777] with comma discarded that disappears in 31-tET",
"stepCount": "8",
"steps": ["8/7", "21/16", "343/256", "3/2", "49/32", "12/7", "7/4", "2/1"]
},
{
"id": "efg_55557",
"desc": "Genus [55557]",
"stepCount": "10",
"steps": [
"35/32",
"5/4",
"175/128",
"7/5",
"25/16",
"8/5",
"875/512",
"7/4",
"125/64",
"2/1"
]
},
{
"id": "efg_55577",
"desc": "Genus [55577]",
"stepCount": "12",
"steps": [
"35/32",
"125/112",
"8/7",
"5/4",
"175/128",
"10/7",
"25/16",
"875/512",
"7/4",
"25/14",
"125/64",
"2/1"
]
},
{
"id": "efg_55777",
"desc": "Genus [55777]",
"stepCount": "12",
"steps": [
"35/32",
"8/7",
"49/40",
"5/4",
"7/5",
"10/7",
"49/32",
"8/5",
"7/4",
"64/35",
"245/128",
"2/1"
]
},
{
"id": "efg_57777",
"desc": "Genus [57777]",
"stepCount": "10",
"steps": [
"35/32",
"8/7",
"5/4",
"343/256",
"10/7",
"49/32",
"1715/1024",
"7/4",
"245/128",
"2/1"
]
},
{
"id": "efg_77777",
"desc": "Genus [77777]",
"stepCount": "6",
"steps": ["8/7", "64/49", "343/256", "49/32", "7/4", "2/1"]
},
{
"id": "efg_333357",
"desc": "Genus [333357]",
"stepCount": "20",
"steps": [
"35/32",
"10/9",
"9/8",
"7/6",
"315/256",
"5/4",
"21/16",
"4/3",
"45/32",
"35/24",
"3/2",
"14/9",
"105/64",
"5/3",
"7/4",
"16/9",
"15/8",
"35/18",
"63/32",
"2/1"
]
},
{
"id": "efg_333555",
"desc": "Genus diatonico-hyperchromaticum [333555]",
"stepCount": "16",
"steps": [
"25/24",
"16/15",
"10/9",
"75/64",
"6/5",
"5/4",
"4/3",
"25/18",
"64/45",
"3/2",
"25/16",
"8/5",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "efg_333555_plusmarvwoo",
"desc": "Genus [333555] plus 10125/8192, marvel woo tuning",
"stepCount": "17",
"steps": [
"84.46719",
"151.28207",
"200.69746",
"267.51234",
"351.97953",
"383.74261",
"468.20980",
"584.44007",
"651.25495",
"700.67034",
"767.48522",
"851.95241",
"901.36781",
"968.18268",
"1084.41295",
"1151.22783",
"1200.64322"
]
},
{
"id": "efg_333557",
"desc": "Genus diatonico-enharmonicum [333557]",
"stepCount": "24",
"steps": [
"64/63",
"16/15",
"15/14",
"10/9",
"8/7",
"6/5",
"128/105",
"5/4",
"80/63",
"4/3",
"48/35",
"64/45",
"10/7",
"3/2",
"32/21",
"8/5",
"512/315",
"5/3",
"12/7",
"16/9",
"64/35",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "efg_333577",
"desc": "Genus [333577]",
"stepCount": "24",
"steps": [
"49/48",
"2205/2048",
"35/32",
"9/8",
"147/128",
"7/6",
"315/256",
"5/4",
"245/192",
"21/16",
"4/3",
"45/32",
"735/512",
"35/24",
"3/2",
"49/32",
"105/64",
"5/3",
"441/256",
"7/4",
"15/8",
"245/128",
"63/32",
"2/1"
]
},
{
"id": "efg_335555_marvwoo",
"desc": "Genus [335555] in marvel temperament, woo tuning",
"stepCount": "15",
"steps": [
"66.81488",
"116.23027",
"267.51234",
"316.92773",
"383.74261",
"433.15800",
"499.97288",
"700.67034",
"767.48522",
"816.90061",
"883.71549",
"933.13088",
"1084.41295",
"1133.82835",
"1200.64322"
]
},
{
"id": "efg_335577",
"desc": "Genus chromaticum septimis triplex [335577]",
"stepCount": "27",
"steps": [
"21/20",
"16/15",
"15/14",
"35/32",
"8/7",
"7/6",
"6/5",
"128/105",
"5/4",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"8/5",
"105/64",
"5/3",
"12/7",
"7/4",
"64/35",
"28/15",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "efg_335711",
"desc": "Genus [335711]",
"stepCount": "24",
"steps": [
"33/32",
"35/32",
"9/8",
"1155/1024",
"77/64",
"315/256",
"5/4",
"165/128",
"21/16",
"693/512",
"11/8",
"45/32",
"3/2",
"385/256",
"99/64",
"105/64",
"3465/2048",
"55/32",
"7/4",
"231/128",
"15/8",
"495/256",
"63/32",
"2/1"
]
},
{
"id": "efg_3333555",
"desc": "Genus [3333555]",
"stepCount": "20",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"25/18",
"45/32",
"64/45",
"3/2",
"25/16",
"8/5",
"5/3",
"225/128",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "efg_3335711",
"desc": "Genus [3 3 3 5 7 11], expanded hexany 1 3 5 7 9 11",
"stepCount": "32",
"steps": [
"2079/2048",
"33/32",
"135/128",
"35/32",
"9/8",
"1155/1024",
"297/256",
"77/64",
"315/256",
"5/4",
"10395/8192",
"165/128",
"21/16",
"693/512",
"11/8",
"45/32",
"1485/1024",
"189/128",
"3/2",
"385/256",
"99/64",
"105/64",
"27/16",
"3465/2048",
"55/32",
"7/4",
"231/128",
"945/512",
"15/8",
"495/256",
"63/32",
"2/1"
]
},
{
"id": "efg_3571113",
"desc": "Genus [3 5 7 11 13]",
"stepCount": "32",
"steps": [
"65/64",
"33/32",
"2145/2048",
"273/256",
"35/32",
"143/128",
"1155/1024",
"77/64",
"39/32",
"5005/4096",
"5/4",
"165/128",
"21/16",
"1365/1024",
"11/8",
"715/512",
"91/64",
"3003/2048",
"3/2",
"385/256",
"195/128",
"13/8",
"105/64",
"429/256",
"55/32",
"7/4",
"455/256",
"231/128",
"15015/8192",
"15/8",
"1001/512",
"2/1"
]
},
{
"id": "efg_33335555",
"desc": "Genus bis-ultra-chromaticum [33335555], also dwarf25_5, limmic-magic weak Fokker block",
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"9/5",
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"77/72",
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"21/20",
"16/15",
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"21/20",
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"12/11",
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"id": "eikosanyplusop",
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"id": "eikoseven",
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"21/20",
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{
"id": "ekring_1",
"desc": "Single-tie circular mirroring of 3:4:5",
"stepCount": "12",
"steps": [
"9/8",
"6/5",
"5/4",
"27/20",
"45/32",
"36/25",
"25/16",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "ekring_2",
"desc": "Single-tie circular mirroring of 6:7:8",
"stepCount": "12",
"steps": [
"9/8",
"8/7",
"7/6",
"9/7",
"21/16",
"72/49",
"49/32",
"12/7",
"7/4",
"27/14",
"63/32",
"2/1"
]
},
{
"id": "ekring_3",
"desc": "Single-tie circular mirroring of 4:5:7",
"stepCount": "12",
"steps": [
"50/49",
"8/7",
"400/343",
"5/4",
"125/98",
"64/49",
"25/16",
"8/5",
"80/49",
"7/4",
"25/14",
"2/1"
]
},
{
"id": "ekring_4",
"desc": "Single-tie circular mirroring of 4:5:6",
"stepCount": "12",
"steps": [
"16/15",
"6/5",
"32/25",
"4/3",
"36/25",
"3/2",
"192/125",
"5/3",
"128/75",
"16/9",
"48/25",
"2/1"
]
},
{
"id": "ekring_5",
"desc": "Single-tie circular mirroring of 3:5:7",
"stepCount": "12",
"steps": [
"126/125",
"36/35",
"7/6",
"216/175",
"7/5",
"10/7",
"36/25",
"72/49",
"42/25",
"12/7",
"49/25",
"2/1"
]
},
{
"id": "ekring_5_bp",
"desc": "Single-tie BP circular mirroring of 3:5:7",
"stepCount": "12",
"steps": [
"27/25",
"9/7",
"243/175",
"7/5",
"189/125",
"81/49",
"49/25",
"15/7",
"81/35",
"7/3",
"63/25",
"3/1"
]
},
{
"id": "ekring_6",
"desc": "Single-tie circular mirroring of 6:7:9",
"stepCount": "12",
"steps": [
"54/49",
"8/7",
"9/7",
"4/3",
"72/49",
"3/2",
"14/9",
"81/49",
"16/9",
"648/343",
"96/49",
"2/1"
]
},
{
"id": "ekring_7",
"desc": "Single-tie circular mirroring of 5:7:9",
"stepCount": "12",
"steps": [
"50/49",
"10/9",
"500/441",
"100/81",
"9/7",
"450/343",
"14/9",
"100/63",
"81/49",
"9/5",
"90/49",
"2/1"
]
},
{
"id": "ekring_7_bp",
"desc": "Single-tie BP circular mirroring of 5:7:9",
"stepCount": "12",
"steps": [
"25/21",
"9/7",
"75/49",
"81/49",
"5/3",
"9/5",
"675/343",
"7/3",
"125/49",
"135/49",
"25/9",
"3/1"
]
},
{
"id": "elevenplus",
"desc": "11-tET plus the 22-tET fifth; C-D-Eb-F-Gb-A-Bb-C' form the Orgone[7] scale",
"stepCount": "12",
"steps": [
"109.09091",
"218.18182",
"327.27273",
"436.36364",
"545.45455",
"654.54545",
"709.09091",
"763.63636",
"872.72727",
"981.81818",
"1090.90909",
"2/1"
]
},
{
"id": "elf_12_f",
"desc": "A {352/351, 364/363} 2.3.7.11.13 elf transversal",
"stepCount": "12",
"steps": [
"28/27",
"9/8",
"13/11",
"9/7",
"4/3",
"11/8",
"3/2",
"14/9",
"22/13",
"16/9",
"27/14",
"2/1"
]
},
{
"id": "elf_87",
"desc": "Elf[87], a strictly proper MOS of elf, the 224&311 temperament",
"stepCount": "87",
"steps": [
"15.434084",
"27.009646",
"42.443730",
"54.019293",
"69.453376",
"81.028939",
"96.463023",
"111.897106",
"123.472669",
"138.906752",
"150.482315",
"165.916399",
"177.491961",
"192.926045",
"208.360129",
"219.935691",
"235.369775",
"246.945338",
"262.379421",
"273.954984",
"289.389068",
"304.823151",
"316.398714",
"331.832797",
"343.408360",
"358.842444",
"374.276527",
"385.852090",
"401.286174",
"412.861736",
"428.295820",
"439.871383",
"455.305466",
"470.739550",
"482.315113",
"497.749196",
"509.324759",
"524.758842",
"536.334405",
"551.768489",
"567.202572",
"578.778135",
"594.212219",
"605.787781",
"621.221865",
"632.797428",
"648.231511",
"663.665595",
"675.241158",
"690.675241",
"702.250804",
"717.684887",
"729.260450",
"744.694534",
"760.128617",
"771.704180",
"787.138264",
"798.713826",
"814.147910",
"825.723473",
"841.157556",
"856.591640",
"868.167203",
"883.601286",
"895.176849",
"910.610932",
"926.045016",
"937.620579",
"953.054662",
"964.630225",
"980.064309",
"991.639871",
"1007.073955",
"1022.508039",
"1034.083601",
"1049.517685",
"1061.093248",
"1076.527331",
"1088.102894",
"1103.536977",
"1118.971061",
"1130.546624",
"1145.980707",
"1157.556270",
"1172.990354",
"1184.565916",
"2/1"
]
},
{
"id": "elfjove_7",
"desc": "Jove tempering of [8/7, 11/9, 4/3, 3/2, 18/11, 7/4, 2], 202-tET tuning",
"stepCount": "7",
"steps": [
"231.68317",
"350.49505",
"499.00990",
"700.99010",
"849.50495",
"968.31683",
"2/1"
]
},
{
"id": "elfkeenanismic_7",
"desc": "Keenanismic tempered [8/7, 5/4, 4/3, 3/2, 8/5, 7/4, 2] = cross_7, 284et tuning",
"stepCount": "7",
"steps": [
"232.39437",
"384.50704",
"498.59155",
"701.40845",
"815.49296",
"967.60563",
"2/1"
]
},
{
"id": "elfkeenanismic_11_c",
"desc": "Keenanismic tempered [12/11, 8/7, 5/4, 21/16, 4/3, 3/2, 32/21, 8/5, 7/4, 11/6, 2], 284-tET tuning",
"stepCount": "11",
"steps": [
"152.11268",
"232.39437",
"384.50704",
"469.01408",
"498.59155",
"701.40845",
"730.98592",
"815.49296",
"967.60563",
"1047.88732",
"2/1"
]
},
{
"id": "elfkeenanismic_12",
"desc": "Keenanismic tempered [12/11, 8/7, 6/5, 5/4, 4/3, 11/8, 3/2, 8/5, 5/3, 7/4, 11/6, 2], 284et tuning",
"stepCount": "12",
"steps": [
"152.11268",
"232.39437",
"316.90141",
"384.50704",
"498.59155",
"549.29577",
"701.40845",
"815.49296",
"883.09859",
"967.60563",
"1047.88732",
"2/1"
]
},
{
"id": "elfleapday_7",
"desc": "Leapday tempering of [9/8, 13/11, 4/3, 3/2, 22/13, 16/9, 2], 46-tET tuning, 13-limit patent val elf",
"stepCount": "7",
"steps": [
"208.69565",
"286.95652",
"495.65217",
"704.34783",
"913.04348",
"991.30435",
"2/1"
]
},
{
"id": "elfleapday_8_d",
"desc": "Leapday tempering of [21/20, 9/8, 4/3, 7/5, 3/2, 16/9, 13/7, 2], 46-tET tuning, 13-limit 8d elf",
"stepCount": "8",
"steps": [
"78.26087",
"208.69565",
"495.65217",
"573.91304",
"704.34783",
"991.30435",
"1069.56522",
"2/1"
]
},
{
"id": "elfleapday_9",
"desc": "Leapday tempering of [9/8, 13/11, 14/11, 4/3, 3/2, 11/7, 22/13, 16/9, 2], 46-tET tuning, 13-limit patent val elf",
"stepCount": "9",
"steps": [
"208.69565",
"286.95652",
"417.39130",
"495.65217",
"704.34783",
"782.60870",
"913.04348",
"991.30435",
"2/1"
]
},
{
"id": "elfleapday_10",
"desc": "Leapday tempering of [21/20, 9/8, 14/11, 4/3, 7/5, 3/2, 11/7, 16/9, 21/11, 2], 46-tET tuning, 13-limit patent val elf",
"stepCount": "10",
"steps": [
"78.26087",
"208.69565",
"417.39130",
"495.65217",
"573.91304",
"704.34783",
"782.60870",
"991.30435",
"1121.73913",
"2/1"
]
},
{
"id": "elfleapday_12_f",
"desc": "Leapday tempering of [21/20, 9/8, 13/11, 14/11, 4/3, 7/5, 3/2, 11/7, 22/13, 16/9, 21/11, 2], in 46-tET, 13-limit 12f elf",
"stepCount": "12",
"steps": [
"78.26087",
"208.69565",
"286.95652",
"417.39130",
"495.65217",
"573.91304",
"704.34783",
"782.60870",
"913.04348",
"991.30435",
"1121.73913",
"2/1"
]
},
{
"id": "elfmadagascar_12_f",
"desc": "Madagascar tempering of [26/25, 15/13, 6/5, 9/7, 4/3, 7/5, 3/2, 14/9, 5/3, 26/15, 25/13, 2], 313-tET tuning",
"stepCount": "12",
"steps": [
"65.17572",
"249.20128",
"314.37700",
"433.22684",
"498.40256",
"582.74760",
"701.59744",
"766.77316",
"885.62300",
"950.79872",
"1134.82428",
"2/1"
]
},
{
"id": "elfmagic_7",
"desc": "Magic tempering of [10/9, 5/4, 4/3, 3/2, 8/5, 27/14, 2], 104-tET tuning, patent val elf",
"stepCount": "7",
"steps": [
"173.07692",
"380.76923",
"496.15385",
"703.84615",
"819.23077",
"1142.30769",
"2/1"
]
},
{
"id": "elfmagic_8",
"desc": "Magic tempering of [25/24, 6/5, 5/4, 9/7, 8/5, 5/3, 12/7, 2], 104-tET tuning, patent val elf",
"stepCount": "8",
"steps": [
"57.69231",
"323.07692",
"380.76923",
"438.46154",
"819.23077",
"876.92308",
"934.61538",
"2/1"
]
},
{
"id": "elfmagic_9",
"desc": "Magic tempering of [25/24, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3, 27/14, 2], 104-tET tuning, patent val elf",
"stepCount": "9",
"steps": [
"57.69231",
"323.07692",
"380.76923",
"496.15385",
"703.84615",
"819.23077",
"876.92308",
"1142.30769",
"2/1"
]
},
{
"id": "elfmagic_10",
"desc": "Magic tempering of [15/14, 7/6, 5/4, 9/7, 11/8, 14/9, 8/5, 12/7, 15/8, 2], 104-tET tuning, patent val elf",
"stepCount": "10",
"steps": [
"115.38462",
"265.38462",
"380.76923",
"438.46154",
"553.84615",
"761.53846",
"819.23077",
"934.61538",
"1084.61538",
"2/1"
]
},
{
"id": "elfmagic_12",
"desc": "Magic tempering of [25/24, 10/9, 6/5, 5/4, 4/3, 11/8, 3/2, 8/5, 5/3, 9/5, 27/14, 2], 104-tET tuning, patent val elf",
"stepCount": "12",
"steps": [
"57.69231",
"173.07692",
"323.07692",
"380.76923",
"496.15385",
"553.84615",
"703.84615",
"819.23077",
"876.92308",
"1026.92308",
"1142.30769",
"2/1"
]
},
{
"id": "elfmiracle_7",
"desc": "Miracle tempered [8/7, 11/9, 21/16, 32/21, 18/11, 15/8, 2], 72-tET tuning, 11-limit patent val elf",
"stepCount": "7",
"steps": [
"233.33333",
"350.00000",
"466.66667",
"733.33333",
"850.00000",
"1083.33333",
"2/1"
]
},
{
"id": "elfmiracle_12",
"desc": "Miracle tempered [15/14, 8/7, 7/6, 11/9, 21/16, 7/5, 32/21, 18/11, 12/7, 7/4, 15/8, 2], 72et tuning, 11-limit patent val elf",
"stepCount": "12",
"steps": [
"116.66667",
"233.33333",
"266.66667",
"350.00000",
"466.66667",
"583.33333",
"733.33333",
"850.00000",
"933.33333",
"966.66667",
"1083.33333",
"2/1"
]
},
{
"id": "elfmyna_7",
"desc": "Myna tempered [8/7, 6/5, 7/5, 10/7, 5/3, 7/4, 2] in 58-tET tuning, 13-limit patent val elf",
"stepCount": "7",
"steps": [
"227.58621",
"310.34483",
"579.31034",
"620.68966",
"889.65517",
"972.41379",
"2/1"
]
},
{
"id": "elfoctacot_12_f",
"desc": "Octacot tempered [21/20, 10/9, 7/6, 11/9, 15/11, 7/5, 22/15, 14/9, 12/7, 9/5, 21/11, 2], 150-tET tuning, 13-limit 12f val",
"stepCount": "12",
"steps": [
"88.00000",
"176.00000",
"264.00000",
"352.00000",
"528.00000",
"584.00000",
"672.00000",
"760.00000",
"936.00000",
"1024.00000",
"1112.00000",
"2/1"
]
},
{
"id": "elfqilin_10",
"desc": "Qilin tempering of [26/25, 15/13, 6/5, 9/7, 13/9, 14/9, 5/3, 26/15, 25/13, 2], POTE tuning, 13-limit patent val elf",
"stepCount": "10",
"steps": [
"62.19704",
"248.78817",
"310.98521",
"435.37929",
"640.22663",
"764.62071",
"889.01479",
"951.21183",
"1137.80296",
"2/1"
]
},
{
"id": "elfthrush_8_d",
"desc": "Thrush tempering of [21/20, 6/5, 5/4, 10/7, 3/2, 11/7, 21/11, 2], 89-tET tuning",
"stepCount": "8",
"steps": [
"80.89888",
"310.11236",
"391.01124",
"620.22472",
"701.12360",
"782.02247",
"1119.10112",
"2/1"
]
},
{
"id": "elfvalentine_8_d",
"desc": "Valentine tempered [21/20, 6/5, 5/4, 21/16, 8/5, 5/3, 11/6, 2] in 77-tET tuning, 11-limit 8d elf",
"stepCount": "8",
"steps": [
"77.92208",
"311.68831",
"389.61039",
"467.53247",
"810.38961",
"888.31169",
"1044.15584",
"2/1"
]
},
{
"id": "elfvalinorsmic_10",
"desc": "Valinorsmic tempering of [16/15, 11/10, 5/4, 4/3, 11/8, 3/2, 8/5, 20/11, 15/8, 2], 111-tET tuning",
"stepCount": "10",
"steps": [
"108.10811",
"162.16216",
"389.18919",
"497.29730",
"551.35135",
"702.70270",
"810.81081",
"1037.83784",
"1091.89189",
"2/1"
]
},
{
"id": "elfvalinorsmic_11",
"desc": "Valinorsmic tempering of [11/10, 9/8, 5/4, 4/3, 15/11, 22/15, 3/2, 8/5, 16/9, 20/11, 2], 111-tET tuning",
"stepCount": "11",
"steps": [
"162.16216",
"205.40541",
"389.18919",
"497.29730",
"540.54054",
"659.45946",
"702.70270",
"810.81081",
"994.59459",
"1037.83784",
"2/1"
]
},
{
"id": "elfzeus_10",
"desc": "Zeus tempering of [16/15, 11/10, 5/4, 4/3, 11/8, 3/2, 8/5, 7/4, 11/6, 2], 99-tET tuning",
"stepCount": "10",
"steps": [
"109.09091",
"157.57576",
"387.87879",
"496.96970",
"545.45455",
"703.03030",
"812.12121",
"969.69697",
"1042.42424",
"2/1"
]
},
{
"id": "elfzeus_12",
"desc": "Zeus tempering of [16/15, 11/10, 6/5, 5/4, 4/3, 11/8, 3/2, 8/5, 5/3, 7/4, 11/6, 2], 99-tET tuning",
"stepCount": "12",
"steps": [
"109.09091",
"157.57576",
"315.15152",
"387.87879",
"496.96970",
"545.45455",
"703.03030",
"812.12121",
"884.84848",
"969.69697",
"1042.42424",
"2/1"
]
},
{
"id": "ellis_24",
"desc": "Ellis, from p. 421 of Helmholtz, 24 tones of JI for 1 manual harmonium",
"stepCount": "24",
"steps": [
"81/80",
"25/24",
"135/128",
"9/8",
"729/640",
"75/64",
"1215/1024",
"5/4",
"81/64",
"4/3",
"27/20",
"45/32",
"729/512",
"3/2",
"243/160",
"25/16",
"405/256",
"5/3",
"27/16",
"225/128",
"3645/2048",
"15/8",
"243/128",
"2/1"
]
},
{
"id": "ellis_eb",
"desc": "Ellis's new equal beating temperament for pianofortes (1885)",
"stepCount": "12",
"steps": [
"100.20762",
"199.93511",
"300.36652",
"400.30420",
"499.94415",
"600.12513",
"699.74785",
"800.07968",
"899.92383",
"1000.46612",
"1100.50792",
"2/1"
]
},
{
"id": "ellis_harm",
"desc": "Ellis's Just Harmonium",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"27/20",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2"
]
},
{
"id": "ellis_mteb",
"desc": "Ellis's equal beating meantone tuning (1885)",
"stepCount": "12",
"steps": [
"75.70000",
"192.20000",
"310.70000",
"385.80000",
"504.75363",
"580.20000",
"696.26231",
"772.60000",
"889.10000",
"1007.81330",
"1083.40000",
"2/1"
]
},
{
"id": "ellis_r",
"desc": "Ellis's rational approximation of equal temperament",
"stepCount": "12",
"steps": [
"89/84",
"449/400",
"44/37",
"63/50",
"303/227",
"140/99",
"433/289",
"100/63",
"37/22",
"98/55",
"168/89",
"2/1"
]
},
{
"id": "ellis",
"desc": "Alexander John Ellis' imitation equal temperament (1875)",
"stepCount": "12",
"steps": [
"99.48477",
"199.49288",
"299.22463",
"399.46708",
"499.41938",
"599.87102",
"699.74785",
"799.35595",
"899.48110",
"999.32300",
"1099.66996",
"2/1"
]
},
{
"id": "enh_invcon",
"desc": "Inverted Enharmonic Conjunct Phrygian Harmonia",
"stepCount": "7",
"steps": ["13/12", "17/12", "35/24", "3/2", "23/12", "47/24", "2/1"]
},
{
"id": "enh_mod",
"desc": "Enharmonic After Wilson's Purvi Modulations, See page 111",
"stepCount": "7",
"steps": ["9/8", "7/6", "4/3", "3/2", "14/9", "8/5", "2/1"]
},
{
"id": "enh_perm",
"desc": "Permuted Enharmonic, After Wilson's Marwa Permutations, See page 110.",
"stepCount": "7",
"steps": ["28/27", "16/15", "4/3", "3/2", "14/9", "16/9", "2/1"]
},
{
"id": "enh_2",
"desc": "1:2 Enharmonic. New genus 2 + 4 + 24 parts",
"stepCount": "7",
"steps": [
"33.33333",
"100.00000",
"500.00000",
"700.00000",
"733.33333",
"800.00000",
"2/1"
]
},
{
"id": "enh_14",
"desc": "14/11 Enharmonic",
"stepCount": "7",
"steps": ["44/43", "22/21", "4/3", "3/2", "66/43", "11/7", "2/1"]
},
{
"id": "enh_15_inv",
"desc": "Inverted Enharmonic Tonos-15 Harmonia",
"stepCount": "7",
"steps": ["19/15", "13/10", "4/3", "22/15", "28/15", "29/15", "2/1"]
},
{
"id": "enh_15_inv_2",
"desc": "Inverted harmonic form of the enharmonic Tonos-15",
"stepCount": "7",
"steps": ["31/30", "16/15", "4/3", "22/15", "3/2", "23/15", "2/1"]
},
{
"id": "enh_15",
"desc": "Tonos-15 Enharmonic",
"stepCount": "7",
"steps": ["30/29", "15/14", "15/11", "3/2", "20/13", "30/19", "2/1"]
},
{
"id": "enh_17_con",
"desc": "Conjunct Tonos-17 Enharmonic",
"stepCount": "7",
"steps": ["34/33", "17/16", "17/12", "68/47", "34/23", "17/9", "2/1"]
},
{
"id": "enh_17",
"desc": "Tonos-17 Enharmonic",
"stepCount": "7",
"steps": ["34/33", "17/16", "17/12", "17/11", "68/43", "34/21", "2/1"]
},
{
"id": "enh_19_con",
"desc": "Conjunct Tonos-19 Enharmonic",
"stepCount": "7",
"steps": ["38/37", "19/18", "19/14", "76/55", "38/27", "19/11", "2/1"]
},
{
"id": "enh_19",
"desc": "Tonos-19 Enharmonic",
"stepCount": "7",
"steps": ["38/37", "19/18", "19/14", "19/13", "76/51", "38/25", "2/1"]
},
{
"id": "enh_21_inv",
"desc": "Inverted Enharmonic Tonos-21 Harmonia",
"stepCount": "7",
"steps": ["9/7", "55/42", "4/3", "32/21", "40/21", "41/21", "2/1"]
},
{
"id": "enh_21_inv_2",
"desc": "Inverted harmonic form of the enharmonic Tonos-21",
"stepCount": "7",
"steps": ["32/31", "16/15", "4/3", "32/21", "11/7", "34/21", "2/1"]
},
{
"id": "enh_21",
"desc": "Tonos-21 Enharmonic",
"stepCount": "7",
"steps": ["42/41", "21/20", "21/16", "3/2", "84/55", "14/9", "2/1"]
},
{
"id": "enh_23_con",
"desc": "Conjunct Tonos-23 Enharmonic",
"stepCount": "7",
"steps": ["46/45", "23/22", "23/18", "46/35", "23/17", "23/13", "2/1"]
},
{
"id": "enh_23",
"desc": "Tonos-23 Enharmonic",
"stepCount": "7",
"steps": ["46/45", "23/22", "23/18", "23/16", "46/31", "23/15", "2/1"]
},
{
"id": "enh_25_con",
"desc": "Conjunct Tonos-25 Enharmonic",
"stepCount": "7",
"steps": ["100/97", "50/47", "25/18", "10/7", "25/17", "25/13", "2/1"]
},
{
"id": "enh_25",
"desc": "Tonos-25 Enharmonic",
"stepCount": "7",
"steps": ["100/97", "50/47", "25/18", "25/16", "50/31", "5/3", "2/1"]
},
{
"id": "enh_27_inv",
"desc": "Inverted Enharmonic Tonos-27 Harmonia",
"stepCount": "7",
"steps": ["34/27", "35/27", "4/3", "40/27", "17/9", "35/18", "2/1"]
},
{
"id": "enh_27_inv_2",
"desc": "Inverted harmonic form of the enharmonic Tonos-27",
"stepCount": "7",
"steps": ["56/55", "28/27", "4/3", "40/27", "41/27", "14/9", "2/1"]
},
{
"id": "enh_27",
"desc": "Tonos-27 Enharmonic",
"stepCount": "7",
"steps": ["36/35", "18/17", "27/20", "3/2", "54/35", "27/17", "2/1"]
},
{
"id": "enh_29_con",
"desc": "Conjunct Tonos-29 Enharmonic",
"stepCount": "7",
"steps": ["58/57", "29/28", "29/22", "58/43", "29/21", "29/16", "2/1"]
},
{
"id": "enh_29",
"desc": "Tonos-29 Enharmonic",
"stepCount": "7",
"steps": ["58/57", "29/28", "29/22", "29/20", "58/39", "29/19", "2/1"]
},
{
"id": "enh_31_con",
"desc": "Conjunct Tonos-31 Enharmonic",
"stepCount": "8",
"steps": [
"31/30",
"31/29",
"31/24",
"31/23",
"62/45",
"31/22",
"31/18",
"2/1"
]
},
{
"id": "enh_31",
"desc": "Tonos-31 Enharmonic. Tone 24 alternates with 23 as MESE or A",
"stepCount": "8",
"steps": [
"31/30",
"31/29",
"31/24",
"31/23",
"31/22",
"62/43",
"31/21",
"2/1"
]
},
{
"id": "enh_33_con",
"desc": "Conjunct Tonos-33 Enharmonic",
"stepCount": "7",
"steps": ["33/32", "33/31", "11/8", "66/47", "33/23", "11/6", "2/1"]
},
{
"id": "enh_33",
"desc": "Tonos-33 Enharmonic",
"stepCount": "7",
"steps": ["33/32", "33/31", "11/8", "3/2", "66/43", "11/7", "2/1"]
},
{
"id": "enlil_19_13",
"desc": "Enlil[19] hobbit 13 limit minimax, commas 15625/15552, 385/384 and 325/324",
"stepCount": "19",
"steps": [
"68.28318",
"152.64336",
"180.50443",
"248.78761",
"317.07080",
"385.35398",
"469.71415",
"497.57523",
"565.85841",
"634.14159",
"702.42477",
"730.28585",
"814.64602",
"882.92920",
"951.21239",
"1019.49557",
"1047.35664",
"1131.71682",
"2/1"
]
},
{
"id": "ennea_45",
"desc": "Ennealimmal-45, in a 7-limit least-squares tuning, g=48.999, G.W. Smith",
"stepCount": "45",
"steps": [
"35.33500",
"48.99920",
"84.33420",
"97.99830",
"133.33330",
"168.66840",
"182.33250",
"217.66750",
"231.33160",
"266.66670",
"302.00170",
"315.66580",
"351.00080",
"364.66500",
"400.00000",
"435.33500",
"448.99920",
"484.33420",
"497.99830",
"533.33330",
"568.66840",
"582.33250",
"617.66750",
"631.33160",
"666.66670",
"702.00170",
"715.66580",
"751.00080",
"764.66500",
"800.00000",
"835.33500",
"848.99920",
"884.33420",
"897.99830",
"933.33330",
"968.66840",
"982.33250",
"1017.66750",
"1031.33160",
"1066.66670",
"1102.00170",
"1115.66580",
"1151.00080",
"1164.66500",
"2/1"
]
},
{
"id": "ennea_45_ji",
"desc": "Detempered Ennealimma-45, Hahn reduced",
"stepCount": "45",
"steps": [
"49/48",
"36/35",
"21/20",
"200/189",
"27/25",
"54/49",
"10/9",
"245/216",
"8/7",
"7/6",
"25/21",
"6/5",
"49/40",
"216/175",
"63/50",
"9/7",
"35/27",
"250/189",
"4/3",
"49/36",
"25/18",
"7/5",
"10/7",
"36/25",
"72/49",
"3/2",
"189/125",
"54/35",
"14/9",
"100/63",
"175/108",
"49/30",
"5/3",
"42/25",
"12/7",
"7/4",
"432/245",
"9/5",
"49/27",
"50/27",
"189/100",
"40/21",
"35/18",
"49/25",
"2/1"
]
},
{
"id": "ennea_72",
"desc": "Ennealimmal-72 in 612-tET tuning (strictly proper)",
"stepCount": "72",
"steps": [
"13.725490",
"35.294118",
"49.019608",
"62.745098",
"84.313725",
"98.039216",
"119.607843",
"133.333333",
"147.058824",
"168.627451",
"182.352941",
"196.078431",
"217.647059",
"231.372549",
"252.941176",
"266.666667",
"280.392157",
"301.960784",
"315.686275",
"329.411765",
"350.980392",
"364.705882",
"386.274510",
"400.000000",
"413.725490",
"435.294118",
"449.019608",
"462.745098",
"484.313725",
"498.039216",
"519.607843",
"533.333333",
"547.058824",
"568.627451",
"582.352941",
"596.078431",
"617.647059",
"631.372549",
"652.941176",
"666.666667",
"680.392157",
"701.960784",
"715.686275",
"729.411765",
"750.980392",
"764.705882",
"786.274510",
"800.000000",
"813.725490",
"835.294118",
"849.019608",
"862.745098",
"884.313725",
"898.039216",
"919.607843",
"933.333333",
"947.058824",
"968.627451",
"982.352941",
"996.078431",
"1017.647059",
"1031.372549",
"1052.941176",
"1066.666667",
"1080.392157",
"1101.960784",
"1115.686275",
"1129.411765",
"1150.980392",
"1164.705882",
"1186.274510",
"2/1"
]
},
{
"id": "ennea_72_synch",
"desc": "Poptimal synchonized beating ennealimmal tuning, TM 10-10-2005",
"stepCount": "72",
"steps": [
"13.65437",
"27.30874",
"48.99590",
"62.65027",
"76.30464",
"97.99180",
"111.64617",
"133.33333",
"146.98770",
"160.64207",
"182.32923",
"195.98360",
"209.63797",
"231.32513",
"244.97950",
"266.66667",
"280.32103",
"293.97540",
"315.66257",
"329.31694",
"342.97130",
"364.65847",
"378.31284",
"400.00000",
"413.65437",
"427.30874",
"448.99590",
"462.65027",
"476.30464",
"497.99180",
"511.64617",
"533.33333",
"546.98770",
"560.64207",
"582.32923",
"595.98360",
"609.63797",
"631.32513",
"644.97950",
"666.66666",
"680.32103",
"693.97540",
"715.66257",
"729.31693",
"742.97130",
"764.65847",
"778.31283",
"800.00000",
"813.65437",
"827.30874",
"848.99590",
"862.65027",
"876.30464",
"897.99180",
"911.64617",
"933.33333",
"946.98770",
"960.64207",
"982.32923",
"995.98360",
"1009.63797",
"1031.32513",
"1044.97950",
"1066.66666",
"1080.32103",
"1093.97540",
"1115.66256",
"1129.31693",
"1142.97130",
"1164.65847",
"1178.31283",
"2/1"
]
},
{
"id": "enneadecal_57",
"desc": "Enneadecal-57 (152&171) in 171-tET tuning",
"stepCount": "57",
"steps": [
"7.01754",
"14.03509",
"63.15790",
"70.17544",
"77.19298",
"126.31579",
"133.33333",
"140.35088",
"189.47368",
"196.49123",
"203.50877",
"252.63158",
"259.64912",
"266.66667",
"315.78947",
"322.80702",
"329.82456",
"378.94737",
"385.96491",
"392.98246",
"442.10526",
"449.12281",
"456.14035",
"505.26316",
"512.28070",
"519.29825",
"568.42105",
"575.43860",
"582.45614",
"631.57895",
"638.59649",
"645.61403",
"694.73684",
"701.75439",
"708.77193",
"757.89474",
"764.91228",
"771.92983",
"821.05263",
"828.07017",
"835.08772",
"884.21053",
"891.22807",
"898.24561",
"947.36842",
"954.38597",
"961.40351",
"1010.52632",
"1017.54386",
"1024.56140",
"1073.68421",
"1080.70175",
"1087.71930",
"1136.84210",
"1143.85965",
"1150.87719",
"2/1"
]
},
{
"id": "ennealimmal_45_trans",
"desc": "Ennealimmal-45 symmetric 5-limit transversal",
"stepCount": "45",
"steps": [
"78732/78125",
"250/243",
"6561/6250",
"3125/2916",
"27/25",
"390625/354294",
"10/9",
"177147/156250",
"125/108",
"729/625",
"15625/13122",
"6/5",
"1953125/1594323",
"5/4",
"19683/15625",
"625/486",
"162/125",
"78125/59049",
"4/3",
"531441/390625",
"25/18",
"4374/3125",
"3125/2187",
"36/25",
"781250/531441",
"3/2",
"118098/78125",
"125/81",
"972/625",
"31250/19683",
"8/5",
"3188646/1953125",
"5/3",
"26244/15625",
"1250/729",
"216/125",
"312500/177147",
"9/5",
"708588/390625",
"50/27",
"5832/3125",
"12500/6561",
"243/125",
"78125/39366",
"2/1"
]
},
{
"id": "ennon_28",
"desc": "Nonoctave Ennealimmal, [3, 5/3] just tuning",
"stepCount": "28",
"steps": [
"21/20",
"27/25",
"245/216",
"7/6",
"49/40",
"63/50",
"250/189",
"49/36",
"10/7",
"72/49",
"54/35",
"100/63",
"5/3",
"7/4",
"9/5",
"189/100",
"35/18",
"49/24",
"21/10",
"108/49",
"245/108",
"50/21",
"49/20",
"18/7",
"500/189",
"25/9",
"20/7",
"3/1"
]
},
{
"id": "epimore_enh",
"desc": "New Epimoric Enharmonic, Dorian mode of the 4th new Enharmonic on Hofmann's list",
"stepCount": "7",
"steps": ["76/75", "16/15", "4/3", "3/2", "38/25", "8/5", "2/1"]
},
{
"id": "eratos_chrom",
"desc": "Dorian mode of Eratosthenes's Chromatic. same as Ptol. Intense Chromatic",
"stepCount": "7",
"steps": ["20/19", "10/9", "4/3", "3/2", "30/19", "5/3", "2/1"]
},
{
"id": "eratos_diat",
"desc": "Dorian mode of Eratosthenes's Diatonic, Pythagorean. 7-tone Kurdi",
"stepCount": "7",
"steps": ["256/243", "32/27", "4/3", "3/2", "128/81", "16/9", "2/1"]
},
{
"id": "eratos_enh",
"desc": "Dorian mode of Eratosthenes's Enharmonic",
"stepCount": "7",
"steps": ["40/39", "20/19", "4/3", "3/2", "20/13", "30/19", "2/1"]
},
{
"id": "erlangen",
"desc": "Anonymus: Pro clavichordiis faciendis, Erlangen 15th century",
"stepCount": "12",
"steps": [
"256/243",
"4096/3645",
"32/27",
"5/4",
"4/3",
"1024/729",
"3/2",
"128/81",
"2048/1215",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "erlangen_2",
"desc": "Revised Erlangen",
"stepCount": "12",
"steps": [
"135/128",
"9/8",
"32/27",
"5/4",
"4/3",
"45/32",
"3/2",
"405/256",
"27/16",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "erlich_bpf",
"desc": "Erlich's 39-tone Triple Bohlen-Pierce scale",
"stepCount": "39",
"steps": [
"65/63",
"35/33",
"27/25",
"55/49",
"15/13",
"25/21",
"11/9",
"49/39",
"9/7",
"65/49",
"15/11",
"7/5",
"13/9",
"49/33",
"75/49",
"11/7",
"21/13",
"5/3",
"77/45",
"135/77",
"9/5",
"13/7",
"21/11",
"49/25",
"99/49",
"27/13",
"15/7",
"11/5",
"147/65",
"7/3",
"117/49",
"27/11",
"63/25",
"13/5",
"147/55",
"25/9",
"99/35",
"189/65",
"3/1"
]
},
{
"id": "erlich_bpp",
"desc": "Periodicity block for erlich_bpf, 1625/1617 1331/1323 275/273 245/243",
"stepCount": "39",
"steps": [
"77/75",
"35/33",
"27/25",
"55/49",
"63/55",
"25/21",
"11/9",
"1701/1375",
"9/7",
"33/25",
"15/11",
"7/5",
"275/189",
"81/55",
"75/49",
"11/7",
"441/275",
"5/3",
"77/45",
"135/77",
"9/5",
"275/147",
"21/11",
"49/25",
"99/49",
"567/275",
"15/7",
"11/5",
"25/11",
"7/3",
"825/343",
"27/11",
"63/25",
"55/21",
"147/55",
"135/49",
"99/35",
"225/77",
"3/1"
]
},
{
"id": "erlich_bpp_2",
"desc": "Improved shape for erlich_bpp",
"stepCount": "39",
"steps": [
"77/75",
"35/33",
"27/25",
"91/81",
"63/55",
"25/21",
"11/9",
"81/65",
"9/7",
"33/25",
"15/11",
"7/5",
"13/9",
"81/55",
"75/49",
"11/7",
"21/13",
"5/3",
"77/45",
"135/77",
"9/5",
"13/7",
"21/11",
"49/25",
"99/49",
"27/13",
"15/7",
"11/5",
"25/11",
"7/3",
"65/27",
"27/11",
"63/25",
"55/21",
"243/91",
"25/9",
"99/35",
"225/77",
"3/1"
]
},
{
"id": "erlich_bppe",
"desc": "LS optimal 3:5:7:11:13 tempering, virtually equal, g=780.2702 cents",
"stepCount": "39",
"steps": [
"48.35012",
"97.44116",
"145.79129",
"194.88233",
"243.23245",
"292.32349",
"340.67362",
"389.76466",
"438.85570",
"487.20582",
"536.29686",
"584.64699",
"633.73803",
"682.08815",
"731.17919",
"780.27023",
"828.62036",
"877.71140",
"926.06152",
"975.15256",
"1023.50269",
"1072.59373",
"1120.94385",
"1170.03489",
"1219.12593",
"1267.47606",
"1316.56710",
"1364.91722",
"1414.00826",
"1462.35839",
"1511.44943",
"1560.54047",
"1608.89059",
"1657.98163",
"1706.33176",
"1755.42280",
"1803.77292",
"1852.86396",
"3/1"
]
},
{
"id": "erlich_bppm",
"desc": "MM optimal 3:5:7:11:13 tempering, g=780.352 cents",
"stepCount": "39",
"steps": [
"50.14837",
"97.84986",
"147.99823",
"195.69972",
"245.84809",
"293.54957",
"343.69795",
"391.39943",
"439.10091",
"489.24929",
"536.95077",
"587.09915",
"634.80063",
"684.94900",
"732.65049",
"780.35197",
"830.50035",
"878.20183",
"928.35020",
"976.05169",
"1026.20006",
"1073.90154",
"1124.04992",
"1171.75140",
"1219.45289",
"1269.60126",
"1317.30274",
"1367.45112",
"1415.15260",
"1465.30098",
"1513.00246",
"1560.70394",
"1610.85232",
"1658.55380",
"1708.70217",
"1756.40366",
"1806.55203",
"1854.25352",
"3/1"
]
},
{
"id": "erlich_1",
"desc": "Asymmetrical Major decatonic mode of 22-tET, Paul Erlich",
"stepCount": "10",
"steps": [
"109.091 cents",
"218.182 cents",
"381.818 cents",
"490.909 cents",
"600.000 cents",
"709.091 cents",
"872.727 cents",
"981.818 cents",
"1090.909 cents",
"2/1"
]
},
{
"id": "erlich_2",
"desc": "Asymmetrical Minor decatonic mode of 22-tET, Paul Erlich",
"stepCount": "10",
"steps": [
"109.091 cents",
"218.182 cents",
"327.273 cents",
"490.909 cents",
"600.000 cents",
"709.091 cents",
"818.182 cents",
"927.273 cents",
"1036.364 cents",
"2/1"
]
},
{
"id": "erlich_3",
"desc": "Symmetrical Major decatonic mode of 22-tET, Paul Erlich",
"stepCount": "10",
"steps": [
"109.091 cents",
"218.182 cents",
"381.818 cents",
"490.909 cents",
"600.000 cents",
"709.091 cents",
"818.182 cents",
"981.818 cents",
"1090.909 cents",
"2/1"
]
},
{
"id": "erlich_4",
"desc": "Symmetrical Minor decatonic mode of 22-tET, Paul Erlich",
"stepCount": "10",
"steps": [
"109.091 cents",
"218.182 cents",
"327.273 cents",
"490.909 cents",
"600.000 cents",
"709.091 cents",
"818.182 cents",
"927.273 cents",
"1090.909 cents",
"2/1"
]
},
{
"id": "erlich_5",
"desc": "Unequal 22-note compromise between decatonic & Indian srutis, Paul Erlich",
"stepCount": "22",
"steps": [
"50.25000",
"105.75000",
"161.25000",
"211.50000",
"272.25000",
"322.50000",
"383.25000",
"428.25000",
"494.25000",
"539.25000",
"594.75000",
"650.25000",
"705.75000",
"761.25000",
"816.75000",
"872.25000",
"917.25000",
"983.25000",
"1028.25000",
"1089.00000",
"1139.25000",
"2/1"
]
},
{
"id": "erlich_6",
"desc": "Scale of consonant tones against 1/1-3/2 drone. TL 23-9-1998",
"stepCount": "22",
"steps": [
"21/20",
"15/14",
"12/11",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"21/16",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "erlich_7",
"desc": "Meantone-like circle of sinuoidally varying fifths, TL 08-12-99",
"stepCount": "26",
"steps": [
"71.40000",
"105.00000",
"128.90000",
"193.00000",
"257.10000",
"281.00000",
"314.60000",
"386.00000",
"438.60000",
"458.00000",
"504.10000",
"577.10000",
"616.80000",
"637.70000",
"696.40000",
"764.80000",
"793.00000",
"821.20000",
"889.60000",
"948.30000",
"969.20000",
"1008.90000",
"1081.90000",
"1128.00000",
"1147.40000",
"2/1"
]
},
{
"id": "erlich_8",
"desc": "Two 12-tET scales 15 cents shifted, Paul Erlich",
"stepCount": "24",
"steps": [
"15.00000",
"100.00000",
"115.00000",
"200.00000",
"215.00000",
"300.00000",
"315.00000",
"400.00000",
"415.00000",
"500.00000",
"515.00000",
"600.00000",
"615.00000",
"700.00000",
"715.00000",
"800.00000",
"815.00000",
"900.00000",
"915.00000",
"1000.00000",
"1015.00000",
"1100.00000",
"1115.00000",
"2/1"
]
},
{
"id": "erlich_9",
"desc": "Just scale by Paul Erlich (2002)",
"stepCount": "10",
"steps": [
"33/32",
"9/8",
"5/4",
"21/16",
"11/8",
"3/2",
"27/16",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "erlich_10",
"desc": "Canonical JI interpretation of the Pentachordal decatonic mode of 22-tET",
"stepCount": "10",
"steps": [
"21/20",
"8/7",
"6/5",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"2/1"
]
},
{
"id": "erlich_10_a",
"desc": "erlich10 in 50/49 (-1,5) tuning",
"stepCount": "10",
"steps": [
"108.33710",
"217.52687",
"325.86396",
"491.66290",
"600.00000",
"708.33710",
"817.52687",
"925.86396",
"1034.20106",
"2/1"
]
},
{
"id": "erlich_10_coh",
"desc": "Differential coherent version of erlich10 with subharmonic 40",
"stepCount": "10",
"steps": [
"21/20",
"23/20",
"6/5",
"53/40",
"7/5",
"3/2",
"8/5",
"69/40",
"9/5",
"2/1"
]
},
{
"id": "erlich_10_s_1",
"desc": "Superparticular version of erlich10 using 50/49 decatonic comma",
"stepCount": "10",
"steps": [
"15/14",
"8/7",
"6/5",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"2/1"
]
},
{
"id": "erlich_10_s_2",
"desc": "Other superparticular version of erlich10 using 50/49 decatonic comma",
"stepCount": "10",
"steps": [
"21/20",
"28/25",
"6/5",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"9/5",
"2/1"
]
},
{
"id": "erlich_11",
"desc": "Canonical JI interpretation of the Symmetrical decatonic mode of 22-tET",
"stepCount": "10",
"steps": [
"15/14",
"7/6",
"5/4",
"4/3",
"10/7",
"3/2",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "erlich_11_s_1",
"desc": "Superparticular version of erlich11 using 50/49 decatonic comma",
"stepCount": "10",
"steps": [
"21/20",
"7/6",
"5/4",
"4/3",
"10/7",
"3/2",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "erlich_11_s_2",
"desc": "Other superparticular version of erlich11 using 50/49 decatonic comma",
"stepCount": "10",
"steps": [
"15/14",
"7/6",
"25/21",
"4/3",
"10/7",
"3/2",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "erlich_12",
"desc": "Two 9-tET scales 3/2 shifted, Paul Erlich, TL 5-12-2001",
"stepCount": "18",
"steps": [
"35.28833",
"133.33333",
"168.62167",
"266.66667",
"301.95500",
"400.00000",
"435.28833",
"533.33333",
"568.62167",
"666.66667",
"3/2",
"800.00000",
"835.28833",
"933.33333",
"968.62167",
"1066.66667",
"1101.95500",
"2/1"
]
},
{
"id": "erlich_13",
"desc": "Just 7-limit scale by Paul Erlich",
"stepCount": "12",
"steps": [
"15/14",
"8/7",
"5/4",
"9/7",
"10/7",
"3/2",
"45/28",
"12/7",
"7/4",
"25/14",
"15/8",
"2/1"
]
},
{
"id": "erlichpump",
"desc": "Scale from a 385/384 comma pump by Paul Erlich (11-limit POTE tuning)",
"stepCount": "15",
"steps": [
"50.64769",
"119.28478",
"202.90337",
"283.43640",
"316.40730",
"385.04439",
"435.69208",
"549.19601",
"701.45169",
"752.09938",
"934.24039",
"967.21129",
"1098.39201",
"1137.14376",
"2/1"
]
},
{
"id": "escot",
"desc": "Nicolas Escot, Arcane 17 temperament",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"81/68",
"81/64",
"729/544",
"729/512",
"3/2",
"51/32",
"27/16",
"243/136",
"243/128",
"2/1"
]
},
{
"id": "et_mix_6",
"desc": "Mix of equal temperaments from 1-6 (= 4-6)",
"stepCount": "12",
"steps": [
"200.00000",
"240.00000",
"300.00000",
"400.00000",
"480.00000",
"600.00000",
"720.00000",
"800.00000",
"900.00000",
"960.00000",
"1000.00000",
"2/1"
]
},
{
"id": "et_mix_24",
"desc": "Mix of all equal temperaments from 1-24 (= 13-24)",
"stepCount": "180",
"steps": [
"50.00000",
"52.17391",
"54.54545",
"57.14286",
"60.00000",
"63.15789",
"66.66667",
"70.58824",
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"133.33333",
"141.17647",
"150.00000",
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"160.00000",
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"208.69565",
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"225.00000",
"228.57143",
"240.00000",
"250.00000",
"252.63158",
"257.14286",
"260.86957",
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"272.72727",
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"300.00000",
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"1136.84211",
"1140.00000",
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"1145.45455",
"1147.82609",
"1150.00000",
"2/1"
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},
{
"id": "etdays",
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"stepCount": "366",
"steps": [
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"16.42746",
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},
{
"id": "etdays_2",
"desc": "365.2563542th root of 2, average number of days per sidereal year",
"stepCount": "366",
"steps": [
"3.28536",
"6.57073",
"9.85609",
"13.14146",
"16.42682",
"19.71218",
"22.99755",
"26.28291",
"29.56827",
"32.85364",
"36.13900",
"39.42437",
"42.70973",
"45.99509",
"49.28046",
"52.56582",
"55.85118",
"59.13655",
"62.42191",
"65.70728",
"68.99264",
"72.27800",
"75.56337",
"78.84873",
"82.13409",
"85.41946",
"88.70482",
"91.99019",
"95.27555",
"98.56091",
"101.84628",
"105.13164",
"108.41701",
"111.70237",
"114.98773",
"118.27310",
"121.55846",
"124.84382",
"128.12919",
"131.41455",
"134.69992",
"137.98528",
"141.27064",
"144.55601",
"147.84137",
"151.12673",
"154.41210",
"157.69746",
"160.98283",
"164.26819",
"167.55355",
"170.83892",
"174.12428",
"177.40964",
"180.69501",
"183.98037",
"187.26574",
"190.55110",
"193.83646",
"197.12183",
"200.40719",
"203.69255",
"206.97792",
"210.26328",
"213.54865",
"216.83401",
"220.11937",
"223.40474",
"226.69010",
"229.97547",
"233.26083",
"236.54619",
"239.83156",
"243.11692",
"246.40228",
"249.68765",
"252.97301",
"256.25838",
"259.54374",
"262.82910",
"266.11447",
"269.39983",
"272.68519",
"275.97056",
"279.25592",
"282.54129",
"285.82665",
"289.11201",
"292.39738",
"295.68274",
"298.96810",
"302.25347",
"305.53883",
"308.82420",
"312.10956",
"315.39492",
"318.68029",
"321.96565",
"325.25102",
"328.53638",
"331.82174",
"335.10711",
"338.39247",
"341.67783",
"344.96320",
"348.24856",
"351.53393",
"354.81929",
"358.10465",
"361.39002",
"364.67538",
"367.96074",
"371.24611",
"374.53147",
"377.81684",
"381.10220",
"384.38756",
"387.67293",
"390.95829",
"394.24365",
"397.52902",
"400.81438",
"404.09975",
"407.38511",
"410.67047",
"413.95584",
"417.24120",
"420.52657",
"423.81193",
"427.09729",
"430.38266",
"433.66802",
"436.95338",
"440.23875",
"443.52411",
"446.80948",
"450.09484",
"453.38020",
"456.66557",
"459.95093",
"463.23629",
"466.52166",
"469.80702",
"473.09239",
"476.37775",
"479.66311",
"482.94848",
"486.23384",
"489.51920",
"492.80457",
"496.08993",
"499.37530",
"502.66066",
"505.94602",
"509.23139",
"512.51675",
"515.80211",
"519.08748",
"522.37284",
"525.65821",
"528.94357",
"532.22893",
"535.51430",
"538.79966",
"542.08503",
"545.37039",
"548.65575",
"551.94112",
"555.22648",
"558.51184",
"561.79721",
"565.08257",
"568.36794",
"571.65330",
"574.93866",
"578.22403",
"581.50939",
"584.79475",
"588.08012",
"591.36548",
"594.65085",
"597.93621",
"601.22157",
"604.50694",
"607.79230",
"611.07766",
"614.36303",
"617.64839",
"620.93376",
"624.21912",
"627.50448",
"630.78985",
"634.07521",
"637.36058",
"640.64594",
"643.93130",
"647.21667",
"650.50203",
"653.78739",
"657.07276",
"660.35812",
"663.64349",
"666.92885",
"670.21421",
"673.49958",
"676.78494",
"680.07030",
"683.35567",
"686.64103",
"689.92640",
"693.21176",
"696.49712",
"699.78249",
"703.06785",
"706.35321",
"709.63858",
"712.92394",
"716.20931",
"719.49467",
"722.78003",
"726.06540",
"729.35076",
"732.63613",
"735.92149",
"739.20685",
"742.49222",
"745.77758",
"749.06294",
"752.34831",
"755.63367",
"758.91904",
"762.20440",
"765.48976",
"768.77513",
"772.06049",
"775.34585",
"778.63122",
"781.91658",
"785.20195",
"788.48731",
"791.77267",
"795.05804",
"798.34340",
"801.62876",
"804.91413",
"808.19949",
"811.48486",
"814.77022",
"818.05558",
"821.34095",
"824.62631",
"827.91167",
"831.19704",
"834.48240",
"837.76777",
"841.05313",
"844.33849",
"847.62386",
"850.90922",
"854.19459",
"857.47995",
"860.76531",
"864.05068",
"867.33604",
"870.62140",
"873.90677",
"877.19213",
"880.47750",
"883.76286",
"887.04822",
"890.33359",
"893.61895",
"896.90431",
"900.18968",
"903.47504",
"906.76041",
"910.04577",
"913.33113",
"916.61650",
"919.90186",
"923.18722",
"926.47259",
"929.75795",
"933.04332",
"936.32868",
"939.61404",
"942.89941",
"946.18477",
"949.47014",
"952.75550",
"956.04086",
"959.32623",
"962.61159",
"965.89695",
"969.18232",
"972.46768",
"975.75305",
"979.03841",
"982.32377",
"985.60914",
"988.89450",
"992.17986",
"995.46523",
"998.75059",
"1002.03596",
"1005.32132",
"1008.60668",
"1011.89205",
"1015.17741",
"1018.46277",
"1021.74814",
"1025.03350",
"1028.31887",
"1031.60423",
"1034.88959",
"1038.17496",
"1041.46032",
"1044.74569",
"1048.03105",
"1051.31641",
"1054.60178",
"1057.88714",
"1061.17250",
"1064.45787",
"1067.74323",
"1071.02860",
"1074.31396",
"1077.59932",
"1080.88469",
"1084.17005",
"1087.45541",
"1090.74078",
"1094.02614",
"1097.31151",
"1100.59687",
"1103.88223",
"1107.16760",
"1110.45296",
"1113.73832",
"1117.02369",
"1120.30905",
"1123.59442",
"1126.87978",
"1130.16514",
"1133.45051",
"1136.73587",
"1140.02123",
"1143.30660",
"1146.59196",
"1149.87733",
"1153.16269",
"1156.44805",
"1159.73342",
"1163.01878",
"1166.30415",
"1169.58951",
"1172.87487",
"1176.16024",
"1179.44560",
"1182.73096",
"1186.01633",
"1189.30169",
"1192.58706",
"1195.87242",
"1199.15778",
"1202.44315"
]
},
{
"id": "euler_diat",
"desc": "Euler's genus diatonicum veterum correctum, 8-tone triadic cluster 4:5:6, genus [3335]",
"stepCount": "8",
"steps": ["9/8", "5/4", "4/3", "45/32", "3/2", "5/3", "15/8", "2/1"]
},
{
"id": "euler_enh",
"desc": "Euler's Old Enharmonic, From Tentamen Novae Theoriae Musicae",
"stepCount": "7",
"steps": ["128/125", "256/243", "4/3", "3/2", "192/125", "128/81", "2/1"]
},
{
"id": "euler_gm",
"desc": "Euler's Genus Musicum, Octony based on Archytas's Enharmonic",
"stepCount": "8",
"steps": [
"28/27",
"16/15",
"448/405",
"4/3",
"112/81",
"64/45",
"1792/1215",
"2/1"
]
},
{
"id": "euler",
"desc": "Euler's Monochord (a mode of Ellis's duodene) (1739), genus [33355]",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"75/64",
"5/4",
"4/3",
"45/32",
"3/2",
"25/16",
"5/3",
"225/128",
"15/8",
"2/1"
]
},
{
"id": "euler_20",
"desc": "Genus [3333555] tempered by 225/224-planar",
"stepCount": "20",
"steps": [
"83.67670",
"152.13946",
"199.68304",
"268.14580",
"351.82250",
"384.15214",
"399.36609",
"467.82884",
"583.83518",
"652.29794",
"699.84152",
"768.30428",
"783.51823",
"851.98098",
"899.52456",
"967.98732",
"1083.99366",
"1152.45642",
"1167.67037",
"2/1"
]
},
{
"id": "euler_24",
"desc": "Genus [33333555] tempered by 225/224-planar",
"stepCount": "24",
"steps": [
"83.67670",
"152.13946",
"199.68304",
"268.14580",
"283.35975",
"351.82250",
"384.15214",
"399.36609",
"467.82884",
"583.83518",
"652.29794",
"667.51189",
"699.84152",
"768.30428",
"783.51823",
"851.98098",
"899.52456",
"967.98732",
"1051.66402",
"1083.99366",
"1099.20761",
"1152.45642",
"1167.67037",
"2/1"
]
},
{
"id": "even_12_a",
"desc": "first maximally even {15/14,16/15,21/20,25/24} scale",
"stepCount": "12",
"steps": [
"21/20",
"35/32",
"7/6",
"5/4",
"21/16",
"45/32",
"3/2",
"25/16",
"105/64",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "even_12_b",
"desc": "second maximally even {15/14,16/15,21/20,25/24} scale",
"stepCount": "12",
"steps": [
"21/20",
"28/25",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"63/40",
"42/25",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "exptriad_2",
"desc": "Two times expanded major triad",
"stepCount": "7",
"steps": ["75/64", "5/4", "45/32", "3/2", "225/128", "15/8", "2/1"]
},
{
"id": "exptriad_3",
"desc": "Three times expanded major triad",
"stepCount": "30",
"steps": [
"16875/16384",
"135/128",
"16/15",
"1125/1024",
"9/8",
"256/225",
"151875/131072",
"75/64",
"6/5",
"10125/8192",
"5/4",
"675/512",
"4/3",
"5625/4096",
"45/32",
"64/45",
"759375/524288",
"375/256",
"3/2",
"50625/32768",
"25/16",
"8/5",
"3375/2048",
"5/3",
"128/75",
"225/128",
"15/8",
"253125/131072",
"2025/1024",
"2/1"
]
},
{
"id": "farey_3",
"desc": "Farey fractions between 0 and 1 until 3rd level, normalised by 2/1",
"stepCount": "5",
"steps": ["6/5", "4/3", "3/2", "8/5", "2/1"]
},
{
"id": "farey_4",
"desc": "Farey fractions between 0 and 1 until 4th level, normalised by 2/1",
"stepCount": "9",
"steps": ["8/7", "6/5", "5/4", "4/3", "10/7", "3/2", "8/5", "12/7", "2/1"]
},
{
"id": "farey_5",
"desc": "Farey fractions between 0 and 1 until 5th level, normalised by 2/1",
"stepCount": "20",
"steps": [
"12/11",
"10/9",
"8/7",
"7/6",
"6/5",
"16/13",
"5/4",
"14/11",
"4/3",
"7/5",
"10/7",
"16/11",
"3/2",
"20/13",
"14/9",
"8/5",
"5/3",
"12/7",
"16/9",
"2/1"
]
},
{
"id": "farey_12_65",
"desc": "Common denominator=65 Farey approximation to 12-tET",
"stepCount": "12",
"steps": [
"69/65",
"73/65",
"77/65",
"82/65",
"87/65",
"92/65",
"97/65",
"103/65",
"109/65",
"116/65",
"123/65",
"2/1"
]
},
{
"id": "farey_12_80",
"desc": "Common denominator=80 Farey approximation to 12-tET",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"101/80",
"107/80",
"113/80",
"3/2",
"127/80",
"27/16",
"143/80",
"151/80",
"2/1"
]
},
{
"id": "farey_12_101",
"desc": "Common denominator=101 Farey approximation to 12-tET",
"stepCount": "12",
"steps": [
"107/101",
"113/101",
"120/101",
"127/101",
"135/101",
"143/101",
"151/101",
"160/101",
"169/101",
"180/101",
"191/101",
"2/1"
]
},
{
"id": "farey_12_116",
"desc": "Common denominator=116 Farey approximation to 12-tET, well-temperament",
"stepCount": "12",
"steps": [
"123/116",
"65/58",
"69/58",
"73/58",
"155/116",
"41/29",
"3/2",
"46/29",
"195/116",
"207/116",
"219/116",
"2/1"
]
},
{
"id": "farnsworth",
"desc": "Farnsworth's scale",
"stepCount": "7",
"steps": ["9/8", "5/4", "21/16", "3/2", "27/16", "15/8", "2/1"]
},
{
"id": "fibo_9",
"desc": "First 9 Fibonacci terms reduced by 2/1, B. McLaren, XH 13, 1991",
"stepCount": "8",
"steps": ["17/16", "5/4", "21/16", "89/64", "3/2", "13/8", "55/32", "2/1"]
},
{
"id": "fibo_10",
"desc": "First 13 Fibonacci numbers reduced by 2/1",
"stepCount": "10",
"steps": [
"17/16",
"9/8",
"5/4",
"21/16",
"89/64",
"3/2",
"13/8",
"55/32",
"233/128",
"2/1"
]
},
{
"id": "finnamore_7",
"desc": "David J. Finnamore, TL 1 Sept '98. 7-tone Pyth. with 9/8 div. in 21/20 &15/14",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"189/160",
"81/64",
"4/3",
"7/5",
"3/2",
"63/40",
"27/16",
"567/320",
"243/128",
"2/1"
]
},
{
"id": "finnamore_7_a",
"desc": "David J. Finnamore, TL 1 Sept '98. 7-tone Pyth. with 9/8 div. in 15/14 &21/20",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"135/112",
"81/64",
"4/3",
"10/7",
"3/2",
"45/28",
"27/16",
"405/224",
"243/128",
"2/1"
]
},
{
"id": "finnamore_11",
"desc": "David J. Finnamore, 11-limit scale, TL 3-9-98",
"stepCount": "14",
"steps": [
"11/10",
"9/8",
"7/6",
"99/80",
"81/64",
"21/16",
"4/3",
"3/2",
"33/20",
"27/16",
"7/4",
"297/160",
"63/32",
"2/1"
]
},
{
"id": "finnamore_jc",
"desc": "Chalmers' modification of finnamore.scl, 19/18 x 9/8 x 64/57, TL 9-5-97",
"stepCount": "7",
"steps": ["19/18", "19/16", "4/3", "3/2", "19/12", "57/32", "2/1"]
},
{
"id": "finnamore",
"desc": "David J. Finnamore, tetrachordal scale, 17/16x19/17x64/57, TL 9-5-97",
"stepCount": "8",
"steps": ["17/16", "19/16", "4/3", "3/2", "51/32", "7/4", "57/32", "2/1"]
},
{
"id": "finnamore_53",
"desc": "David J. Finnamore, 53-limit tuning for \"Crawlspace\"(1998)",
"stepCount": "16",
"steps": [
"35/32",
"19/16",
"5/4",
"21/16",
"11/8",
"45/32",
"23/16",
"3/2",
"25/16",
"51/32",
"13/8",
"53/32",
"27/16",
"7/4",
"29/16",
"2/1"
]
},
{
"id": "fisher",
"desc": "Alexander Metcalf Fisher's modified meantone temperament (1818)",
"stepCount": "12",
"steps": [
"76.04900",
"193.15686",
"297.48515",
"5/4",
"502.42827",
"579.47058",
"696.57843",
"780.06791",
"889.73529",
"1004.85654",
"1082.89215",
"2/1"
]
},
{
"id": "fj_5_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 5-tet",
"stepCount": "5",
"steps": ["85/74", "95/72", "97/64", "47/27", "2/1"]
},
{
"id": "fj_7_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 7-tet",
"stepCount": "7",
"steps": ["53/48", "39/32", "35/26", "52/35", "64/39", "96/53", "2/1"]
},
{
"id": "fj_8_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 8-tet",
"stepCount": "8",
"steps": [
"12/11",
"44/37",
"83/64",
"99/70",
"91/59",
"37/22",
"11/6",
"2/1"
]
},
{
"id": "fj_9_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 9-tet",
"stepCount": "9",
"steps": [
"27/25",
"7/6",
"63/50",
"83/61",
"97/66",
"27/17",
"12/7",
"50/27",
"2/1"
]
},
{
"id": "fj_10_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 10-tet",
"stepCount": "10",
"steps": [
"15/14",
"85/74",
"16/13",
"95/72",
"99/70",
"97/64",
"13/8",
"47/27",
"28/15",
"2/1"
]
},
{
"id": "fj_12_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 12-tet",
"stepCount": "12",
"steps": [
"89/84",
"55/49",
"44/37",
"63/50",
"4/3",
"99/70",
"442/295",
"27/17",
"37/22",
"98/55",
"15/8",
"2/1"
]
},
{
"id": "fj_13_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 13-tet",
"stepCount": "13",
"steps": [
"77/73",
"89/80",
"88/75",
"26/21",
"47/36",
"84/61",
"61/42",
"72/47",
"21/13",
"75/44",
"7/44",
"55/29",
"2"
]
},
{
"id": "fj_14_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 14-tet",
"stepCount": "14",
"steps": [
"62/59",
"53/48",
"29/25",
"39/32",
"73/57",
"35/26",
"99/70",
"52/35",
"89/57",
"64/39",
"50/29",
"96/53",
"59/31",
"2/1"
]
},
{
"id": "fj_15_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 15-tet",
"stepCount": "15",
"steps": [
"22/21",
"34/31",
"85/74",
"77/64",
"63/50",
"95/72",
"76/55",
"55/38",
"97/64",
"27/17",
"3/2",
"47/27",
"31/17",
"21/11",
"2/1"
]
},
{
"id": "fj_16_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 16-tet",
"stepCount": "16",
"steps": [
"47/45",
"12/11",
"41/36",
"44/37",
"77/62",
"83/64",
"65/48",
"99/70",
"96/65",
"91/59",
"29/18",
"37/22",
"72/41",
"11/6",
"90/47",
"2/1"
]
},
{
"id": "fj_17_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 17-tet",
"stepCount": "17",
"steps": [
"25/24",
"51/47",
"26/23",
"93/79",
"38/31",
"23/18",
"145/109",
"97/70",
"10/7",
"3/2",
"83/53",
"31/19",
"17/10",
"23/13",
"59/32",
"48/25",
"2/1"
]
},
{
"id": "fj_18_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 18-tet",
"stepCount": "18",
"steps": [
"53/51",
"27/25",
"55/49",
"7/6",
"40/33",
"63/50",
"55/42",
"83/61",
"99/70",
"97/66",
"84/55",
"27/17",
"33/20",
"12/7",
"98/55",
"50/27",
"25/13",
"2/1"
]
},
{
"id": "fj_19_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 19-tet",
"stepCount": "19",
"steps": [
"28/27",
"71/66",
"29/26",
"81/70",
"6/5",
"61/49",
"71/55",
"79/59",
"25/18",
"36/25",
"118/79",
"79/51",
"45/28",
"5/3",
"19/11",
"95/53",
"13/7",
"27/14",
"2/1"
]
},
{
"id": "fj_20_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 20-tet",
"stepCount": "20",
"steps": [
"88/85",
"15/14",
"81/73",
"85/74",
"44/37",
"16/13",
"65/51",
"95/72",
"56/41",
"99/70",
"41/28",
"97/64",
"91/58",
"13/8",
"37/22",
"47/27",
"9/5",
"28/15",
"85/44",
"2/1"
]
},
{
"id": "fj_21_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 21-tet",
"stepCount": "21",
"steps": [
"31/30",
"47/44",
"53/48",
"97/85",
"46/39",
"39/32",
"63/50",
"56/43",
"35/26",
"32/23",
"23/16",
"52/35",
"43/28",
"27/17",
"64/39",
"39/23",
"7/4",
"96/53",
"88/47",
"89/46",
"2/1"
]
},
{
"id": "fj_22_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 22-tet",
"stepCount": "22",
"steps": [
"32/31",
"49/46",
"122/111",
"76/67",
"48/41",
"29/24",
"96/77",
"9/7",
"81/61",
"37/27",
"99/70",
"54/37",
"3/2",
"3/2",
"77/48",
"48/29",
"41/24",
"67/38",
"20/11",
"77/41",
"31/16",
"2/1"
]
},
{
"id": "fj_23_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 23-tet",
"stepCount": "23",
"steps": [
"34/33",
"17/16",
"81/74",
"44/39",
"50/43",
"133/111",
"21/17",
"14/11",
"80/61",
"73/54",
"39/28",
"56/39",
"37/25",
"61/40",
"11/7",
"34/21",
"5/3",
"43/25",
"39/22",
"95/52",
"32/17",
"33/17",
"2/1"
]
},
{
"id": "fj_24_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 24-tet",
"stepCount": "24",
"steps": [
"35/34",
"89/84",
"12/11",
"55/49",
"52/45",
"44/37",
"71/58",
"63/50",
"83/64",
"4/3",
"4/3",
"99/70",
"16/11",
"442/295",
"91/59",
"27/17",
"67/41",
"37/22",
"45/26",
"98/55",
"11/6",
"15/8",
"68/35",
"2/1"
]
},
{
"id": "fj_26_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 26-tet",
"stepCount": "26",
"steps": [
"38/37",
"77/73",
"13/12",
"89/80",
"8/7",
"88/75",
"47/39",
"26/21",
"75/59",
"47/36",
"59/44",
"84/61",
"99/70",
"61/42",
"88/59",
"72/47",
"11/7",
"21/13",
"78/47",
"75/44",
"7/4",
"7/4",
"24/13",
"55/29",
"37/19",
"2/1"
]
},
{
"id": "fj_30_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 30-tet",
"stepCount": "30",
"steps": [
"44/43",
"22/21",
"15/14",
"34/31",
"55/49",
"85/74",
"67/57",
"77/64",
"16/13",
"63/50",
"49/38",
"95/72",
"27/20",
"76/55",
"99/70",
"55/38",
"40/27",
"97/64",
"76/49",
"27/17",
"13/8",
"3/2",
"17/10",
"47/27",
"98/55",
"31/17",
"28/15",
"21/11",
"43/22",
"2/1"
]
},
{
"id": "fj_31_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 31-tet",
"stepCount": "31",
"steps": [
"45/44",
"23/22",
"77/72",
"35/32",
"85/76",
"8/7",
"69/59",
"55/46",
"11/9",
"5/4",
"78/61",
"17/13",
"111/83",
"93/68",
"7/5",
"10/7",
"19/13",
"166/111",
"26/17",
"61/39",
"8/5",
"18/11",
"97/58",
"65/38",
"7/4",
"93/52",
"64/35",
"43/23",
"44/23",
"88/45",
"2/1"
]
},
{
"id": "fj_36_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 36-tet",
"stepCount": "36",
"steps": [
"52/51",
"53/51",
"89/84",
"27/25",
"98/89",
"55/49",
"8/7",
"7/6",
"44/37",
"40/33",
"21/17",
"63/50",
"5/4",
"55/42",
"4/3",
"83/61",
"43/31",
"99/70",
"62/43",
"97/66",
"442/295",
"84/55",
"14/9",
"27/17",
"89/55",
"33/20",
"37/22",
"12/7",
"5/3",
"98/55",
"89/49",
"50/27",
"15/8",
"25/13",
"51/26",
"2/1"
]
},
{
"id": "fj_41_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 41-tet",
"stepCount": "41",
"steps": [
"60/59",
"30/29",
"81/77",
"46/43",
"37/34",
"83/75",
"9/8",
"87/76",
"85/73",
"45/38",
"53/44",
"49/40",
"76/61",
"19/15",
"67/52",
"38/29",
"4/3",
"61/45",
"91/66",
"7/5",
"87/61",
"29/20",
"90/61",
"3/2",
"29/19",
"45/29",
"30/19",
"61/38",
"80/49",
"93/56",
"76/45",
"67/39",
"5/3",
"16/9",
"47/26",
"68/37",
"43/23",
"19/10",
"29/15",
"59/30",
"2/1"
]
},
{
"id": "fj_42_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 42-tet",
"stepCount": "42",
"steps": [
"61/60",
"31/30",
"62/59",
"47/44",
"38/35",
"53/48",
"55/49",
"97/85",
"29/25",
"46/39",
"253/211",
"39/32",
"57/46",
"63/50",
"73/57",
"56/43",
"94/71",
"35/26",
"26/19",
"32/23",
"99/70",
"23/16",
"19/13",
"52/35",
"71/47",
"43/28",
"89/57",
"27/17",
"71/44",
"64/39",
"5/3",
"39/23",
"50/29",
"7/4",
"98/55",
"96/53",
"35/19",
"88/47",
"59/31",
"89/46",
"61/31",
"2/1"
]
},
{
"id": "fj_43_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 43-tet",
"stepCount": "43",
"steps": [
"63/62",
"63/61",
"21/20",
"16/15",
"13/12",
"76/69",
"75/67",
"33/29",
"37/32",
"47/40",
"80/67",
"91/75",
"37/30",
"99/79",
"14/11",
"22/17",
"25/19",
"4/3",
"72/53",
"98/71",
"94/67",
"67/47",
"71/49",
"53/36",
"199/133",
"73/48",
"17/11",
"3/2",
"75/47",
"60/37",
"89/54",
"67/40",
"80/47",
"64/37",
"58/33",
"25/14",
"69/38",
"24/13",
"15/8",
"40/21",
"31/16",
"61/31",
"2/1"
]
},
{
"id": "fj_53_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 53-tet",
"stepCount": "53",
"steps": [
"77/76",
"39/38",
"26/25",
"98/93",
"79/74",
"53/49",
"80/73",
"151/136",
"9/8",
"49/43",
"97/84",
"62/53",
"32/27",
"6/5",
"73/60",
"53/43",
"306/245",
"62/49",
"50/39",
"9/7",
"25/19",
"4/3",
"77/57",
"26/19",
"43/31",
"59/42",
"37/26",
"75/52",
"19/13",
"37/25",
"3/2",
"38/25",
"97/63",
"39/25",
"49/31",
"8/5",
"73/45",
"23/14",
"5/3",
"27/16",
"53/31",
"97/56",
"93/53",
"16/9",
"9/5",
"73/40",
"98/53",
"13/7",
"93/49",
"25/13",
"76/39",
"75/38",
"2/1"
]
},
{
"id": "fj_54_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 54-tet",
"stepCount": "54",
"steps": [
"78/77",
"79/77",
"53/51",
"20/19",
"16/15",
"27/25",
"35/32",
"41/37",
"55/49",
"83/73",
"38/33",
"7/6",
"13/11",
"79/66",
"40/33",
"70/57",
"51/41",
"63/50",
"97/76",
"53/41",
"55/42",
"61/46",
"43/32",
"83/61",
"51/37",
"74/53",
"99/70",
"53/37",
"74/51",
"97/66",
"67/45",
"95/63",
"84/55",
"82/53",
"47/30",
"27/17",
"82/51",
"57/35",
"33/20",
"5/3",
"22/13",
"12/7",
"33/19",
"95/54",
"98/55",
"74/41",
"64/35",
"50/27",
"15/8",
"19/10",
"25/13",
"39/20",
"77/39",
"2/1"
]
},
{
"id": "fj_55_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 55-tet",
"stepCount": "55",
"steps": [
"80/79",
"40/39",
"27/26",
"61/58",
"49/46",
"55/51",
"71/65",
"73/66",
"28/25",
"76/67",
"85/74",
"57/49",
"86/73",
"68/57",
"29/24",
"11/9",
"83/67",
"69/55",
"47/37",
"9/7",
"43/33",
"95/72",
"4/3",
"23/17",
"37/27",
"68/49",
"52/37",
"37/26",
"49/34",
"54/37",
"34/23",
"229/153",
"97/64",
"66/43",
"143/92",
"85/54",
"51/32",
"8/5",
"85/52",
"48/29",
"57/34",
"73/43",
"98/57",
"47/27",
"67/38",
"25/14",
"47/26",
"130/71",
"89/48",
"77/41",
"97/51",
"52/27",
"39/20",
"79/40",
"2/1"
]
},
{
"id": "fj_60_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 60-tet",
"stepCount": "60",
"steps": [
"87/86",
"44/43",
"88/85",
"22/21",
"89/84",
"15/14",
"90/83",
"34/31",
"81/73",
"55/49",
"67/59",
"85/74",
"43/37",
"67/57",
"44/37",
"77/64",
"28/23",
"16/13",
"66/53",
"63/50",
"65/51",
"49/38",
"30/23",
"95/72",
"4/3",
"27/20",
"56/41",
"76/55",
"137/98",
"99/70",
"93/65",
"55/38",
"41/28",
"40/27",
"442/295",
"97/64",
"23/15",
"76/49",
"91/58",
"27/17",
"53/33",
"13/8",
"23/14",
"128/77",
"37/22",
"17/10",
"74/43",
"47/27",
"37/21",
"98/55",
"9/5",
"31/17",
"83/45",
"28/15",
"15/8",
"21/11",
"85/44",
"43/22",
"87/44",
"2/1"
]
},
{
"id": "fj_66_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 66-tet",
"stepCount": "66",
"steps": [
"96/95",
"48/47",
"32/31",
"73/70",
"39/37",
"49/46",
"127/118",
"62/57",
"122/111",
"10/9",
"55/49",
"76/67",
"47/41",
"22/19",
"48/41",
"97/82",
"55/46",
"29/24",
"94/77",
"95/77",
"96/77",
"63/50",
"14/11",
"9/7",
"13/10",
"46/35",
"81/61",
"51/38",
"80/59",
"37/27",
"18/13",
"7/5",
"99/70",
"10/7",
"13/9",
"54/37",
"59/40",
"79/53",
"3/2",
"35/23",
"20/13",
"143/92",
"11/7",
"27/17",
"77/48",
"47/29",
"77/47",
"48/29",
"87/52",
"71/42",
"41/24",
"19/11",
"82/47",
"67/38",
"98/55",
"9/5",
"20/11",
"57/31",
"13/7",
"77/41",
"74/39",
"23/12",
"31/16",
"47/24",
"95/48",
"2/1"
]
},
{
"id": "fj_72_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 72-tet",
"stepCount": "72",
"steps": [
"104/103",
"52/51",
"35/34",
"53/51",
"85/81",
"89/84",
"46/43",
"27/25",
"12/11",
"98/89",
"10/9",
"55/49",
"17/15",
"8/7",
"52/45",
"7/6",
"53/45",
"44/37",
"6/5",
"40/33",
"71/58",
"21/17",
"141/113",
"63/50",
"14/11",
"140/109",
"83/64",
"55/42",
"78/59",
"4/3",
"31/23",
"83/61",
"158/115",
"43/31",
"7/5",
"99/70",
"10/7",
"62/43",
"16/11",
"97/66",
"46/31",
"442/295",
"59/39",
"84/55",
"91/59",
"14/9",
"11/7",
"27/17",
"8/5",
"89/55",
"67/41",
"33/20",
"558/335",
"37/22",
"90/53",
"12/7",
"45/26",
"194/111",
"30/17",
"98/55",
"9/5",
"89/49",
"11/6",
"50/27",
"43/23",
"15/8",
"61/32",
"25/13",
"68/35",
"51/26",
"103/52",
"2/1"
]
},
{
"id": "fj_78_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 78-tet",
"stepCount": "78",
"steps": [
"113/112",
"57/56",
"38/37",
"86/83",
"23/22",
"77/73",
"83/78",
"73/68",
"13/12",
"47/43",
"43/39",
"89/80",
"55/49",
"94/83",
"8/7",
"83/72",
"57/49",
"88/75",
"45/38",
"43/36",
"47/39",
"45/37",
"92/75",
"26/21",
"251/201",
"63/50",
"75/59",
"59/46",
"22/17",
"47/36",
"54/41",
"97/73",
"59/44",
"23/17",
"15/11",
"84/61",
"25/18",
"7/5",
"99/70",
"117/82",
"36/25",
"61/42",
"85/58",
"34/23",
"88/59",
"3/2",
"41/27",
"72/47",
"17/11",
"92/59",
"11/7",
"27/17",
"8/5",
"21/13",
"75/46",
"51/31",
"78/47",
"72/43",
"49/29",
"75/44",
"43/25",
"85/49",
"7/4",
"83/47",
"98/55",
"151/84",
"78/43",
"86/47",
"24/13",
"95/51",
"47/25",
"55/29",
"44/23",
"83/43",
"37/19",
"55/28",
"111/56",
"2/1"
]
},
{
"id": "fj_84_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 84-tet",
"stepCount": "84",
"steps": [
"121/120",
"61/60",
"41/40",
"31/30",
"99/95",
"62/59",
"89/84",
"47/44",
"14/13",
"38/35",
"23/21",
"53/48",
"59/53",
"55/49",
"43/38",
"97/85",
"84/73",
"29/25",
"62/53",
"46/39",
"44/37",
"253/211",
"81/67",
"39/32",
"59/48",
"57/46",
"5/4",
"63/50",
"47/37",
"73/57",
"31/24",
"56/43",
"21/16",
"94/71",
"4/3",
"35/26",
"19/14",
"26/19",
"40/29",
"32/23",
"7/5",
"99/70",
"77/54",
"23/16",
"29/20",
"19/13",
"28/19",
"52/35",
"442/295",
"71/47",
"99/65",
"43/28",
"48/31",
"89/57",
"74/47",
"27/17",
"8/5",
"71/44",
"96/59",
"64/39",
"43/26",
"5/3",
"37/22",
"39/23",
"53/31",
"50/29",
"73/42",
"7/4",
"76/43",
"98/55",
"97/54",
"96/53",
"42/23",
"35/19",
"13/7",
"88/47",
"15/8",
"59/31",
"71/37",
"89/46",
"80/41",
"61/31",
"119/60",
"2/1"
]
},
{
"id": "fj_90_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 90-tet",
"stepCount": "90",
"steps": [
"130/129",
"65/64",
"44/43",
"33/32",
"53/51",
"22/21",
"19/18",
"67/63",
"15/14",
"27/25",
"37/34",
"34/31",
"21/19",
"88/79",
"55/49",
"69/61",
"57/50",
"85/74",
"22/19",
"7/6",
"67/57",
"77/65",
"37/31",
"77/64",
"40/33",
"11/9",
"16/13",
"67/54",
"5/4",
"63/50",
"33/26",
"87/68",
"49/38",
"13/10",
"55/42",
"95/72",
"121/91",
"67/50",
"27/20",
"83/61",
"48/35",
"76/55",
"39/28",
"80/57",
"99/70",
"57/40",
"56/39",
"55/38",
"35/24",
"97/66",
"40/27",
"100/67",
"3/2",
"97/64",
"84/55",
"20/13",
"76/49",
"25/16",
"63/40",
"27/17",
"8/5",
"79/49",
"13/8",
"18/11",
"33/20",
"128/77",
"62/37",
"27/16",
"17/10",
"12/7",
"19/11",
"47/27",
"93/53",
"122/69",
"98/55",
"79/44",
"38/21",
"31/17",
"68/37",
"50/27",
"28/15",
"47/25",
"36/19",
"21/11",
"25/13",
"64/33",
"43/22",
"65/33",
"129/65",
"2/1"
]
},
{
"id": "fj_96_tet",
"desc": "Franck Jedrzejewski continued fractions approx. of 96-tet",
"stepCount": "96",
"steps": [
"138/137",
"70/69",
"47/46",
"35/34",
"28/27",
"47/45",
"61/58",
"89/84",
"16/15",
"43/40",
"131/121",
"12/11",
"67/61",
"52/47",
"39/35",
"55/49",
"26/23",
"41/36",
"39/34",
"52/45",
"64/55",
"34/29",
"98/83",
"44/37",
"109/91",
"76/63",
"96/79",
"71/58",
"90/73",
"77/62",
"5/4",
"63/50",
"33/26",
"23/18",
"94/73",
"83/64",
"64/49",
"25/19",
"53/40",
"4/3",
"39/29",
"65/48",
"15/11",
"158/115",
"18/13",
"46/33",
"73/52",
"99/70",
"47/33",
"33/23",
"13/9",
"16/11",
"22/15",
"96/65",
"61/41",
"442/295",
"83/55",
"38/25",
"49/32",
"91/59",
"73/47",
"97/62",
"52/33",
"27/17",
"291/182",
"29/18",
"73/45",
"67/41",
"79/48",
"63/38",
"5/3",
"37/22",
"83/49",
"29/17",
"55/32",
"45/26",
"68/39",
"72/41",
"23/13",
"98/55",
"70/39",
"47/26",
"71/39",
"11/6",
"24/13",
"80/43",
"15/8",
"168/89",
"19/10",
"90/47",
"27/14",
"68/35",
"92/47",
"69/35",
"137/69",
"2/1"
]
},
{
"id": "flattone_12",
"desc": "Flattone[12] in 13-limit POTE tuning",
"stepCount": "12",
"steps": [
"134.71117",
"186.11553",
"320.82670",
"372.23106",
"506.94223",
"558.34660",
"693.05777",
"827.76894",
"879.17330",
"1013.88447",
"1065.28883",
"2/1"
]
},
{
"id": "flavel",
"desc": "Bill Flavel's just tuning, mode of Ellis's Just Harmonium. Tuning List 06-05-98",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"9/8",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "flippery_9",
"desc": "A 9-note flippery scale",
"stepCount": "9",
"steps": ["9/8", "6/5", "5/4", "45/32", "3/2", "8/5", "5/3", "15/8", "2/1"]
},
{
"id": "fogliano",
"desc": "Fogliano's Monochord with D-/D and Bb-/Bb",
"stepCount": "14",
"steps": [
"25/24",
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"16/9",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "fogliano_1",
"desc": "Fogliano's Monochord no.1, Musica theorica (1529). Fokker block 81/80 128/125",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "fogliano_2",
"desc": "Fogliano's Monochord no.2",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "fokker_12",
"desc": "Fokker's 7-limit 12-tone just scale",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"7/6",
"5/4",
"4/3",
"45/32",
"3/2",
"45/28",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "fokker_12_a",
"desc": "Fokker's 7-limit periodicity block of 2048/2025 & 3969/4000 & 225/224",
"stepCount": "12",
"steps": [
"21/20",
"28/25",
"189/160",
"5/4",
"4/3",
"45/32",
"112/75",
"63/40",
"42/25",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "fokker_12_b",
"desc": "Fokker's 7-limit semitone scale KNAW B72, 1969",
"stepCount": "12",
"steps": [
"135/128",
"28/25",
"189/160",
"80/63",
"4/3",
"45/32",
"3/2",
"63/40",
"42/25",
"25/14",
"256/135",
"2/1"
]
},
{
"id": "fokker_12_c",
"desc": "Fokker's 7-limit complementary semitone scale, KNAW B72, 1969",
"stepCount": "12",
"steps": [
"135/128",
"28/25",
"25/21",
"80/63",
"4/3",
"64/45",
"3/2",
"63/40",
"320/189",
"25/14",
"256/135",
"2/1"
]
},
{
"id": "fokker_12_m",
"desc": "Fokker's 12-tone 31-tET mode, has 3 4:5:6:7 tetrads + 3 inv.",
"stepCount": "12",
"steps": [
"116.12903",
"193.54839",
"270.96774",
"387.09677",
"503.22581",
"580.64516",
"696.77419",
"812.90323",
"890.32258",
"967.74194",
"1083.87097",
"2/1"
]
},
{
"id": "fokker_12_t",
"desc": "Tempered version of fokker_12.scl with egalised 225/224, see also lumma.scl",
"stepCount": "12",
"steps": [
"114.61072",
"199.23744",
"268.08492",
"384.35188",
"499.28244",
"584.20487",
"699.21999",
"815.58633",
"884.32517",
"968.96547",
"1083.57434",
"2/1"
]
},
{
"id": "fokker_12_t_2",
"desc": "Another tempered version of fokker_12.scl with egalised 225/224",
"stepCount": "12",
"steps": [
"114.60324",
"199.20699",
"268.10105",
"384.35373",
"499.38740",
"584.17762",
"699.21129",
"815.46396",
"5/3",
"968.96178",
"1083.56502",
"2/1"
]
},
{
"id": "fokker_22",
"desc": "Fokker's 22-tone periodicity block of 2048/2025 & 3125/3072. KNAW B71, 1968",
"stepCount": "22",
"steps": [
"25/24",
"16/15",
"1125/1024",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"27/20",
"45/32",
"375/256",
"3/2",
"25/16",
"8/5",
"5/3",
"128/75",
"225/128",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "fokker_22_a",
"desc": "Fokker's 22-tone periodicity block of 2048/2025 & 2109375/2097152 = semicomma",
"stepCount": "22",
"steps": [
"16875/16384",
"16/15",
"1125/1024",
"256/225",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"512/375",
"45/32",
"375/256",
"3/2",
"25/16",
"8/5",
"3375/2048",
"128/75",
"225/128",
"2048/1125",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "fokker_31",
"desc": "Fokker's 31-tone just system",
"stepCount": "31",
"steps": [
"64/63",
"135/128",
"15/14",
"35/32",
"9/8",
"8/7",
"7/6",
"135/112",
"315/256",
"5/4",
"9/7",
"21/16",
"4/3",
"175/128",
"45/32",
"10/7",
"35/24",
"3/2",
"32/21",
"14/9",
"45/28",
"105/64",
"5/3",
"12/7",
"7/4",
"16/9",
"945/512",
"15/8",
"40/21",
"63/32",
"2/1"
]
},
{
"id": "fokker_31_a",
"desc": "Fokker's 31-tone first alternate septimal tuning",
"stepCount": "31",
"steps": [
"36/35",
"25/24",
"15/14",
"35/32",
"9/8",
"8/7",
"7/6",
"25/21",
"315/256",
"5/4",
"9/7",
"21/16",
"4/3",
"175/128",
"45/32",
"10/7",
"35/24",
"3/2",
"32/21",
"63/40",
"45/28",
"105/64",
"5/3",
"12/7",
"7/4",
"9/5",
"175/96",
"15/8",
"40/21",
"63/32",
"2/1"
]
},
{
"id": "fokker_31_b",
"desc": "Fokker's 31-tone second alternate septimal tuning",
"stepCount": "31",
"steps": [
"49/48",
"21/20",
"15/14",
"35/32",
"9/8",
"8/7",
"7/6",
"6/5",
"315/256",
"5/4",
"9/7",
"21/16",
"4/3",
"175/128",
"45/32",
"10/7",
"35/24",
"3/2",
"32/21",
"25/16",
"45/28",
"105/64",
"5/3",
"12/7",
"7/4",
"25/14",
"90/49",
"15/8",
"40/21",
"63/32",
"2/1"
]
},
{
"id": "fokker_31_c",
"desc": "Fokker's 31-tone periodicity block of 81/80 & 2109375/2097152 = semicomma",
"stepCount": "31",
"steps": [
"16875/16384",
"25/24",
"16/15",
"1125/1024",
"9/8",
"256/225",
"75/64",
"6/5",
"625/512",
"5/4",
"32/25",
"675/512",
"4/3",
"5625/4096",
"45/32",
"64/45",
"375/256",
"3/2",
"1024/675",
"25/16",
"8/5",
"3375/2048",
"5/3",
"128/75",
"225/128",
"16/9",
"1875/1024",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "fokker_31_d",
"desc": "Fokker's 31-tone periodicity block of 81/80 & W�rschmidt's comma",
"stepCount": "31",
"steps": [
"3125/3072",
"25/24",
"16/15",
"1125/1024",
"9/8",
"9375/8192",
"75/64",
"6/5",
"625/512",
"5/4",
"32/25",
"125/96",
"4/3",
"5625/4096",
"45/32",
"36/25",
"375/256",
"3/2",
"3125/2048",
"25/16",
"8/5",
"625/384",
"5/3",
"15625/9216",
"225/128",
"9/5",
"1875/1024",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "fokker_31_d_2",
"desc": "Reduced version of fokker_31d by Prooijen expressibility",
"stepCount": "31",
"steps": [
"128/125",
"25/24",
"16/15",
"625/576",
"10/9",
"144/125",
"75/64",
"6/5",
"625/512",
"5/4",
"32/25",
"125/96",
"4/3",
"512/375",
"25/18",
"36/25",
"375/256",
"3/2",
"192/125",
"25/16",
"8/5",
"625/384",
"5/3",
"128/75",
"125/72",
"16/9",
"1152/625",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "fokker_41",
"desc": "Fokker's 7-limit supracomma per.bl. 10976/10935 & 225/224 & 496125/262144",
"stepCount": "41",
"steps": [
"81/80",
"28/27",
"21/20",
"15/14",
"243/224",
"10/9",
"9/8",
"225/196",
"7/6",
"25/21",
"6/5",
"896/729",
"56/45",
"63/50",
"9/7",
"98/75",
"4/3",
"27/20",
"112/81",
"7/5",
"10/7",
"81/56",
"40/27",
"3/2",
"75/49",
"14/9",
"100/63",
"45/28",
"729/448",
"5/3",
"42/25",
"12/7",
"392/225",
"16/9",
"9/5",
"448/243",
"28/15",
"40/21",
"27/14",
"160/81",
"2/1"
]
},
{
"id": "fokker_41_a",
"desc": "Fokker's 41-tone periodicity block of schisma & 34171875/33554432",
"stepCount": "41",
"steps": [
"2048/2025",
"273375/262144",
"135/128",
"16/15",
"1125/1024",
"18225/16384",
"9/8",
"256/225",
"75/64",
"1215/1024",
"6/5",
"10125/8192",
"5/4",
"81/64",
"32/25",
"675/512",
"4/3",
"27/20",
"91125/65536",
"45/32",
"64/45",
"131072/91125",
"6075/4096",
"3/2",
"1024/675",
"25/16",
"405/256",
"8/5",
"3375/2048",
"5/3",
"27/16",
"128/75",
"225/128",
"16/9",
"9/5",
"30375/16384",
"15/8",
"256/135",
"48/25",
"2025/1024",
"2/1"
]
},
{
"id": "fokker_41_b",
"desc": "Fokker's 41-tone periodicity block of schisma & 3125/3072",
"stepCount": "41",
"steps": [
"81/80",
"25/24",
"135/128",
"16/15",
"1125/1024",
"10/9",
"9/8",
"256/225",
"75/64",
"1215/1024",
"6/5",
"10125/8192",
"5/4",
"81/64",
"125/96",
"675/512",
"4/3",
"27/20",
"25/18",
"45/32",
"64/45",
"375/256",
"6075/4096",
"3/2",
"243/160",
"25/16",
"405/256",
"8/5",
"3375/2048",
"5/3",
"27/16",
"125/72",
"225/128",
"16/9",
"9/5",
"30375/16384",
"15/8",
"243/128",
"125/64",
"2025/1024",
"2/1"
]
},
{
"id": "fokker_53",
"desc": "Fokker's 53-tone system, degree 37 has alternatives",
"stepCount": "53",
"steps": [
"126/125",
"525/512",
"25/24",
"21/20",
"16/15",
"27/25",
"35/32",
"10/9",
"9/8",
"8/7",
"147/128",
"7/6",
"189/160",
"6/5",
"243/200",
"315/256",
"5/4",
"63/50",
"32/25",
"125/96",
"21/16",
"4/3",
"27/20",
"175/128",
"441/320",
"7/5",
"10/7",
"36/25",
"35/24",
"189/128",
"3/2",
"32/21",
"49/32",
"384/245",
"63/40",
"8/5",
"81/50",
"105/64",
"5/3",
"42/25",
"12/7",
"441/256",
"7/4",
"16/9",
"9/5",
"175/96",
"147/80",
"15/8",
"40/21",
"48/25",
"35/18",
"63/32",
"2/1"
]
},
{
"id": "fokker_53_a",
"desc": "Fokker's 53-tone periodicity block of schisma & kleisma",
"stepCount": "53",
"steps": [
"81/80",
"16875/16384",
"25/24",
"135/128",
"2187/2048",
"625/576",
"1125/1024",
"10/9",
"9/8",
"729/640",
"125/108",
"75/64",
"1215/1024",
"6/5",
"625/512",
"10125/8192",
"5/4",
"81/64",
"32/25",
"125/96",
"675/512",
"4/3",
"27/20",
"5625/4096",
"25/18",
"45/32",
"729/512",
"625/432",
"375/256",
"6075/4096",
"3/2",
"243/160",
"125/81",
"25/16",
"405/256",
"8/5",
"625/384",
"3375/2048",
"5/3",
"27/16",
"2187/1280",
"125/72",
"225/128",
"3645/2048",
"9/5",
"1875/1024",
"50/27",
"15/8",
"243/128",
"625/324",
"125/64",
"2025/1024",
"2/1"
]
},
{
"id": "fokker_53_b",
"desc": "Fokker's 53-tone periodicity block of schisma & 2109375/2097152",
"stepCount": "53",
"steps": [
"2048/2025",
"128/125",
"25/24",
"135/128",
"16/15",
"27/25",
"1125/1024",
"10/9",
"9/8",
"256/225",
"144/125",
"75/64",
"32/27",
"6/5",
"4096/3375",
"10125/8192",
"5/4",
"81/64",
"32/25",
"125/96",
"675/512",
"4/3",
"27/20",
"512/375",
"25/18",
"45/32",
"64/45",
"36/25",
"375/256",
"6075/4096",
"3/2",
"1024/675",
"192/125",
"25/16",
"405/256",
"8/5",
"16384/10125",
"3375/2048",
"5/3",
"27/16",
"128/75",
"262144/151875",
"225/128",
"16/9",
"9/5",
"2048/1125",
"30375/16384",
"15/8",
"256/135",
"48/25",
"125/64",
"2025/1024",
"2/1"
]
},
{
"id": "fokker_av",
"desc": "Fokker's suggestion for a shrinked octave by averaging approximations",
"stepCount": "31",
"steps": [
"38.65161",
"77.30323",
"115.95484",
"154.60645",
"193.25806",
"231.90968",
"270.56129",
"309.21290",
"347.86452",
"386.51613",
"425.16774",
"463.81935",
"502.47097",
"541.12258",
"579.77419",
"618.42581",
"657.07742",
"695.72903",
"734.38065",
"773.03226",
"811.68387",
"850.33548",
"888.98710",
"927.63871",
"966.29032",
"1004.94194",
"1043.59355",
"1082.24516",
"1120.89677",
"1159.54839",
"1198.20000"
]
},
{
"id": "fokker_bosch",
"desc": "Scale of \"Naar Den Bosch toe\", genus diatonicum cum septimis. 1/1=D",
"stepCount": "9",
"steps": ["9/8", "5/4", "21/16", "4/3", "3/2", "5/3", "7/4", "15/8", "2/1"]
},
{
"id": "fokker_sr",
"desc": "Fokker's 7-limit sruti scale, KNAW B72, 1969",
"stepCount": "22",
"steps": [
"36/35",
"16/15",
"192/175",
"245/216",
"7/6",
"135/112",
"56/45",
"9/7",
"896/675",
"48/35",
"45/32",
"35/24",
"3/2",
"14/9",
"8/5",
"224/135",
"128/75",
"432/245",
"49/27",
"15/8",
"784/405",
"2/1"
]
},
{
"id": "fokker_sr_2",
"desc": "Fokker's complementary 7-limit sruti scale, KNAW B72, 1969",
"stepCount": "22",
"steps": [
"405/392",
"16/15",
"54/49",
"245/216",
"75/64",
"135/112",
"5/4",
"9/7",
"4/3",
"48/35",
"64/45",
"35/24",
"675/448",
"14/9",
"45/28",
"224/135",
"12/7",
"432/245",
"175/96",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "fokker_sra",
"desc": "Two-step approximation 9-13 to Fokker's 7-limit sruti scale",
"stepCount": "22",
"steps": [
"53.06891",
"109.74715",
"162.81606",
"215.88498",
"268.95389",
"322.02280",
"378.70104",
"435.37928",
"488.44819",
"541.51710",
"594.58602",
"651.26425",
"704.33317",
"761.01140",
"817.68964",
"874.36787",
"927.43679",
"980.50570",
"1033.57461",
"1086.64353",
"1143.32176",
"2/1"
]
},
{
"id": "fokker_uv",
"desc": "Table of Unison Vectors, Microsons and Minisons, from article KNAW, 1969",
"stepCount": "70",
"steps": [
"4375/4374",
"2401/2400",
"420175/419904",
"2460375/2458624",
"32805/32768",
"65625/65536",
"2100875/2097152",
"102760448/102515625",
"6144/6125",
"3136/3125",
"10976/10935",
"225/224",
"15625/15552",
"321489/320000",
"1029/1024",
"2109375/2097152",
"2097152/2083725",
"1728/1715",
"4000/3969",
"126/125",
"245/243",
"413343/409600",
"33075/32768",
"65536/64827",
"110592/109375",
"2048/2025",
"2430/2401",
"81/80",
"875/864",
"531441/524288",
"1063125/1048576",
"34034175/33554432",
"4194304/4134375",
"2097152/2066715",
"31104/30625",
"64/63",
"686/675",
"3125/3072",
"300125/294912",
"131072/128625",
"327680/321489",
"100352/98415",
"50/49",
"49/48",
"234375/229376",
"535815/524288",
"1071875/1048576",
"12288/12005",
"128/125",
"2240/2187",
"5625/5488",
"525/512",
"16807/16384",
"786432/765625",
"131072/127575",
"36/35",
"12005/11664",
"540225/524288",
"16128/15625",
"6272/6075",
"405/392",
"1323/1280",
"42875/41472",
"648/625",
"28/27",
"25/24",
"21/20",
"135/128",
"3584/3375",
"625/588"
]
},
{
"id": "fokker_h",
"desc": "Fokker-H 5-limit per.bl. synt.comma&small diesis, KNAW B71, 1968",
"stepCount": "19",
"steps": [
"25/24",
"16/15",
"10/9",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"128/75",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "fokker_ht",
"desc": "Tempered version of Fokker-H per.bl. with better 6 tetrads, OdC",
"stepCount": "19",
"steps": [
"69.30466",
"115.48142",
"183.57143",
"269.36988",
"315.48232",
"384.38240",
"431.05761",
"499.97378",
"568.70373",
"631.29627",
"700.02622",
"768.94239",
"815.61760",
"884.51768",
"930.63012",
"1016.42857",
"1084.51858",
"1130.69534",
"2/1"
]
},
{
"id": "fokker_k",
"desc": "Fokker-K 5-limit per.bl. of 225/224 & 81/80 & 10976/10935, KNAW B71, 1968",
"stepCount": "19",
"steps": [
"25/24",
"27/25",
"10/9",
"125/108",
"6/5",
"5/4",
"162/125",
"4/3",
"25/18",
"36/25",
"3/2",
"125/81",
"8/5",
"5/3",
"216/125",
"9/5",
"50/27",
"48/25",
"2/1"
]
},
{
"id": "fokker_l",
"desc": "Fokker-L 7-limit periodicity block 10976/10935 & 225/224 & 15625/15552, 1969",
"stepCount": "19",
"steps": [
"28/27",
"175/162",
"125/112",
"144/125",
"6/5",
"56/45",
"35/27",
"75/56",
"25/18",
"36/25",
"112/75",
"54/35",
"45/28",
"5/3",
"125/72",
"224/125",
"324/175",
"27/14",
"2/1"
]
},
{
"id": "fokker_lt",
"desc": "Tempered version of Fokker-L per.bl. with more triads",
"stepCount": "19",
"steps": [
"67.78818",
"133.37074",
"188.80751",
"249.65319",
"315.36950",
"383.07905",
"451.53821",
"503.52651",
"567.66084",
"632.33916",
"696.47350",
"748.46179",
"816.92095",
"884.63050",
"950.34681",
"1011.19249",
"1066.62926",
"1132.21182",
"2/1"
]
},
{
"id": "fokker_m",
"desc": "Fokker-M 7-limit periodicity block 81/80 & 225/224 & 1029/1024, KNAW B72, 1969",
"stepCount": "31",
"steps": [
"64/63",
"21/20",
"16/15",
"35/32",
"9/8",
"8/7",
"7/6",
"6/5",
"128/105",
"5/4",
"9/7",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"14/9",
"8/5",
"105/64",
"5/3",
"12/7",
"7/4",
"16/9",
"64/35",
"15/8",
"40/21",
"63/32",
"2/1"
]
},
{
"id": "fokker_n",
"desc": "Fokker-N 7-limit periodicity block 81/80 & 2100875/2097152 & 1029/1024, 1969",
"stepCount": "31",
"steps": [
"64/63",
"256/245",
"16384/15435",
"35/32",
"10/9",
"8/7",
"512/441",
"6/5",
"128/105",
"5145/4096",
"245/192",
"21/16",
"4/3",
"48/35",
"1024/735",
"735/512",
"35/24",
"3/2",
"32/21",
"384/245",
"8192/5145",
"105/64",
"5/3",
"441/256",
"7/4",
"9/5",
"64/35",
"15435/8192",
"245/128",
"63/32",
"2/1"
]
},
{
"id": "fokker_n_2",
"desc": "Fokker-N different block shape",
"stepCount": "31",
"steps": [
"64/63",
"25/24",
"16/15",
"35/32",
"10/9",
"8/7",
"7/6",
"6/5",
"128/105",
"5/4",
"32/25",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"25/16",
"8/5",
"105/64",
"5/3",
"12/7",
"7/4",
"9/5",
"64/35",
"15/8",
"48/25",
"63/32",
"2/1"
]
},
{
"id": "fokker_p",
"desc": "Fokker-P 7-limit periodicity block 65625/65536 & 6144/6125 & 2401/2400, 1969",
"stepCount": "31",
"steps": [
"128/125",
"256/245",
"15/14",
"35/32",
"10/9",
"8/7",
"1024/875",
"1225/1024",
"60/49",
"5/4",
"32/25",
"98/75",
"75/56",
"175/128",
"7/5",
"10/7",
"256/175",
"112/75",
"75/49",
"25/16",
"8/5",
"49/30",
"2048/1225",
"875/512",
"7/4",
"9/5",
"64/35",
"28/15",
"245/128",
"125/64",
"2/1"
]
},
{
"id": "fokker_q",
"desc": "Fokker-Q 7-limit per.bl. 225/224 & 4000/3969 & 6144/6125, KNAW B72, 1969",
"stepCount": "53",
"steps": [
"64/63",
"36/35",
"25/24",
"21/20",
"16/15",
"160/147",
"35/32",
"10/9",
"9/8",
"8/7",
"144/125",
"7/6",
"25/21",
"6/5",
"128/105",
"315/256",
"5/4",
"80/63",
"32/25",
"125/96",
"21/16",
"4/3",
"27/20",
"48/35",
"25/18",
"7/5",
"10/7",
"36/25",
"35/24",
"40/27",
"3/2",
"32/21",
"192/125",
"25/16",
"63/40",
"8/5",
"512/315",
"105/64",
"5/3",
"42/25",
"12/7",
"125/72",
"7/4",
"16/9",
"9/5",
"64/35",
"147/80",
"15/8",
"40/21",
"48/25",
"35/18",
"63/32",
"2/1"
]
},
{
"id": "fokker_r",
"desc": "Fokker-R 7-limit per.bl. 4375/4374 & 65625/65536 & 6144/6125, 1969",
"stepCount": "53",
"steps": [
"875/864",
"525/512",
"25/24",
"4608/4375",
"16/15",
"175/162",
"192/175",
"10/9",
"9/8",
"875/768",
"4725/4096",
"1024/875",
"32/27",
"6/5",
"175/144",
"216/175",
"5/4",
"4375/3456",
"32/25",
"2048/1575",
"1152/875",
"4/3",
"27/20",
"175/128",
"25/18",
"45/32",
"64/45",
"36/25",
"256/175",
"40/27",
"3/2",
"875/576",
"1575/1024",
"25/16",
"6912/4375",
"8/5",
"175/108",
"288/175",
"5/3",
"27/16",
"875/512",
"8192/4725",
"1536/875",
"16/9",
"9/5",
"175/96",
"324/175",
"15/8",
"4375/2304",
"48/25",
"1024/525",
"1728/875",
"2/1"
]
},
{
"id": "fokker_s",
"desc": "Fokker-S 7-limit per.bl. 4375/4374 & 323/322 & 64827/65536, 1969",
"stepCount": "53",
"steps": [
"64/63",
"36/35",
"256/245",
"8575/8192",
"1225/1152",
"27/25",
"35/32",
"10/9",
"6912/6125",
"8/7",
"512/441",
"42875/36864",
"189/160",
"6/5",
"175/144",
"216/175",
"1536/1225",
"80/63",
"245/192",
"1323/1024",
"21/16",
"4/3",
"27/20",
"48/35",
"1024/735",
"800/567",
"567/400",
"735/512",
"35/24",
"40/27",
"3/2",
"32/21",
"2048/1323",
"384/245",
"63/40",
"1225/768",
"175/108",
"288/175",
"5/3",
"320/189",
"73728/42875",
"441/256",
"7/4",
"6125/3456",
"9/5",
"64/35",
"50/27",
"2304/1225",
"16384/8575",
"245/128",
"35/18",
"63/32",
"2/1"
]
},
{
"id": "foote",
"desc": "Ed Foote, piano temperament. TL 9 Jun 1999, almost equal to Coleman",
"stepCount": "12",
"steps": [
"97.00000",
"197.00000",
"297.00000",
"394.00000",
"501.00000",
"595.00000",
"699.00000",
"797.00000",
"896.00000",
"999.00000",
"1094.00000",
"2/1"
]
},
{
"id": "foote_2",
"desc": "Ed Foote�s temperament with 1/6, 1/8 and 1/12 Pyth comma fractions",
"stepCount": "12",
"steps": [
"98.04500",
"197.06750",
"298.04500",
"394.13500",
"501.95500",
"596.09000",
"699.02250",
"798.04500",
"896.09000",
"1000.00000",
"1094.13500",
"2/1"
]
},
{
"id": "forster",
"desc": "Cris Forster's Chrysalis tuning, XH 7+8",
"stepCount": "32",
"steps": [
"16/15",
"13/12",
"11/10",
"8/7",
"13/11",
"11/9",
"5/4",
"9/7",
"13/10",
"21/16",
"27/20",
"11/8",
"7/5",
"10/7",
"13/9",
"16/11",
"40/27",
"3/2",
"32/21",
"20/13",
"14/9",
"8/5",
"18/11",
"27/16",
"22/13",
"12/7",
"7/4",
"16/9",
"24/13",
"15/8",
"64/33",
"2/1"
]
},
{
"id": "fortuna_a_1",
"desc": "Clem Fortuna, Arabic mode of 24-tET, try C or G major, superset of Basandida, trivalent",
"stepCount": "12",
"steps": [
"100.00000",
"200.00000",
"300.00000",
"350.00000",
"500.00000",
"600.00000",
"700.00000",
"800.00000",
"900.00000",
"1000.00000",
"1050.00000",
"2/1"
]
},
{
"id": "fortuna_a_2",
"desc": "Clem Fortuna, Arabic mode of 24-tET, try C or F minor",
"stepCount": "12",
"steps": [
"100.00000",
"150.00000",
"300.00000",
"400.00000",
"500.00000",
"600.00000",
"700.00000",
"18/11",
"900.00000",
"1000.00000",
"1100.00000",
"2/1"
]
},
{
"id": "fortuna_bag",
"desc": "Bagpipe tuning from Fortuna, try key of G with F natural",
"stepCount": "12",
"steps": [
"117/115",
"146/131",
"196/169",
"89/73",
"141/106",
"81/59",
"150/101",
"125/82",
"139/84",
"205/116",
"11/6",
"2/1"
]
},
{
"id": "fortuna_eth",
"desc": "Ethiopian Tunings from Fortuna",
"stepCount": "12",
"steps": [
"15/14",
"32/29",
"97/83",
"26/21",
"41/31",
"55/39",
"53/36",
"19/12",
"21/13",
"70/39",
"37/20",
"2/1"
]
},
{
"id": "fortuna_sheng",
"desc": "Sheng scale on naturals starting on d, from Fortuna",
"stepCount": "12",
"steps": [
"141/134",
"34/31",
"55/46",
"71/58",
"4/3",
"80/57",
"117/80",
"107/67",
"63/38",
"59/33",
"63/34",
"2/1"
]
},
{
"id": "fortuna_11",
"desc": "11-limit scale from Clem Fortuna",
"stepCount": "12",
"steps": [
"21/20",
"8/7",
"7/6",
"14/11",
"21/16",
"10/7",
"32/21",
"11/7",
"12/7",
"7/4",
"40/21",
"2/1"
]
},
{
"id": "francis_924_1",
"desc": "J. Charles Francis, Bach temperament for BWV 924 version 1 (2005)",
"stepCount": "12",
"steps": [
"92.18000",
"9/8",
"296.09000",
"400.65167",
"500.00000",
"590.22500",
"3/2",
"794.13500",
"27/16",
"998.04500",
"1095.43833",
"2/1"
]
},
{
"id": "francis_924_2",
"desc": "J. Charles Francis, Bach temperament for BWV 924 version 2 (2005)",
"stepCount": "12",
"steps": [
"92.18000",
"9/8",
"296.09000",
"400.65167",
"500.00000",
"590.22500",
"3/2",
"801.30333",
"27/16",
"998.04500",
"1095.43833",
"2/1"
]
},
{
"id": "francis_924_3",
"desc": "J. Charles Francis, Bach temperament for BWV 924 version 3 (2005)",
"stepCount": "12",
"steps": [
"99.34833",
"9/8",
"303.25833",
"400.65167",
"507.16834",
"597.39333",
"3/2",
"801.30333",
"27/16",
"1005.21334",
"1095.43833",
"2/1"
]
},
{
"id": "francis_924_4",
"desc": "J. Charles Francis, Bach temperament for BWV 924 version 4 (2005)",
"stepCount": "12",
"steps": [
"99.34833",
"9/8",
"303.25833",
"400.65167",
"507.16834",
"597.39333",
"3/2",
"808.47167",
"27/16",
"1005.21334",
"1095.43833",
"2/1"
]
},
{
"id": "francis_r_2_1",
"desc": "J. Charles Francis, Bach WTC temperament R2-1, fifths beat ratios 0, 1, 2. C=249.072 Cammerton",
"stepCount": "12",
"steps": [
"95.21360",
"198.49541",
"299.12360",
"395.50525",
"499.78177",
"593.25860",
"699.63654",
"797.16860",
"896.31362",
"999.12823",
"1093.76889",
"2/1"
]
},
{
"id": "francis_r_2_14_p",
"desc": "Bach WTC theoretical temperament, 1/14 Pyth. comma, Cammerton",
"stepCount": "12",
"steps": [
"95.25214",
"198.88286",
"299.16214",
"396.09000",
"499.72071",
"593.29714",
"700.27929",
"797.20714",
"897.48643",
"999.44143",
"1094.69357",
"2/1"
]
},
{
"id": "francis_r_12_2",
"desc": "J. Charles Francis, Bach WTC temperament R12-2, fifths beat ratios 0, 1, 2. C=279.331 Cornet-ton",
"stepCount": "12",
"steps": [
"100.62819",
"197.00984",
"301.28636",
"394.76319",
"501.14108",
"598.67319",
"697.81820",
"800.63282",
"895.27348",
"1001.50455",
"1096.71819",
"2/1"
]
},
{
"id": "francis_r_12_14_p",
"desc": "Bach WTC theoretical temperament, 1/14 Pyth. comma, Cornet-ton, same Maunder III",
"stepCount": "12",
"steps": [
"100.27929",
"197.20714",
"300.83786",
"394.41428",
"501.39643",
"598.32428",
"698.60357",
"800.55857",
"895.81071",
"1001.11714",
"1096.36928",
"2/1"
]
},
{
"id": "francis_seal",
"desc": "J. Charles Francis, Bach tuning interpretion as beats/sec. from seal",
"stepCount": "12",
"steps": [
"91.96620",
"196.15000",
"295.87600",
"391.05000",
"499.78600",
"590.01100",
"697.30300",
"793.92100",
"891.87200",
"997.83100",
"1089.29000",
"2/1"
]
},
{
"id": "francis_suppig",
"desc": "J. Charles Francis, Suppig Calculus musicus, 5ths beat ratios 0, 1, 2.",
"stepCount": "12",
"steps": [
"94.70000",
"196.90000",
"297.30000",
"394.50000",
"501.20000",
"592.80000",
"697.70000",
"796.70000",
"895.00000",
"999.30000",
"1093.10000",
"2/1"
]
},
{
"id": "freiberg",
"desc": "Temperament of G. Silbermann organ (1735), St. Petri in Freiberg (1985), a=476.3",
"stepCount": "12",
"steps": [
"256/243",
"196.09000",
"298.04500",
"394.13500",
"500.00000",
"590.22500",
"698.04500",
"790.22500",
"896.09000",
"1000.00000",
"1092.18000",
"2/1"
]
},
{
"id": "freivald_canton",
"desc": "Jake Freivald, a 2.3.11/7.13/7 subgroup scale",
"stepCount": "12",
"steps": [
"14/13",
"9/8",
"13/11",
"14/11",
"4/3",
"39/28",
"3/2",
"11/7",
"22/13",
"16/9",
"13/7",
"2/1"
]
},
{
"id": "freivald_lucky",
"desc": "Jake Freivald, Lucky sevens and elevens, two chords 3/2 apart, superparticular",
"stepCount": "9",
"steps": [
"12/11",
"13/11",
"14/11",
"7/5",
"3/2",
"18/11",
"39/22",
"21/11",
"2/1"
]
},
{
"id": "freivald_sub",
"desc": "Jake Freivald, just scale in 5.11.31 subgroup. TL 30-5-2011",
"stepCount": "12",
"steps": [
"125/121",
"33275/29791",
"34375/29791",
"31/25",
"155/121",
"1331/961",
"1375/961",
"961/625",
"961/605",
"1331/775",
"55/31",
"29791/15625"
]
},
{
"id": "freivald_sup",
"desc": "Jake Freivald, 4/3 divided into 7 superparticulars, repeated at 3/2, and the 4/3-3/2 divide split into 25/24, 26/25, 27/26",
"stepCount": "17",
"steps": [
"22/21",
"23/21",
"8/7",
"25/21",
"26/21",
"9/7",
"4/3",
"25/18",
"13/9",
"3/2",
"11/7",
"23/14",
"12/7",
"25/14",
"13/7",
"27/14",
"2/1"
]
},
{
"id": "freivald_star",
"desc": "Jake Freivald, starling scale, approximately 8, 15, 20, 25, 28, 32, 40, 45, 60, 65, 72, 77 steps of 77-tET",
"stepCount": "12",
"steps": [
"123.54000",
"232.17300",
"311.10200",
"390.03100",
"434.64100",
"498.66300",
"622.20300",
"701.13200",
"933.30400",
"1012.23300",
"1120.86600",
"2/1"
]
},
{
"id": "freivald_11",
"desc": "Jake Freivald, scale derived mostly from elevens (2011)",
"stepCount": "17",
"steps": [
"33/32",
"12/11",
"25/22",
"33/28",
"11/9",
"14/11",
"4/3",
"7/5",
"16/11",
"3/2",
"11/7",
"18/11",
"56/33",
"16/9",
"11/6",
"21/11",
"2/1"
]
},
{
"id": "freivaldthree",
"desc": "JI tritave repeating scale, similar to ennon13. Mode of the 13-note tritave MOS of ennealimmal",
"stepCount": "13",
"steps": [
"27/25",
"729/625",
"19683/15625",
"3125/2187",
"125/81",
"5/3",
"9/5",
"243/125",
"6561/3125",
"15625/6561",
"625/243",
"25/9",
"3/1"
]
},
{
"id": "fribourg",
"desc": "Manderscheidt organ in Fribourg (1640), modified meantone",
"stepCount": "12",
"steps": [
"91.20250",
"195.11250",
"306.84250",
"387.29249",
"500.97750",
"589.24750",
"698.04500",
"781.42749",
"892.18000",
"1004.88750",
"1087.29249",
"2/1"
]
},
{
"id": "fusc_4",
"desc": "All rationals with fusc value <= 4",
"stepCount": "15",
"steps": [
"16/15",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "fusc_5",
"desc": "All rationals with fusc value <= 5",
"stepCount": "23",
"steps": [
"17/16",
"16/15",
"9/8",
"8/7",
"7/6",
"6/5",
"16/13",
"5/4",
"4/3",
"11/8",
"7/5",
"10/7",
"16/11",
"3/2",
"8/5",
"13/8",
"5/3",
"12/7",
"7/4",
"16/9",
"15/8",
"32/17",
"2/1"
]
},
{
"id": "fusc_6",
"desc": "All rationals with fusc value <= 6",
"stepCount": "35",
"steps": [
"17/16",
"16/15",
"15/14",
"13/12",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"16/13",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"24/17",
"17/12",
"10/7",
"16/11",
"3/2",
"14/9",
"8/5",
"13/8",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"24/13",
"28/15",
"15/8",
"32/17",
"2/1"
]
},
{
"id": "galilei",
"desc": "Vincenzo Galilei's approximation",
"stepCount": "12",
"steps": [
"103.00000",
"198.00000",
"301.00000",
"396.00000",
"495.00000",
"594.00000",
"693.00000",
"792.00000",
"891.00000",
"990.00000",
"1089.00000",
"2/1"
]
},
{
"id": "gamelan_udan",
"desc": "Gamelan Udan Mas (approx) s6,p6,p7,s1,p1,s2,p2,p3,s3,p4,s5,p5",
"stepCount": "12",
"steps": [
"1/1",
"10/9",
"7/6",
"32/25",
"47/35",
"32/23",
"3/2",
"20/13",
"16/9",
"16/9",
"23/12",
"2/1"
]
},
{
"id": "ganassi",
"desc": "Sylvestro Ganassi's temperament (1543)",
"stepCount": "12",
"steps": [
"20/19",
"10/9",
"20/17",
"5/4",
"4/3",
"24/17",
"3/2",
"30/19",
"5/3",
"30/17",
"15/8",
"2/1"
]
},
{
"id": "gann_arcana",
"desc": "Kyle Gann, scale for Arcana XVI",
"stepCount": "24",
"steps": [
"21/20",
"16/15",
"9/8",
"7/6",
"6/5",
"11/9",
"5/4",
"21/16",
"4/3",
"27/20",
"7/5",
"22/15",
"3/2",
"55/36",
"8/5",
"44/27",
"5/3",
"42/25",
"7/4",
"9/5",
"11/6",
"15/8",
"88/45",
"2/1"
]
},
{
"id": "gann_charingcross",
"desc": "Kyle Gann, scale for Charing Cross (2007)",
"stepCount": "39",
"steps": [
"81/80",
"65/64",
"33/32",
"15/14",
"35/32",
"143/128",
"9/8",
"55/48",
"77/64",
"135/112",
"39/32",
"5/4",
"81/64",
"21/16",
"75/56",
"27/20",
"65/48",
"11/8",
"45/32",
"91/64",
"35/24",
"165/112",
"3/2",
"195/128",
"49/32",
"99/64",
"45/28",
"13/8",
"5/3",
"27/16",
"12/7",
"55/32",
"7/4",
"25/14",
"117/64",
"15/8",
"121/64",
"63/32",
"2/1"
]
},
{
"id": "gann_cinderella",
"desc": "Kyle Gann, scale for Cinderella's Bad Magic",
"stepCount": "30",
"steps": [
"25/24",
"21/20",
"135/128",
"27/25",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"125/96",
"4/3",
"27/20",
"25/18",
"45/32",
"36/25",
"22/15",
"3/2",
"55/36",
"25/16",
"8/5",
"81/50",
"5/3",
"125/72",
"7/4",
"9/5",
"175/96",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "gann_custer",
"desc": "Kyle Gann, scale from Custer's Ghost to Sitting Bull, 1/1=G",
"stepCount": "31",
"steps": [
"33/32",
"21/20",
"16/15",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"9/7",
"21/16",
"4/3",
"27/20",
"11/8",
"7/5",
"16/11",
"3/2",
"14/9",
"8/5",
"18/11",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"11/6",
"15/8",
"64/33",
"2/1"
]
},
{
"id": "gann_fractured",
"desc": "Kyle Gann, scale from Fractured Paradise, 1/1=B",
"stepCount": "16",
"steps": [
"81/80",
"9/8",
"7/6",
"189/160",
"6/5",
"4/3",
"27/20",
"7/5",
"3/2",
"243/160",
"63/40",
"8/5",
"81/50",
"7/4",
"9/5",
"2/1"
]
},
{
"id": "gann_fugitive",
"desc": "Kyle Gann, scale for Fugitive Objects (2007)",
"stepCount": "21",
"steps": [
"49/48",
"21/20",
"13/12",
"9/8",
"8/7",
"55/48",
"7/6",
"6/5",
"11/9",
"5/4",
"21/16",
"11/8",
"7/5",
"16/11",
"3/2",
"11/7",
"13/8",
"7/4",
"11/6",
"55/28",
"2/1"
]
},
{
"id": "gann_ghost",
"desc": "Kyle Gann, scale from Ghost Town, 1/1=E",
"stepCount": "8",
"steps": ["9/8", "7/6", "21/16", "4/3", "3/2", "14/9", "7/4", "2/1"]
},
{
"id": "gann_love",
"desc": "Kyle Gann, scale for Love Scene",
"stepCount": "21",
"steps": [
"33/32",
"25/24",
"35/32",
"9/8",
"77/64",
"5/4",
"81/64",
"21/16",
"11/8",
"45/32",
"35/24",
"3/2",
"99/64",
"25/16",
"27/16",
"55/32",
"7/4",
"15/8",
"121/64",
"63/32",
"2/1"
]
},
{
"id": "gann_new_aunts",
"desc": "Kyle Gann, scale from New Aunts (2008), 1/1=A",
"stepCount": "27",
"steps": [
"33/32",
"11/10",
"10/9",
"9/8",
"7/6",
"6/5",
"5/4",
"81/64",
"9/7",
"35/27",
"4/3",
"11/8",
"45/32",
"81/56",
"35/24",
"3/2",
"14/9",
"8/5",
"45/28",
"5/3",
"27/16",
"7/4",
"15/8",
"27/14",
"35/18",
"63/32",
"2/1"
]
},
{
"id": "gann_revisited",
"desc": "Kyle Gann, scale for The Day Revisited (2005)",
"stepCount": "29",
"steps": [
"33/32",
"12/11",
"35/32",
"10/9",
"9/8",
"8/7",
"5/4",
"9/7",
"21/16",
"4/3",
"11/8",
"45/32",
"10/7",
"16/11",
"40/27",
"3/2",
"49/32",
"99/64",
"25/16",
"18/11",
"5/3",
"27/16",
"12/7",
"55/32",
"7/4",
"20/11",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "gann_sitting",
"desc": "Kyle Gann, tuning for Sitting Bull (1998), 1/1=B",
"stepCount": "21",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"189/160",
"6/5",
"4/3",
"48/35",
"7/5",
"189/128",
"40/27",
"3/2",
"14/9",
"63/40",
"8/5",
"7/4",
"16/9",
"9/5",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "gann_solitaire",
"desc": "Kyle Gann, scale from Solitaire (2009), 1/1=Eb",
"stepCount": "36",
"steps": [
"65/64",
"33/32",
"15/14",
"35/32",
"10/9",
"9/8",
"8/7",
"55/48",
"6/5",
"77/64",
"39/32",
"5/4",
"9/7",
"165/128",
"21/16",
"4/3",
"11/8",
"91/64",
"10/7",
"35/24",
"3/2",
"99/64",
"13/8",
"105/64",
"5/3",
"27/16",
"12/7",
"55/32",
"7/4",
"9/5",
"117/64",
"15/8",
"40/21",
"495/256",
"63/32",
"2/1"
]
},
{
"id": "gann_suntune",
"desc": "Kyle Gann, tuning for Sun Dance / Battle of the Greasy Grass River, 1/1=F#",
"stepCount": "30",
"steps": [
"15/14",
"12/11",
"10/9",
"9/8",
"8/7",
"7/6",
"25/21",
"6/5",
"5/4",
"21/16",
"4/3",
"27/20",
"11/8",
"7/5",
"10/7",
"16/11",
"40/27",
"3/2",
"8/5",
"45/28",
"18/11",
"5/3",
"12/7",
"7/4",
"16/9",
"25/14",
"9/5",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "gann_super",
"desc": "Kyle Gann, scale from Superparticular Woman (1992), 1/1=G",
"stepCount": "22",
"steps": [
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"11/7",
"14/9",
"8/5",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"2/1"
]
},
{
"id": "gann_things",
"desc": "Kyle Gann, scale from How Miraculous Things Happen, 1/1=A",
"stepCount": "24",
"steps": [
"55/54",
"25/24",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"9/7",
"21/16",
"4/3",
"10/7",
"40/27",
"3/2",
"14/9",
"25/16",
"5/3",
"12/7",
"16/9",
"15/8",
"40/21",
"35/18",
"2/1"
]
},
{
"id": "gann_wolfe",
"desc": "Kyle Gann from Anatomy of an Octave, edited by Kristina Wolfe (2015)",
"stepCount": "579",
"steps": [
"32805/32768",
"126/125",
"121/120",
"100/99",
"99/98",
"81/80",
"531441/524288",
"65/64",
"64/63",
"63/62",
"58/57",
"57/56",
"56/55",
"55/54",
"52/51",
"51/50",
"50/49",
"49/48",
"46/45",
"45/44",
"128/125",
"525/512",
"40/39",
"39/38",
"77/75",
"36/35",
"250/243",
"35/34",
"34/33",
"33/32",
"32/31",
"125/121",
"31/30",
"30/29",
"29/28",
"57/55",
"28/27",
"80/77",
"27/26",
"26/25",
"51/49",
"126/121",
"25/24",
"24/23",
"117/112",
"23/22",
"67/64",
"22/21",
"21/20",
"81/77",
"20/19",
"256/243",
"58/55",
"135/128",
"96/91",
"19/18",
"55/52",
"128/121",
"18/17",
"25/12",
"89/84",
"35/33",
"52/49",
"86/81",
"17/16",
"33/31",
"49/46",
"16/15",
"31/29",
"77/72",
"15/14",
"29/27",
"14/13",
"69/64",
"55/51",
"27/25",
"121/112",
"13/12",
"64/59",
"38/35",
"63/58",
"88/81",
"25/23",
"62/57",
"135/124",
"49/45",
"12/11",
"59/54",
"35/32",
"23/21",
"57/52",
"34/31",
"800/729",
"56/51",
"11/10",
"54/49",
"32/29",
"21/19",
"31/28",
"567/512",
"51/46",
"71/64",
"10/9",
"49/44",
"39/35",
"29/26",
"125/112",
"48/43",
"19/17",
"160/143",
"28/25",
"121/108",
"55/49",
"13/6",
"64/57",
"9/8",
"62/55",
"44/39",
"35/31",
"26/23",
"112/99",
"17/15",
"25/22",
"58/51",
"256/225",
"33/29",
"729/640",
"57/50",
"73/64",
"8/7",
"63/55",
"55/48",
"39/34",
"225/196",
"31/27",
"147/128",
"169/147",
"23/20",
"2187/1900",
"38/33",
"144/125",
"121/105",
"15/13",
"52/45",
"37/32",
"81/70",
"125/108",
"22/19",
"51/44",
"196/169",
"29/25",
"36/31",
"93/80",
"57/49",
"64/55",
"7/6",
"90/77",
"75/64",
"34/29",
"88/75",
"27/23",
"20/17",
"33/28",
"46/39",
"13/11",
"58/49",
"45/38",
"32/27",
"19/16",
"9/4",
"25/21",
"31/26",
"105/88",
"55/46",
"6/5",
"77/64",
"35/29",
"29/24",
"75/62",
"98/81",
"121/100",
"23/19",
"63/52",
"40/33",
"17/14",
"243/200",
"62/51",
"28/23",
"39/32",
"128/105",
"8000/6561",
"11/9",
"60/49",
"49/40",
"38/31",
"27/22",
"16/13",
"79/64",
"100/81",
"121/98",
"21/17",
"99/80",
"26/21",
"57/46",
"31/25",
"36/29",
"56/45",
"96/77",
"8192/6561",
"5/4",
"64/51",
"49/39",
"44/35",
"39/31",
"34/27",
"7/3",
"63/50",
"121/96",
"29/23",
"125/99",
"24/19",
"512/405",
"62/49",
"81/64",
"19/15",
"33/26",
"80/63",
"14/11",
"51/40",
"125/98",
"23/18",
"32/25",
"41/32",
"50/39",
"77/60",
"9/7",
"58/45",
"49/38",
"40/31",
"31/24",
"1323/1024",
"128/99",
"22/17",
"57/44",
"162/125",
"35/27",
"83/64",
"100/77",
"13/10",
"125/96",
"30/23",
"64/49",
"98/75",
"17/13",
"72/55",
"55/42",
"38/29",
"21/16",
"46/35",
"25/19",
"320/243",
"29/22",
"675/512",
"33/25",
"45/34",
"85/64",
"4/3",
"29/12",
"75/56",
"51/38",
"43/32",
"121/90",
"39/29",
"35/26",
"66/49",
"31/23",
"27/20",
"23/17",
"42/31",
"19/14",
"110/81",
"87/64",
"34/25",
"49/36",
"15/11",
"512/375",
"26/19",
"63/46",
"48/35",
"1000/729",
"11/8",
"62/45",
"40/29",
"29/21",
"112/81",
"18/13",
"25/18",
"89/64",
"32/23",
"39/28",
"46/33",
"88/63",
"7/5",
"108/77",
"1024/729",
"45/32",
"38/27",
"31/22",
"55/39",
"24/17",
"577/408",
"99/70",
"17/12",
"44/31",
"125/88",
"27/19",
"91/64",
"64/45",
"729/512",
"57/40",
"77/54",
"10/7",
"63/44",
"33/23",
"56/39",
"23/16",
"36/25",
"121/84",
"49/34",
"13/9",
"81/56",
"55/38",
"42/29",
"29/20",
"45/31",
"93/64",
"16/11",
"51/35",
"729/500",
"35/24",
"19/13",
"375/256",
"22/15",
"47/32",
"72/49",
"25/17",
"81/55",
"28/19",
"31/21",
"189/128",
"34/23",
"40/27",
"46/31",
"95/64",
"49/33",
"52/35",
"58/39",
"125/84",
"112/75",
"121/81",
"31/12",
"3/2",
"121/80",
"50/33",
"97/64",
"1024/675",
"44/29",
"243/160",
"38/25",
"35/23",
"32/21",
"29/19",
"84/55",
"55/36",
"26/17",
"75/49",
"49/32",
"23/15",
"192/125",
"20/13",
"77/50",
"54/35",
"125/81",
"17/11",
"99/64",
"48/31",
"31/20",
"45/29",
"14/9",
"120/77",
"39/25",
"25/16",
"36/23",
"11/7",
"63/40",
"52/33",
"101/64",
"30/19",
"128/81",
"49/31",
"405/256",
"19/12",
"46/29",
"100/63",
"8/3",
"27/17",
"62/39",
"35/22",
"51/32",
"8/5",
"6561/4096",
"77/48",
"45/28",
"103/64",
"29/18",
"50/31",
"121/75",
"21/13",
"55/34",
"34/21",
"81/50",
"125/77",
"13/8",
"57/35",
"44/27",
"31/19",
"80/49",
"49/30",
"18/11",
"105/64",
"64/39",
"23/14",
"51/31",
"400/243",
"28/17",
"33/20",
"38/23",
"81/49",
"48/29",
"53/32",
"58/35",
"63/38",
"128/77",
"107/64",
"5/3",
"57/34",
"52/31",
"42/25",
"121/72",
"11/4",
"32/19",
"27/16",
"49/29",
"22/13",
"39/23",
"56/33",
"17/10",
"109/64",
"46/27",
"75/44",
"29/17",
"128/75",
"77/45",
"12/7",
"55/32",
"31/18",
"441/256",
"50/29",
"19/11",
"216/125",
"121/70",
"45/26",
"26/15",
"111/64",
"125/72",
"33/19",
"40/23",
"54/31",
"96/55",
"110/63",
"7/4",
"58/33",
"225/128",
"51/29",
"44/25",
"30/17",
"113/64",
"99/56",
"23/13",
"62/35",
"39/22",
"55/31",
"16/9",
"57/32",
"17/6",
"98/55",
"25/14",
"34/19",
"52/29",
"88/49",
"115/64",
"9/5",
"56/31",
"38/21",
"29/16",
"49/27",
"20/11",
"51/28",
"729/400",
"31/17",
"42/23",
"117/64",
"64/35",
"4000/2187",
"11/6",
"90/49",
"57/31",
"46/25",
"81/44",
"35/19",
"59/32",
"24/13",
"50/27",
"63/34",
"13/7",
"119/64",
"54/29",
"28/15",
"58/31",
"15/8",
"62/33",
"32/17",
"49/26",
"66/35",
"35/12",
"17/9",
"121/64",
"125/66",
"36/19",
"256/135",
"55/29",
"243/128",
"19/10",
"40/21",
"61/32",
"21/11",
"44/23",
"23/12",
"48/25",
"121/63",
"123/64",
"25/13",
"77/40",
"52/27",
"27/14",
"56/29",
"29/15",
"60/31",
"31/16",
"64/33",
"33/17",
"243/125",
"35/18",
"39/20",
"125/64",
"88/45",
"45/23",
"96/49",
"49/25",
"51/26",
"108/55",
"55/28",
"57/29",
"63/32",
"160/81",
"99/50",
"125/63",
"127/64",
"2/1"
]
},
{
"id": "garcia",
"desc": "Linear 29-tone scale by Jos� L. Garcia (1988) 15/13-52/45 alternating",
"stepCount": "29",
"steps": [
"40/39",
"27/26",
"16/15",
"128/117",
"9/8",
"15/13",
"32/27",
"6/5",
"16/13",
"81/64",
"135/104",
"4/3",
"160/117",
"18/13",
"64/45",
"512/351",
"3/2",
"20/13",
"81/52",
"8/5",
"64/39",
"27/16",
"45/26",
"16/9",
"9/5",
"24/13",
"256/135",
"405/208",
"2/1"
]
},
{
"id": "garibaldi_24_opt",
"desc": "13-limit lesfip optimization, 5 cent tolerance",
"stepCount": "24",
"steps": [
"64.4815",
"90.9590",
"180.7956",
"204.3728",
"269.9424",
"293.5196",
"383.3563",
"409.8338",
"474.3152",
"497.3269",
"562.3192",
"588.7007",
"678.9717",
"702.1072",
"766.8945",
"792.8508",
"881.4644",
"907.4207",
"972.2080",
"995.3435",
"1085.6145",
"1111.9961",
"1176.9884",
"2/1"
]
},
{
"id": "genggong",
"desc": "Genggong polos scale, harmonics 5-9",
"stepCount": "5",
"steps": ["6/5", "7/5", "8/5", "9/5", "2/1"]
},
{
"id": "genovese_12",
"desc": "Denny Genovese's superposition of harmonics 8-16 and subharmonics 6-12",
"stepCount": "12",
"steps": [
"12/11",
"9/8",
"6/5",
"5/4",
"4/3",
"11/8",
"3/2",
"13/8",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "genovese_38",
"desc": "Denny Genovese's 38-note scale of harmonics 1-16 and subharmonics 1-12",
"stepCount": "38",
"steps": [
"15/14",
"13/12",
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"13/11",
"6/5",
"11/9",
"5/4",
"14/11",
"9/7",
"13/10",
"4/3",
"15/11",
"11/8",
"7/5",
"10/7",
"13/9",
"16/11",
"3/2",
"14/9",
"11/7",
"8/5",
"13/8",
"18/11",
"5/3",
"12/7",
"7/4",
"16/9",
"9/5",
"20/11",
"11/6",
"13/7",
"15/8",
"2/1"
]
},
{
"id": "gf_1_2",
"desc": "16-note scale with all possible quadruplets of 50 & 100 c. Galois Field GF(2)",
"stepCount": "16",
"steps": [
"50.00000",
"100.00000",
"150.00000",
"200.00000",
"300.00000",
"350.00000",
"450.00000",
"500.00000",
"550.00000",
"650.00000",
"750.00000",
"800.00000",
"900.00000",
"1000.00000",
"1100.00000",
"2/1"
]
},
{
"id": "gf_2_3",
"desc": "16-note scale with all possible quadruplets of 60 & 90 c. Galois Field GF(2)",
"stepCount": "16",
"steps": [
"60.00000",
"120.00000",
"180.00000",
"240.00000",
"330.00000",
"390.00000",
"480.00000",
"540.00000",
"600.00000",
"690.00000",
"780.00000",
"840.00000",
"930.00000",
"1020.00000",
"1110.00000",
"2/1"
]
},
{
"id": "gibelius",
"desc": "Otto Gibelius, Propositiones Mathematico-musicae, 1666, p.35",
"stepCount": "14",
"steps": [
"25/24",
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "gilson_7",
"desc": "Gilson septimal",
"stepCount": "9",
"steps": [
"8/7",
"6/5",
"5/4",
"10/7",
"3/2",
"25/16",
"25/14",
"15/8",
"2/1"
]
},
{
"id": "gilson_7_a",
"desc": "Gilson septimal 2",
"stepCount": "9",
"steps": ["15/14", "8/7", "6/5", "9/7", "10/7", "3/2", "8/5", "9/5", "2/1"]
},
{
"id": "gizmo_14_ji_transversal",
"desc": "Possible JI transversal of gizmo14.scl or gizmo14-pote.scl",
"stepCount": "14",
"steps": [
"91/88",
"9/8",
"11/9",
"14/11",
"21/16",
"11/8",
"3/2",
"14/9",
"13/8",
"22/13",
"7/4",
"11/6",
"63/32",
"2/1"
]
},
{
"id": "gizmo_14_pote",
"desc": "Gizmo in Parapyth POTE, three ~4:6:7:9:11:13 hexads on 1/1, 9/8, 3/2",
"stepCount": "14",
"steps": [
"58.33900",
"207.71200",
"346.77100",
"415.42400",
"473.76300",
"554.48300",
"703.85600",
"762.19500",
"842.91500",
"911.56800",
"969.90700",
"1050.62700",
"1177.61900",
"2/1"
]
},
{
"id": "gizmo_14",
"desc": "Parapyth set, three ~4:6:7:9:11:13 hexads on 1/1, 9/8, 3/2 (MET-24 version)",
"stepCount": "14",
"steps": [
"57.42187",
"207.42187",
"346.28906",
"414.84375",
"472.26562",
"553.71094",
"703.71094",
"761.13281",
"842.57812",
"911.13281",
"968.55469",
"1050.00000",
"1175.97656",
"2/1"
]
},
{
"id": "glacial_6",
"desc": "Glacial[6] 2.9.5.11.13 subgroup MOS in 13\\84 tuning",
"stepCount": "6",
"steps": [
"185.71429",
"371.42857",
"557.14286",
"828.57143",
"1014.28571",
"2/1"
]
},
{
"id": "gluck",
"desc": "Thomas Gl�ck Bach temperament",
"stepCount": "12",
"steps": [
"99.02250",
"198.04500",
"299.02250",
"396.09000",
"500.97750",
"598.04500",
"699.02250",
"799.02250",
"897.06750",
"999.02250",
"1097.06750",
"2/1"
]
},
{
"id": "godmeankeeflat_1",
"desc": "Godzilla-meantone-keemun-flattone wakalix",
"stepCount": "19",
"steps": [
"21/20",
"16/15",
"10/9",
"7/6",
"6/5",
"5/4",
"35/27",
"4/3",
"7/5",
"35/24",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"16/9",
"28/15",
"35/18",
"2/1"
]
},
{
"id": "godmeankeeflat_3",
"desc": "Godzilla-meantone-keemun-flattone wakalix",
"stepCount": "19",
"steps": [
"21/20",
"16/15",
"10/9",
"7/6",
"6/5",
"5/4",
"35/27",
"4/3",
"7/5",
"35/24",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"9/5",
"28/15",
"35/18",
"2/1"
]
},
{
"id": "goebel",
"desc": "Joseph Goebel quasi equal temperament (1967)",
"stepCount": "12",
"steps": [
"100.27800",
"200.37700",
"300.29700",
"400.28700",
"500.02900",
"600.19500",
"700.18900",
"800.15000",
"900.16900",
"1000.11800",
"1100.05200",
"2/1"
]
},
{
"id": "golden_5",
"desc": "Golden pentatonic",
"stepCount": "5",
"steps": ["5/4", "21/16", "3/2", "13/8", "2/1"]
},
{
"id": "gorgo_pelog",
"desc": "Pelog-like subset of gorgo[9]",
"stepCount": "7",
"steps": [
"64.82352",
"293.02282",
"521.22213",
"684.59791",
"749.42143",
"977.62074",
"1205.82004"
]
},
{
"id": "gradus_3",
"desc": "Intervals > 1 with Gradus = 3",
"stepCount": "2",
"steps": ["3/1", "4/1"]
},
{
"id": "gradus_4",
"desc": "Intervals > 1 with Gradus = 4",
"stepCount": "3",
"steps": ["3/2", "6/1", "8/1"]
},
{
"id": "gradus_5",
"desc": "Intervals > 1 with Gradus = 5",
"stepCount": "5",
"steps": ["4/3", "5/1", "9/1", "12/1", "16/1"]
},
{
"id": "gradus_6",
"desc": "Intervals > 1 with Gradus = 6",
"stepCount": "7",
"steps": ["5/2", "8/3", "9/2", "10/1", "18/1", "24/1", "32/1"]
},
{
"id": "gradus_7",
"desc": "Intervals > 1 with Gradus = 7",
"stepCount": "11",
"steps": [
"5/4",
"5/3",
"9/4",
"16/3",
"7/1",
"15/1",
"20/1",
"27/1",
"36/1",
"48/1",
"64/1"
]
},
{
"id": "gradus_8",
"desc": "Intervals > 1 with Gradus = 8",
"stepCount": "15",
"steps": [
"9/8",
"6/5",
"8/5",
"10/3",
"7/2",
"15/2",
"32/3",
"27/2",
"14/1",
"30/1",
"40/1",
"54/1",
"72/1",
"96/1",
"128/1"
]
},
{
"id": "gradus_9",
"desc": "Intervals > 1 with Gradus = 9",
"stepCount": "21",
"steps": [
"7/4",
"16/9",
"9/5",
"7/3",
"12/5",
"16/5",
"15/4",
"20/3",
"27/4",
"21/1",
"64/3",
"25/1",
"28/1",
"45/1",
"60/1",
"80/1",
"81/1",
"108/1",
"144/1",
"192/1",
"256/1"
]
},
{
"id": "gradus_10",
"desc": "Intervals > 1 with Gradus = 10",
"stepCount": "27",
"steps": [
"10/9",
"8/7",
"7/6",
"15/8",
"27/8",
"32/9",
"18/5",
"14/3",
"24/5",
"32/5",
"21/2",
"25/2",
"40/3",
"45/2",
"81/2",
"42/1",
"128/3",
"50/1",
"56/1",
"90/1",
"120/1",
"160/1",
"162/1",
"216/1",
"288/1",
"384/1",
"512/1"
]
},
{
"id": "gradus_10_m",
"desc": "Intervals > 1 with Gradus <= 10",
"stepCount": "92",
"steps": [
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"3/2",
"8/5",
"5/3",
"7/4",
"16/9",
"9/5",
"15/8",
"2/1",
"9/4",
"7/3",
"12/5",
"5/2",
"8/3",
"3/1",
"16/5",
"10/3",
"27/8",
"7/2",
"32/9",
"18/5",
"15/4",
"4/1",
"9/2",
"14/3",
"24/5",
"5/1",
"16/3",
"6/1",
"32/5",
"20/3",
"27/4",
"7/1",
"15/2",
"8/1",
"9/1",
"10/1",
"21/2",
"32/3",
"12/1",
"25/2",
"40/3",
"27/2",
"14/1",
"15/1",
"16/1",
"18/1",
"20/1",
"21/1",
"64/3",
"45/2",
"24/1",
"25/1",
"27/1",
"28/1",
"30/1",
"32/1",
"36/1",
"40/1",
"81/2",
"42/1",
"128/3",
"45/1",
"48/1",
"50/1",
"54/1",
"56/1",
"60/1",
"64/1",
"72/1",
"80/1",
"81/1",
"90/1",
"96/1",
"108/1",
"120/1",
"128/1",
"144/1",
"160/1",
"162/1",
"192/1",
"216/1",
"256/1",
"288/1",
"384/1",
"512/1"
]
},
{
"id": "grady_14",
"desc": "Kraig Grady, letter to Lou Harrison, published in 1/1 vol. 7 no. 1, 1991, p.5",
"stepCount": "14",
"steps": [
"21/20",
"9/8",
"7/6",
"5/4",
"21/16",
"4/3",
"7/5",
"3/2",
"63/40",
"27/16",
"7/4",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "grady_centaur",
"desc": "Kraig Grady's 7-limit Centaur scale (1987), Xenharmonikon 16",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"14/9",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "grady_centaur_17",
"desc": "17-tone extension of Centaur, Kraig Grady & Terumi Narushima (2012)",
"stepCount": "17",
"steps": [
"21/20",
"15/14",
"9/8",
"7/6",
"49/40",
"5/4",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"49/30",
"5/3",
"7/4",
"147/80",
"15/8",
"2/1"
]
},
{
"id": "grady_centaur_19",
"desc": "19-tone extension of Centaur, Kraig Grady & Terumi Narushima (2012). Optional 10/9, 63/40, 16/9, 35/18",
"stepCount": "19",
"steps": [
"21/20",
"35/32",
"9/8",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"7/5",
"35/24",
"3/2",
"14/9",
"8/5",
"5/3",
"7/4",
"9/5",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "grady_centaurmarv",
"desc": "1/4-kleismic marvel tempered centaur/meandin",
"stepCount": "12",
"steps": [
"84.46719",
"200.05424",
"268.79879",
"384.38583",
"499.97288",
"584.44007",
"700.02712",
"768.77167",
"884.35871",
"968.82591",
"1084.41295",
"2/1"
]
},
{
"id": "grady_11",
"desc": "Kraig Grady's dual [5 7 9 11] hexany scale",
"stepCount": "12",
"steps": [
"35/33",
"10/9",
"7/6",
"14/11",
"15/11",
"81/56",
"3/2",
"45/28",
"135/77",
"81/44",
"27/14",
"2/1"
]
},
{
"id": "grammateus",
"desc": "H. Grammateus (Heinrich Schreiber) (1518). B-F# and Bb-F 1/2 P. Also Marpurg nr.6 and Baron von Wiese and Maria Renold",
"stepCount": "12",
"steps": [
"101.95500",
"9/8",
"305.86500",
"81/64",
"4/3",
"600.00000",
"3/2",
"803.91000",
"27/16",
"1007.82000",
"243/128",
"2/1"
]
},
{
"id": "graupner",
"desc": "Johann Gottlieb Graupner's temperament (1819)",
"stepCount": "12",
"steps": [
"99.38085",
"199.56283",
"299.18649",
"399.59949",
"499.43999",
"600.05924",
"700.09326",
"799.57803",
"899.85889",
"999.57536",
"1100.07666",
"2/1"
]
},
{
"id": "groenewald_21",
"desc": "J�rgen Gr�newald, just tuning (2000)",
"stepCount": "21",
"steps": [
"135/128",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"512/405",
"4/3",
"45/32",
"64/45",
"3/2",
"405/256",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"256/135",
"2/1"
]
},
{
"id": "groenewald_bach",
"desc": "J�rgen Gr�newald, simplified Bach temperament, Ars Organi vol.57 no.1, March 2009, p.39",
"stepCount": "12",
"steps": [
"256/243",
"189.25008",
"32/27",
"386.60605",
"4/3",
"1024/729",
"693.17509",
"128/81",
"887.27506",
"16/9",
"1086.80812",
"2/1"
]
},
{
"id": "groenewald",
"desc": "J�rgen Gr�newald, new meantone temperament (2001)",
"stepCount": "12",
"steps": [
"101.95500",
"193.15686",
"304.88814",
"396.09000",
"4/3",
"600.00000",
"3/2",
"803.91000",
"895.11186",
"1006.84314",
"1098.04500",
"2/1"
]
},
{
"id": "groven_ji",
"desc": "Untempered version of Groven's 36-tone scale",
"stepCount": "36",
"steps": [
"81/80",
"25/24",
"135/128",
"16/15",
"10/9",
"9/8",
"256/225",
"75/64",
"32/27",
"6/5",
"5/4",
"81/64",
"32/25",
"675/512",
"4/3",
"27/20",
"25/18",
"45/32",
"64/45",
"40/27",
"3/2",
"1024/675",
"25/16",
"405/256",
"8/5",
"5/3",
"27/16",
"128/75",
"225/128",
"16/9",
"9/5",
"50/27",
"15/8",
"256/135",
"2025/1024",
"2/1"
]
},
{
"id": "groven",
"desc": "Eivind Groven's 36-tone scale with 1/8-schisma temp. fifths and 5/4 (1948)",
"stepCount": "36",
"steps": [
"20.52943",
"70.91664",
"91.44607",
"111.97550",
"182.89214",
"203.42157",
"223.95100",
"274.33821",
"294.86764",
"315.39707",
"5/4",
"406.84314",
"32/25",
"477.75979",
"498.28921",
"518.81864",
"569.20586",
"589.73529",
"610.26471",
"681.18136",
"701.71079",
"722.24021",
"25/16",
"793.15686",
"8/5",
"884.60293",
"905.13236",
"925.66179",
"976.04900",
"996.57843",
"1017.10786",
"1067.49507",
"1088.02450",
"1108.55393",
"1179.47057",
"2/1"
]
},
{
"id": "guanyin_22",
"desc": "Guanyin[22] {176/175, 540/539} hobbit in 111-tET",
"stepCount": "22",
"steps": [
"43.24324",
"108.10811",
"162.16216",
"227.02703",
"270.27027",
"313.51351",
"389.18919",
"432.43243",
"497.29730",
"540.54054",
"583.78378",
"659.45946",
"702.70270",
"767.56757",
"810.81081",
"886.48649",
"929.72973",
"972.97297",
"1037.83784",
"1091.89189",
"1156.75676",
"2/1"
]
},
{
"id": "guanyintet_5",
"desc": "Guanyintet[5] 2.5.7/3.11/3 subgroup MOS in 70\\311 tuning",
"stepCount": "5",
"steps": ["270.09646", "540.19293", "810.28939", "1080.38585", "2/1"]
},
{
"id": "guiron_77",
"desc": "Guiron[77] (118&159 temperament) in 159-tET",
"stepCount": "77",
"steps": [
"22.64151",
"30.18868",
"52.83019",
"60.37736",
"83.01887",
"90.56604",
"113.20755",
"120.75472",
"143.39623",
"150.94340",
"173.58491",
"181.13207",
"203.77359",
"211.32076",
"233.96226",
"256.60377",
"264.15094",
"286.79245",
"294.33962",
"316.98113",
"324.52830",
"347.16981",
"354.71698",
"377.35849",
"384.90566",
"407.54717",
"415.09434",
"437.73585",
"445.28302",
"467.92453",
"490.56604",
"498.11321",
"520.75472",
"528.30189",
"550.94340",
"558.49057",
"581.13207",
"588.67924",
"611.32075",
"618.86792",
"641.50943",
"649.05660",
"671.69811",
"679.24528",
"701.88679",
"709.43396",
"732.07547",
"754.71698",
"762.26415",
"784.90566",
"792.45283",
"815.09434",
"822.64151",
"845.28302",
"852.83019",
"875.47170",
"883.01887",
"905.66038",
"913.20755",
"935.84906",
"943.39623",
"966.03774",
"988.67924",
"996.22642",
"1018.86793",
"1026.41509",
"1049.05660",
"1056.60377",
"1079.24528",
"1086.79245",
"1109.43396",
"1116.98113",
"1139.62264",
"1147.16981",
"1169.81132",
"1177.35849",
"2/1"
]
},
{
"id": "gunkali",
"desc": "Indian mode Gunkali, see Dani�lou: Intr. to the Stud. of Mus. Scales, p.175",
"stepCount": "7",
"steps": ["135/128", "27/25", "4/3", "3/2", "25/16", "8/5", "2/1"]
},
{
"id": "gyaling",
"desc": "Tibetan Buddhist Gyaling tones measured from CD \"The Diamond Path\", Ligon 2002",
"stepCount": "6",
"steps": [
"139.00000",
"280.00000",
"450.00000",
"493.00000",
"707.00000",
"884.00000"
]
},
{
"id": "h_10_27",
"desc": "10-tET harmonic approximation, fundamental=27",
"stepCount": "10",
"steps": [
"29/27",
"31/27",
"11/9",
"4/3",
"38/27",
"41/27",
"44/27",
"47/27",
"50/27",
"2/1"
]
},
{
"id": "h_12_24",
"desc": "12-tET harmonic approximation, fundamental=24",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"29/24",
"5/4",
"4/3",
"17/12",
"3/2",
"19/12",
"5/3",
"43/24",
"15/8",
"2/1"
]
},
{
"id": "h_14_27",
"desc": "14-tET harmonic approximation, fundamental=27",
"stepCount": "14",
"steps": [
"28/27",
"10/9",
"31/27",
"11/9",
"35/27",
"4/3",
"38/27",
"40/27",
"14/9",
"44/27",
"47/27",
"49/27",
"17/9",
"2/1"
]
},
{
"id": "h_15_24",
"desc": "15-tET harmonic approximation, fundamental=24",
"stepCount": "15",
"steps": [
"25/24",
"13/12",
"7/6",
"29/24",
"5/4",
"4/3",
"11/8",
"35/24",
"3/2",
"19/12",
"5/3",
"7/4",
"11/6",
"23/12",
"2/1"
]
},
{
"id": "h_17_32",
"desc": "17-tET harmonic approximation, fundamental=32",
"stepCount": "17",
"steps": [
"33/32",
"35/32",
"9/8",
"19/16",
"39/32",
"41/32",
"43/32",
"11/8",
"23/16",
"3/2",
"25/16",
"13/8",
"27/16",
"57/32",
"59/32",
"61/32",
"2/1"
]
},
{
"id": "hahn_7",
"desc": "Paul Hahn's scale with 32 consonant 7-limit dyads. TL '99, see also smithgw_hahn12.scl",
"stepCount": "12",
"steps": [
"21/20",
"7/6",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"28/15",
"2/1"
]
},
{
"id": "hahn_g",
"desc": "Paul Hahn, fourth of sqrt(2)-1 octave \"recursive\"meantone (1999)",
"stepCount": "12",
"steps": [
"120.60608",
"205.88745",
"291.16882",
"411.77490",
"497.05627",
"617.66235",
"702.94373",
"823.54980",
"908.83118",
"994.11255",
"1114.71863",
"2/1"
]
},
{
"id": "hahn_9",
"desc": "Paul Hahn's just version of 9 out of 31 scale, TL 6-8-98",
"stepCount": "9",
"steps": ["35/32", "6/5", "5/4", "7/5", "3/2", "8/5", "7/4", "15/8", "2/1"]
},
{
"id": "hahnmaxr",
"desc": "Paul Hahn's hahn_7.scl marvel projected to the 5-limit",
"stepCount": "12",
"steps": [
"135/128",
"75/64",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"8/5",
"5/3",
"225/128",
"15/8",
"2/1"
]
},
{
"id": "hamilton_jc",
"desc": "Chalmers' permutation of Hamilton's gamut. Diatonic notes on white",
"stepCount": "12",
"steps": [
"22/21",
"11/10",
"22/19",
"11/9",
"11/8",
"22/17",
"11/7",
"22/15",
"22/13",
"44/27",
"11/6",
"2/1"
]
},
{
"id": "hamilton_jc_2",
"desc": "EH gamut, diatonic notes on white and drops 17 for 25. JC Dorian Harmonia on C. Schlesinger's Solar scale",
"stepCount": "12",
"steps": [
"22/21",
"11/10",
"22/19",
"11/9",
"11/8",
"22/15",
"11/7",
"44/27",
"22/13",
"44/25",
"11/6",
"2/1"
]
},
{
"id": "hamilton",
"desc": "Elsie Hamilton's gamut, from article The Modes of Ancient Greek Music (1953)",
"stepCount": "12",
"steps": [
"22/21",
"11/10",
"22/19",
"11/9",
"22/17",
"11/8",
"22/15",
"11/7",
"44/27",
"22/13",
"11/6",
"2/1"
]
},
{
"id": "hammond",
"desc": "Hammond organ pitch wheel ratios, 1/1=320 Hz. Do \"del 0\"to get 12-tone scale",
"stepCount": "13",
"steps": [
"71/82",
"67/73",
"35/36",
"69/67",
"12/11",
"37/32",
"49/40",
"48/37",
"11/8",
"67/46",
"54/35",
"85/52",
"71/41"
]
},
{
"id": "hammond_12",
"desc": "Hammond organ scale, 1/1=277.0731707 Hz, A=440, see hammond.scl for the ratios",
"stepCount": "12",
"steps": [
"5494/5183",
"1435/1278",
"5658/4757",
"984/781",
"1517/1136",
"2009/1420",
"3936/2627",
"451/284",
"2747/1633",
"4428/2485",
"3485/1846",
"2/1"
]
},
{
"id": "handblue",
"desc": "\"Handy Blues\"of Pitch Palette, 7-limit",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"14/9",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "handel",
"desc": "Well temperament according to Georg Friedrich H�ndel's rules (c. 1780)",
"stepCount": "12",
"steps": [
"93.04020",
"195.46440",
"296.95020",
"395.62080",
"498.98340",
"592.96200",
"697.26300",
"794.99520",
"895.54260",
"997.96680",
"1094.76060",
"2/1"
]
},
{
"id": "handel_2",
"desc": "Another \"H�ndel\"temperament, C. di Veroli",
"stepCount": "12",
"steps": [
"99.71167",
"199.92333",
"299.62167",
"399.83333",
"499.53167",
"599.75666",
"699.45500",
"799.66667",
"899.87833",
"999.57667",
"1100.30166",
"2/1"
]
},
{
"id": "hanson_19",
"desc": "JI version of Hanson's 19 out of 53-tET scale",
"stepCount": "19",
"steps": [
"25/24",
"27/25",
"9/8",
"125/108",
"6/5",
"5/4",
"125/96",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"125/72",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "harm_bastard",
"desc": "Schlesinger's \"Bastard\"Hypodorian Harmonia & inverse 1)7 from 1.3.5.7.9.11.13",
"stepCount": "7",
"steps": ["8/7", "16/13", "4/3", "16/11", "8/5", "16/9", "2/1"]
},
{
"id": "harm_bastinv",
"desc": "Inverse Schlesinger's \"Bastard\"Hypodorian Harmonia & 1)7 from 1.3.5.7.9.11.13",
"stepCount": "7",
"steps": ["9/8", "5/4", "11/8", "3/2", "13/8", "7/4", "2/1"]
},
{
"id": "harm_darreg",
"desc": "Darreg Harmonics 4-15",
"stepCount": "24",
"steps": [
"4/1",
"5/1",
"6/1",
"7/1",
"8/1",
"9/1",
"10/1",
"11/1",
"12/1",
"13/1",
"14/1",
"15/1",
"16/1",
"20/1",
"24/1",
"28/1",
"32/1",
"36/1",
"40/1",
"44/1",
"48/1",
"52/1",
"56/1",
"60/1"
]
},
{
"id": "harm_mean",
"desc": "Harm. mean 9-tonic, 8/7 is HM of 1/1 and 4/3, etc.",
"stepCount": "9",
"steps": [
"32/31",
"16/15",
"8/7",
"4/3",
"3/2",
"48/31",
"8/5",
"12/7",
"2/1"
]
},
{
"id": "harm_pehrson",
"desc": "Harm. 1/4-11/4 and subh. 4/1-4/11. Joseph Pehrson (1999)",
"stepCount": "19",
"steps": [
"1/4",
"4/11",
"2/5",
"4/9",
"1/2",
"4/7",
"2/3",
"3/4",
"4/5",
"1/1",
"5/4",
"4/3",
"3/2",
"7/4",
"2/1",
"9/4",
"5/2",
"11/4",
"4/1"
]
},
{
"id": "harm_perkis",
"desc": "Harmonics 60 to 30 (Perkis)",
"stepCount": "12",
"steps": [
"15/14",
"10/9",
"6/5",
"5/4",
"4/3",
"10/7",
"3/2",
"30/19",
"5/3",
"12/7",
"15/8",
"2/1"
]
},
{
"id": "harm_doreninv_1",
"desc": "1st Inverted Schlesinger's Enharmonic Dorian Harmonia",
"stepCount": "7",
"steps": ["27/22", "5/4", "14/11", "16/11", "21/11", "43/22", "2/1"]
},
{
"id": "harm_dorinv_1",
"desc": "1st Inverted Schlesinger's Chromatic Dorian Harmonia",
"stepCount": "7",
"steps": ["13/11", "27/22", "14/11", "16/11", "20/11", "21/11", "2/1"]
},
{
"id": "harm_lydchrinv_1",
"desc": "1st Inverted Schlesinger's Chromatic Lydian Harmonia",
"stepCount": "7",
"steps": ["16/13", "17/13", "18/13", "20/13", "24/13", "25/13", "2/1"]
},
{
"id": "harm_lydeninv_1",
"desc": "1st Inverted Schlesinger's Enharmonic Lydian Harmonia",
"stepCount": "7",
"steps": ["17/13", "35/26", "18/13", "20/13", "25/13", "51/26", "2/1"]
},
{
"id": "harm_mixochrinv_1",
"desc": "1st Inverted Schlesinger's Chromatic Mixolydian Harmonia",
"stepCount": "7",
"steps": ["9/7", "19/14", "10/7", "11/7", "13/7", "27/14", "2/1"]
},
{
"id": "harm_mix_oeninv_1",
"desc": "1st Inverted Schlesinger's Enharmonic Mixolydian Harmonia",
"stepCount": "7",
"steps": ["19/14", "39/28", "10/7", "11/7", "27/14", "55/28", "2/1"]
},
{
"id": "harm_1_c_hypod",
"desc": "HarmC-Hypodorian",
"stepCount": "8",
"steps": ["5/4", "21/16", "11/8", "23/16", "3/2", "7/4", "15/8", "2/1"]
},
{
"id": "harm_1_c_hypol",
"desc": "HarmC-Hypolydian",
"stepCount": "8",
"steps": ["21/20", "11/10", "13/10", "7/5", "3/2", "8/5", "17/10", "2/1"]
},
{
"id": "harm_1_c_lydian",
"desc": "Harm1C-Lydian",
"stepCount": "8",
"steps": [
"27/26",
"14/13",
"18/13",
"19/13",
"20/13",
"21/13",
"22/13",
"2/1"
]
},
{
"id": "harm_1_c_mix",
"desc": "Harm1C-Con Mixolydian",
"stepCount": "7",
"steps": ["8/7", "10/7", "3/2", "11/7", "13/7", "27/14", "2/1"]
},
{
"id": "harm_1_c_mixolydian",
"desc": "Harm1C-Mixolydian",
"stepCount": "7",
"steps": ["15/14", "8/7", "10/7", "11/7", "23/14", "12/7", "2/1"]
},
{
"id": "harm_6",
"desc": "Harmonics 6 to 12",
"stepCount": "6",
"steps": ["9/8", "5/4", "11/8", "3/2", "7/4", "2/1"]
},
{
"id": "harm_7_lim",
"desc": "7-limit harmonics",
"stepCount": "47",
"steps": [
"2/1",
"3/1",
"4/1",
"5/1",
"6/1",
"7/1",
"8/1",
"9/1",
"10/1",
"12/1",
"14/1",
"15/1",
"16/1",
"18/1",
"20/1",
"21/1",
"22/1",
"24/1",
"25/1",
"28/1",
"30/1",
"32/1",
"35/1",
"36/1",
"40/1",
"42/1",
"45/1",
"48/1",
"49/1",
"50/1",
"56/1",
"60/1",
"63/1",
"64/1",
"70/1",
"72/1",
"75/1",
"80/1",
"81/1",
"84/1",
"90/1",
"96/1",
"98/1",
"100/1",
"105/1",
"112/1",
"120/1"
]
},
{
"id": "harm_8",
"desc": "Harmonics 8 to 16",
"stepCount": "8",
"steps": ["9/8", "5/4", "11/8", "3/2", "13/8", "7/4", "15/8", "2/1"]
},
{
"id": "harm_9",
"desc": "Harmonics 9 to 18",
"stepCount": "9",
"steps": [
"17/16",
"9/8",
"5/4",
"11/8",
"3/2",
"13/8",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "harm_10",
"desc": "Harmonics 10 to 20",
"stepCount": "10",
"steps": [
"11/10",
"6/5",
"13/10",
"7/5",
"3/2",
"8/5",
"17/10",
"9/5",
"19/10",
"2/1"
]
},
{
"id": "harm_12_2",
"desc": "Harmonics 12 to 24, mode 9",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"21/16",
"11/8",
"23/16",
"3/2",
"13/8",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "harm_12",
"desc": "Harmonics 12 to 24",
"stepCount": "12",
"steps": [
"13/12",
"7/6",
"5/4",
"4/3",
"17/12",
"3/2",
"19/12",
"5/3",
"7/4",
"11/6",
"23/12",
"2/1"
]
},
{
"id": "harm_12_s",
"desc": "Harmonics 1 to 12 and subharmonics mixed",
"stepCount": "11",
"steps": [
"9/8",
"8/7",
"5/4",
"4/3",
"11/8",
"16/11",
"3/2",
"8/5",
"7/4",
"16/9",
"2/1"
]
},
{
"id": "harm_14",
"desc": "Harmonics 14 to 28, Tessaradecatonic Harmonium, Jos� Pereira de Sampaio (1903)",
"stepCount": "14",
"steps": [
"15/14",
"8/7",
"17/14",
"9/7",
"19/14",
"10/7",
"3/2",
"11/7",
"23/14",
"12/7",
"25/14",
"13/7",
"27/14",
"2/1"
]
},
{
"id": "harm_15",
"desc": "Harmonics 15 to 30",
"stepCount": "15",
"steps": [
"16/15",
"17/15",
"6/5",
"19/15",
"4/3",
"7/5",
"22/15",
"23/15",
"8/5",
"5/3",
"26/15",
"9/5",
"28/15",
"29/15",
"2/1"
]
},
{
"id": "harm_15_a",
"desc": "Twelve out of harmonics 15 to 30",
"stepCount": "12",
"steps": [
"16/15",
"17/15",
"6/5",
"19/15",
"4/3",
"7/5",
"22/15",
"8/5",
"5/3",
"26/15",
"28/15",
"2/1"
]
},
{
"id": "harm_16",
"desc": "Harmonics 16 to 32, Tom Stone's Guitar Scale",
"stepCount": "16",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"21/16",
"11/8",
"23/16",
"3/2",
"25/16",
"13/8",
"27/16",
"7/4",
"29/16",
"15/8",
"31/16",
"2/1"
]
},
{
"id": "harm_19",
"desc": "Harmonics 19 to 38, odd harmonics until 37",
"stepCount": "19",
"steps": [
"33/32",
"17/16",
"35/32",
"9/8",
"37/32",
"19/16",
"5/4",
"21/16",
"11/8",
"23/16",
"3/2",
"25/16",
"13/8",
"27/16",
"7/4",
"29/16",
"15/8",
"31/16",
"2/1"
]
},
{
"id": "harm_20_12",
"desc": "12-tone subset of harmonics 20 to 40",
"stepCount": "12",
"steps": [
"21/20",
"11/10",
"6/5",
"5/4",
"13/10",
"7/5",
"3/2",
"8/5",
"17/10",
"9/5",
"19/10",
"2/1"
]
},
{
"id": "harm_24_8",
"desc": "Modified Porcupine scale, Mike Sheiman (2011)",
"stepCount": "8",
"steps": ["13/12", "7/6", "5/4", "11/8", "3/2", "5/3", "11/6", "2/1"]
},
{
"id": "harm_24_12",
"desc": "12-tone subset of harmonics 24 to 48",
"stepCount": "12",
"steps": [
"13/12",
"9/8",
"7/6",
"5/4",
"4/3",
"11/8",
"3/2",
"13/8",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "harm_28_8",
"desc": "8-tone subset of harmonics 28 to 56, Mike Sheiman (2011)",
"stepCount": "8",
"steps": ["15/14", "8/7", "9/7", "10/7", "45/28", "12/7", "25/14", "2/1"]
},
{
"id": "harm_28_9",
"desc": "9-tone subset of harmonics 28 to 56, Mike Sheiman (2011)",
"stepCount": "9",
"steps": [
"15/14",
"5/4",
"9/7",
"10/7",
"3/2",
"45/28",
"12/7",
"25/14",
"2/1"
]
},
{
"id": "harm_30",
"desc": "Harmonics 30 to 60",
"stepCount": "30",
"steps": [
"31/30",
"16/15",
"11/10",
"17/15",
"7/6",
"6/5",
"37/30",
"19/15",
"13/10",
"4/3",
"41/30",
"7/5",
"43/30",
"22/15",
"3/2",
"23/15",
"47/30",
"8/5",
"49/30",
"5/3",
"17/10",
"26/15",
"53/30",
"9/5",
"11/6",
"28/15",
"19/10",
"29/15",
"59/30",
"2/1"
]
},
{
"id": "harm_32",
"desc": "Harmonics 32 to 64",
"stepCount": "32",
"steps": [
"33/32",
"17/16",
"35/32",
"9/8",
"37/32",
"19/16",
"39/32",
"5/4",
"41/32",
"21/16",
"43/32",
"11/8",
"45/32",
"23/16",
"47/32",
"3/2",
"49/32",
"25/16",
"51/32",
"13/8",
"53/32",
"27/16",
"55/32",
"7/4",
"57/32",
"29/16",
"59/32",
"15/8",
"61/32",
"31/16",
"63/32",
"2/1"
]
},
{
"id": "harm_256",
"desc": "Harmonics 2 to 256, Johnny Reinhard",
"stepCount": "128",
"steps": [
"129/128",
"65/64",
"131/128",
"33/32",
"133/128",
"67/64",
"135/128",
"17/16",
"137/128",
"69/64",
"139/128",
"35/32",
"141/128",
"71/64",
"143/128",
"9/8",
"145/128",
"73/64",
"147/128",
"37/32",
"149/128",
"75/64",
"151/128",
"19/16",
"153/128",
"77/64",
"155/128",
"39/32",
"157/128",
"79/64",
"159/128",
"5/4",
"161/128",
"81/64",
"163/128",
"41/32",
"165/128",
"83/64",
"167/128",
"21/16",
"169/128",
"85/64",
"171/128",
"43/32",
"173/128",
"87/64",
"175/128",
"11/8",
"177/128",
"89/64",
"179/128",
"45/32",
"181/128",
"91/64",
"183/128",
"23/16",
"185/128",
"93/64",
"187/128",
"47/32",
"189/128",
"95/64",
"191/128",
"3/2",
"193/128",
"97/64",
"195/128",
"49/32",
"197/128",
"99/64",
"199/128",
"25/16",
"201/128",
"101/64",
"203/128",
"51/32",
"205/128",
"103/64",
"207/128",
"13/8",
"209/128",
"105/64",
"211/128",
"53/32",
"213/128",
"107/64",
"215/128",
"27/16",
"217/128",
"109/64",
"219/128",
"55/32",
"221/128",
"111/64",
"223/128",
"7/4",
"225/128",
"113/64",
"227/128",
"57/32",
"229/128",
"115/64",
"231/128",
"29/16",
"233/128",
"117/64",
"235/128",
"59/32",
"237/128",
"119/64",
"239/128",
"15/8",
"241/128",
"121/64",
"243/128",
"61/32",
"245/128",
"123/64",
"247/128",
"31/16",
"249/128",
"125/64",
"251/128",
"63/32",
"253/128",
"127/64",
"255/128",
"2/1"
]
},
{
"id": "harmc_hypop",
"desc": "HarmC-Hypophrygian",
"stepCount": "9",
"steps": [
"11/9",
"23/18",
"4/3",
"25/18",
"13/9",
"14/9",
"16/9",
"17/9",
"2/1"
]
},
{
"id": "harmd_15",
"desc": "HarmD-15-Harmonia",
"stepCount": "7",
"steps": ["16/15", "6/5", "4/3", "22/15", "8/5", "26/15", "2/1"]
},
{
"id": "harmd_conmix",
"desc": "HarmD-ConMixolydian",
"stepCount": "7",
"steps": ["8/7", "9/7", "3/2", "11/7", "12/7", "13/7", "2/1"]
},
{
"id": "harm_d_hypop",
"desc": "HarmD-Hypophrygian",
"stepCount": "9",
"steps": [
"10/9",
"11/9",
"4/3",
"25/18",
"13/9",
"14/9",
"5/3",
"16/9",
"2/1"
]
},
{
"id": "harmd_lyd",
"desc": "HarmD-Lydian",
"stepCount": "9",
"steps": [
"14/13",
"15/13",
"16/13",
"18/13",
"19/13",
"20/13",
"22/13",
"24/13",
"2/1"
]
},
{
"id": "harmd_mix",
"desc": "HarmD-Mixolydian. Harmonics 7-14",
"stepCount": "7",
"steps": ["8/7", "9/7", "10/7", "11/7", "12/7", "13/7", "2/1"]
},
{
"id": "harmd_phr",
"desc": "HarmD-Phryg (with 5 extra tones)",
"stepCount": "12",
"steps": [
"25/24",
"13/12",
"9/8",
"7/6",
"4/3",
"5/4",
"3/2",
"19/12",
"5/3",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "harme_hypod",
"desc": "HarmE-Hypodorian",
"stepCount": "8",
"steps": ["21/16", "43/32", "11/8", "23/16", "3/2", "15/8", "31/16", "2/1"]
},
{
"id": "harme_hypol",
"desc": "HarmE-Hypolydian",
"stepCount": "8",
"steps": ["43/40", "21/20", "13/10", "7/5", "3/2", "31/20", "8/5", "2/1"]
},
{
"id": "harme_hypop",
"desc": "HarmE-Hypophrygian",
"stepCount": "9",
"steps": [
"23/18",
"47/36",
"4/3",
"25/18",
"13/9",
"14/9",
"17/9",
"35/18",
"2/1"
]
},
{
"id": "harmf_9",
"desc": "6/7/8/9 harmonics, First 9 overtones of 5th through 9th harmonics",
"stepCount": "10",
"steps": [
"9/8",
"7/6",
"5/4",
"4/3",
"49/36",
"3/2",
"14/9",
"7/4",
"16/9",
"2/1"
]
},
{
"id": "harmf_10",
"desc": "6/7/8/9/10 harmonics",
"stepCount": "13",
"steps": [
"35/32",
"9/8",
"5/4",
"81/64",
"21/16",
"45/32",
"3/2",
"49/32",
"25/16",
"27/16",
"7/4",
"63/32",
"2/1"
]
},
{
"id": "harmf_12",
"desc": "First 12 harmonics of 6th through 12th harmonics. Also Arnold Dreyblatt's tuning system with 1/1=349.23 Hz",
"stepCount": "20",
"steps": [
"33/32",
"35/32",
"9/8",
"77/64",
"5/4",
"81/64",
"21/16",
"11/8",
"45/32",
"3/2",
"49/32",
"99/64",
"25/16",
"27/16",
"55/32",
"7/4",
"15/8",
"121/64",
"63/32",
"2/1"
]
},
{
"id": "harmf_16",
"desc": "First 16 harmonics and subharmonics",
"stepCount": "30",
"steps": [
"2/1",
"3/1",
"4/1",
"5/1",
"6/1",
"7/1",
"8/1",
"9/1",
"10/1",
"11/1",
"12/1",
"13/1",
"14/1",
"15/1",
"16/1",
"8/1",
"16/3",
"4/1",
"16/5",
"8/3",
"16/7",
"2/1",
"16/9",
"8/5",
"16/11",
"4/3",
"16/13",
"8/7",
"16/15",
"1/1"
]
},
{
"id": "harmf_30",
"desc": "First 30 harmonics and subharmonics",
"stepCount": "59",
"steps": [
"16/15",
"32/29",
"8/7",
"32/27",
"16/13",
"32/25",
"4/3",
"32/23",
"32/21",
"8/5",
"32/19",
"16/9",
"32/17",
"2/1",
"32/15",
"16/7",
"32/13",
"8/3",
"32/11",
"16/5",
"32/9",
"4/1",
"32/7",
"16/3",
"32/5",
"8/1",
"32/3",
"16/1",
"32/1",
"33/1",
"34/1",
"35/1",
"36/1",
"37/1",
"38/1",
"39/1",
"40/1",
"41/1",
"42/1",
"43/1",
"44/1",
"45/1",
"46/1",
"47/1",
"48/1",
"49/1",
"50/1",
"51/1",
"52/1",
"53/1",
"54/1",
"55/1",
"56/1",
"57/1",
"58/1",
"59/1",
"60/1",
"61/1",
"62/1"
]
},
{
"id": "harmjc_15",
"desc": "Rationalized JC Sub-15 Harmonia on C. MD=15, No planetary assignment.",
"stepCount": "12",
"steps": [
"15/14",
"15/13",
"6/5",
"5/4",
"15/11",
"10/7",
"3/2",
"30/19",
"5/3",
"30/17",
"15/8",
"2/1"
]
},
{
"id": "harmjc_17_2",
"desc": "Rationalized JC Sub-17 Harmonia on C. MD=17, No planetary assignment.",
"stepCount": "12",
"steps": [
"17/16",
"17/15",
"17/14",
"17/13",
"17/12",
"34/23",
"17/11",
"34/21",
"17/10",
"34/19",
"17/9",
"2/1"
]
},
{
"id": "harmjc_17",
"desc": "Rationalized JC Sub-17 Harmonia on C. MD=17, No planetary assignment.",
"stepCount": "12",
"steps": [
"34/33",
"17/16",
"17/15",
"17/14",
"17/13",
"34/25",
"17/12",
"34/23",
"17/11",
"34/21",
"17/10",
"2/1"
]
},
{
"id": "harmjc_19_2",
"desc": "Rationalized JC Sub-19 Harmonia on C. MD=19, No planetary assignment.",
"stepCount": "12",
"steps": [
"19/18",
"19/17",
"19/16",
"19/15",
"19/14",
"38/27",
"19/13",
"38/25",
"19/12",
"38/23",
"19/11",
"2/1"
]
},
{
"id": "harmjc_19",
"desc": "Rationalized JC Sub-19 Harmonia on C. MD=19, No planetary assignment.",
"stepCount": "12",
"steps": [
"19/18",
"19/17",
"19/16",
"19/15",
"19/14",
"19/13",
"19/12",
"38/23",
"19/11",
"38/21",
"19/10",
"2/1"
]
},
{
"id": "harmjc_21",
"desc": "Rationalized JC Sub-21 Harmonia on C. MD=21, No planetary assignment.",
"stepCount": "12",
"steps": [
"42/41",
"21/20",
"21/19",
"7/6",
"21/16",
"7/5",
"3/2",
"14/9",
"21/13",
"42/25",
"7/4",
"2/1"
]
},
{
"id": "harmjc_23_2",
"desc": "Rationalized JC Sub-23 Harmonia on C. MD=23, No planetary assignment.",
"stepCount": "12",
"steps": [
"23/22",
"23/21",
"23/20",
"23/19",
"23/18",
"23/17",
"23/16",
"23/15",
"23/14",
"23/13",
"23/12",
"2/1"
]
},
{
"id": "harmjc_23",
"desc": "Rationalized JC Sub-23 Harmonia on C. MD=23, No planetary assignment.",
"stepCount": "12",
"steps": [
"23/22",
"23/20",
"23/19",
"23/18",
"23/16",
"23/15",
"23/14",
"46/27",
"23/13",
"46/25",
"23/12",
"2/1"
]
},
{
"id": "harmjc_25",
"desc": "Rationalized JC Sub-25 Harmonia on C. MD=25, No planetary assignment.",
"stepCount": "12",
"steps": [
"25/24",
"25/22",
"25/21",
"5/4",
"25/18",
"25/17",
"25/16",
"5/3",
"25/14",
"50/27",
"25/13",
"2/1"
]
},
{
"id": "harmjc_27",
"desc": "Rationalized JC Sub-27 Harmonia on C. MD=27, No planetary assignment.",
"stepCount": "12",
"steps": [
"27/26",
"9/8",
"27/23",
"27/22",
"27/20",
"27/19",
"3/2",
"27/17",
"27/16",
"9/5",
"27/14",
"2/1"
]
},
{
"id": "harmjc_hypod_16",
"desc": "Rationalized JC Hypodorian Harmonia on C. Saturn Scale on C, MD=16. (Steiner)",
"stepCount": "12",
"steps": [
"16/15",
"8/7",
"32/27",
"16/13",
"4/3",
"32/23",
"16/11",
"32/21",
"8/5",
"32/19",
"16/9",
"2/1"
]
},
{
"id": "harmjc_hypol_20",
"desc": "Rationalized JC Hypolydian Harmonia on C. Mars scale on C., MD=20",
"stepCount": "12",
"steps": [
"20/19",
"10/9",
"20/17",
"5/4",
"4/3",
"10/7",
"20/13",
"8/5",
"5/3",
"40/23",
"11/5",
"2/1"
]
},
{
"id": "harmjc_hypop_18",
"desc": "Rationalized JC Hypophrygian Harmonia on C. Jupiter scale on C, MD =18",
"stepCount": "12",
"steps": [
"18/17",
"9/8",
"6/5",
"9/7",
"18/13",
"36/25",
"3/2",
"36/23",
"18/11",
"12/7",
"9/5",
"2/1"
]
},
{
"id": "harmjc_lydian_13",
"desc": "Rationalized JC Lydian Harmonia on Schlesinger's Mercury scale on C, MD = 26 or 13",
"stepCount": "12",
"steps": [
"26/25",
"13/12",
"26/23",
"13/11",
"13/10",
"26/19",
"13/9",
"26/17",
"13/8",
"26/15",
"13/7",
"2/1"
]
},
{
"id": "harmjc_mix_14",
"desc": "Rationalized JC Mixolydian Harmonia on Schlesinger's Moon Scale on C, MD = 14",
"stepCount": "12",
"steps": [
"28/27",
"14/13",
"28/25",
"7/6",
"14/11",
"4/3",
"7/5",
"28/19",
"14/9",
"28/17",
"7/4",
"2/1"
]
},
{
"id": "harmjc_phryg_12",
"desc": "Rationalized JC Phrygian Harmonia on Schlesinger's Venus scale on C, MD = 24 or 12",
"stepCount": "12",
"steps": [
"24/23",
"12/11",
"8/7",
"6/5",
"4/3",
"24/17",
"3/2",
"8/5",
"12/7",
"16/9",
"24/13",
"2/1"
]
},
{
"id": "harmonical_up",
"desc": "Upper 2 octaves of Ellis's Harmonical",
"stepCount": "12",
"steps": [
"17/16",
"9/8",
"19/16",
"5/4",
"11/8",
"7/4",
"3/2",
"25/16",
"13/8",
"29/16",
"15/8",
"2/1"
]
},
{
"id": "harmonical",
"desc": "See pages 17 and 466-468 of Helmholtz. Lower 4 oct. instrument designed and tuned by Ellis",
"stepCount": "12",
"steps": [
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"3/2",
"8/5",
"5/3",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "harmsub_16",
"desc": "16 harmonics on 1/1 and 16 subharmonics on 15/8",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"15/13",
"5/4",
"15/11",
"11/8",
"3/2",
"13/8",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "harrison_5_1",
"desc": "From Lou Harrison, a pelog style pentatonic",
"stepCount": "5",
"steps": ["12/11", "6/5", "3/2", "8/5", "2/1"]
},
{
"id": "harrison_5_3",
"desc": "From Lou Harrison, a pelog style pentatonic",
"stepCount": "5",
"steps": ["28/27", "4/3", "3/2", "14/9", "2/1"]
},
{
"id": "harrison_5_4",
"desc": "From Lou Harrison, a pelog style pentatonic",
"stepCount": "5",
"steps": ["16/15", "6/5", "3/2", "15/8", "2/1"]
},
{
"id": "harrison_5",
"desc": "From Lou Harrison, a pelog style pentatonic",
"stepCount": "5",
"steps": ["16/15", "6/5", "3/2", "8/5", "2/1"]
},
{
"id": "harrison_8",
"desc": "Lou Harrison 8-tone tuning for \"Serenade for Guitar\"",
"stepCount": "8",
"steps": ["16/15", "6/5", "5/4", "45/32", "3/2", "5/3", "16/9", "2/1"]
},
{
"id": "harrison_15",
"desc": "15-tone scale found in Music Primer, Lou Harrison",
"stepCount": "15",
"steps": [
"21/20",
"9/8",
"7/6",
"5/4",
"21/16",
"4/3",
"7/5",
"3/2",
"14/9",
"63/40",
"27/16",
"7/4",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "harrison_16",
"desc": "Lou Harrison 16-tone superparticular \"Ptolemy Duple\", an aluminium bars instrument",
"stepCount": "16",
"steps": [
"16/15",
"10/9",
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"17/12",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "harrison_bill",
"desc": "Lou Harrison, \"Music for Bill and Me\"(1966) for guitar",
"stepCount": "6",
"steps": ["9/8", "5/4", "3/2", "27/16", "15/8", "2/1"]
},
{
"id": "harrison_cinna",
"desc": "Lou Harrison, \"Incidental Music for Corneille's Cinna\"(1955-56) 1/1=C",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"21/16",
"45/32",
"3/2",
"8/5",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "harrison_diat",
"desc": "From Lou Harrison, a soft diatonic",
"stepCount": "7",
"steps": ["21/20", "6/5", "4/3", "3/2", "63/40", "9/5", "2/1"]
},
{
"id": "harrison_handel",
"desc": "Lou Harrison, \"In Honor of the Divine Mr. Handel\"(1978-2002) for guitar",
"stepCount": "7",
"steps": ["35/32", "5/4", "21/16", "49/32", "105/64", "7/4", "2/1"]
},
{
"id": "harrison_kyai",
"desc": "Lou Harrison�s Kyai Udan Arum, pelog just gamelan tuning",
"stepCount": "7",
"steps": ["16/15", "7/6", "4/3", "22/15", "47/30", "9/5", "2/1"]
},
{
"id": "harrison_mid",
"desc": "Lou Harrison mid mode",
"stepCount": "7",
"steps": ["9/8", "6/5", "4/3", "3/2", "5/3", "7/4", "2/1"]
},
{
"id": "harrison_mid_2",
"desc": "Lou Harrison mid mode 2",
"stepCount": "7",
"steps": ["9/8", "6/5", "4/3", "3/2", "12/7", "9/5", "2/1"]
},
{
"id": "harrison_min",
"desc": "Lou Harrison, symmetrical pentatonic with minor thirds. Per. block 16/15, 27/25",
"stepCount": "5",
"steps": ["6/5", "4/3", "3/2", "5/3", "2/1"]
},
{
"id": "harrison_mix_1",
"desc": "A \"mixed type\"pentatonic, Lou Harrison",
"stepCount": "5",
"steps": ["12/11", "6/5", "3/2", "13/8", "2/1"]
},
{
"id": "harrison_mix_2",
"desc": "A \"mixed type\"pentatonic, Lou Harrison",
"stepCount": "5",
"steps": ["6/5", "4/3", "3/2", "15/8", "2/1"]
},
{
"id": "harrison_mix_3",
"desc": "A \"mixed type\"pentatonic, Lou Harrison",
"stepCount": "5",
"steps": ["6/5", "9/7", "3/2", "8/5", "2/1"]
},
{
"id": "harrison_mix_4",
"desc": "A \"mixed type\"pentatonic, Lou Harrison",
"stepCount": "5",
"steps": ["15/14", "5/4", "3/2", "12/7", "2/1"]
},
{
"id": "harrison_slye",
"desc": "11-limit scale by Lou Harrison and Bill Slye for National Reso-Phonic Just Intonation Guitar",
"stepCount": "12",
"steps": [
"28/27",
"9/8",
"7/6",
"5/4",
"4/3",
"11/8",
"3/2",
"14/9",
"5/3",
"7/4",
"11/6",
"2/1"
]
},
{
"id": "harrison_songs",
"desc": "Shared gamut of \"Four Strict Songs\"(1951-55), each pentatonic",
"stepCount": "12",
"steps": [
"28/27",
"9/8",
"32/27",
"5/4",
"4/3",
"45/32",
"3/2",
"14/9",
"27/16",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "harrisonj",
"desc": "John Harrison's temperament (1775), almost 3/10-comma. Third = 1200/pi",
"stepCount": "12",
"steps": [
"68.45076",
"190.98593",
"313.52110",
"381.97187",
"504.50703",
"572.95780",
"695.49297",
"763.94373",
"886.47890",
"1009.01407",
"1077.46483",
"2/1"
]
},
{
"id": "harrisonm_rev",
"desc": "Michael Harrison, piano tuning for \"Revelation\"(2001), 1/1=F",
"stepCount": "12",
"steps": [
"63/64",
"9/8",
"567/512",
"81/64",
"21/16",
"729/512",
"3/2",
"189/128",
"27/16",
"7/4",
"243/128",
"2/1"
]
},
{
"id": "harry_58",
"desc": "Harry[58] 11-limit least squares optimized",
"stepCount": "58",
"steps": [
"30.8796",
"48.2704",
"66.0033",
"83.4055",
"114.0944",
"131.4967",
"149.2296",
"166.6204",
"197.5000",
"214.6587",
"232.2926",
"249.9761",
"280.6630",
"297.9611",
"315.5137",
"333.1120",
"363.8916",
"381.1737",
"398.7500",
"416.3263",
"433.6084",
"464.3880",
"481.9863",
"499.5389",
"516.8370",
"547.5239",
"565.2074",
"582.8413",
"600.0000",
"630.8796",
"648.2704",
"666.0033",
"683.4055",
"714.0944",
"731.4967",
"749.2296",
"766.6204",
"797.5000",
"814.6587",
"832.2926",
"849.9761",
"880.6630",
"897.9611",
"915.5137",
"933.1120",
"963.8916",
"981.1737",
"998.7500",
"1016.3263",
"1033.6084",
"1064.3880",
"1081.9863",
"1099.5389",
"1116.8370",
"1147.5239",
"1165.2074",
"1182.8413",
"2/1"
]
},
{
"id": "haverstick_13",
"desc": "Neil Haverstick, scale in 34-tET, MMM 21-5-2006",
"stepCount": "13",
"steps": [
"141.17647 !13/12",
"247.05882 !15/13",
"282.35294 !13/11",
"352.94118 !16/13",
"458.82353 !13/10",
"564.70588 !18/13",
"635.29412 !13/9",
"741.17647 !20/13",
"847.05882 !13/8",
"917.64706 !22/13",
"1058.82353 !24/13",
"1129.41176 !25/13",
"2/1"
]
},
{
"id": "haverstick_21",
"desc": "Neil Haverstick, just guitar tuning, TL 19-07-2007",
"stepCount": "21",
"steps": [
"25/24",
"17/16",
"10/9",
"9/8",
"19/16",
"6/5",
"5/4",
"21/16",
"4/3",
"11/8",
"23/16",
"3/2",
"25/16",
"13/8",
"5/3",
"27/16",
"7/4",
"29/16",
"15/8",
"31/16",
"2/1"
]
},
{
"id": "hawkes",
"desc": "William Hawkes' modified 1/5-comma meantone (1807)",
"stepCount": "12",
"steps": [
"83.57620",
"195.30749",
"295.11186",
"390.61497",
"502.34626",
"585.92246",
"697.65374",
"785.53120",
"892.96123",
"1004.69252",
"15/8",
"2/1"
]
},
{
"id": "hawkes_2",
"desc": "Meantone with fifth tempered 1/6 of 53-tET step by William Hawkes (1808)",
"stepCount": "12",
"steps": [
"87.26991",
"196.36283",
"305.45575",
"392.72566",
"501.81858",
"589.08850",
"698.18142",
"785.45133",
"894.54425",
"1003.63717",
"1090.90708",
"2/1"
]
},
{
"id": "hawkes_3",
"desc": "William Hawkes' modified 1/5-comma meantone (1811)",
"stepCount": "12",
"steps": [
"83.57620",
"195.30749",
"302.73751",
"390.61497",
"502.34626",
"585.92246",
"697.65374",
"785.53120",
"892.96123",
"1004.69251",
"15/8",
"2/1"
]
},
{
"id": "helmholtz_24",
"desc": "Simplified Helmholtz 24",
"stepCount": "24",
"steps": [
"135/128",
"16/15",
"10/9",
"9/8",
"75/64",
"32/27",
"5/4",
"81/64",
"675/512",
"4/3",
"45/32",
"729/512",
"6075/4096",
"3/2",
"25/16",
"405/256",
"5/3",
"27/16",
"225/128",
"3645/2048",
"15/8",
"243/128",
"2025/1024",
"2/1"
]
},
{
"id": "helmholtz_decad",
"desc": "Helmholtz Harmonic Decad, major pentatonic modes mixed",
"stepCount": "9",
"steps": ["9/8", "6/5", "5/4", "4/3", "3/2", "8/5", "5/3", "9/5", "2/1"]
},
{
"id": "helmholtz_pure",
"desc": "Helmholtz's two-keyboard harmonium tuning untempered",
"stepCount": "24",
"steps": [
"135/128",
"16/15",
"10/9",
"9/8",
"75/64",
"32/27",
"5/4",
"512/405",
"675/512",
"4/3",
"45/32",
"64/45",
"40/27",
"3/2",
"25/16",
"128/81",
"5/3",
"27/16",
"225/128",
"16/9",
"15/8",
"256/135",
"160/81",
"2/1"
]
},
{
"id": "helmholtz_temp",
"desc": "Helmholtz's two-keyboard harmonium tuning",
"stepCount": "24",
"steps": [
"91.446 cents",
"111.976 cents",
"182.892 cents",
"203.422 cents",
"274.338 cents",
"294.868 cents",
"5/4",
"406.843 cents",
"477.760 cents",
"498.289 cents",
"589.735 cents",
"610.265 cents",
"681.181 cents",
"701.711 cents",
"25/16",
"793.157 cents",
"884.603 cents",
"905.132 cents",
"976.049 cents",
"996.578 cents",
"1088.025 cents",
"1108.554 cents",
"1179.471 cents",
"2/1"
]
},
{
"id": "helmholtz",
"desc": "Helmholtz's Chromatic scale and Gipsy major from Slovakia",
"stepCount": "7",
"steps": ["16/15", "5/4", "4/3", "3/2", "8/5", "15/8", "2/1"]
},
{
"id": "hem_chrom",
"desc": "Hemiolic Chromatic genus has the strong or 1:2 division of the 12/11 pyknon",
"stepCount": "7",
"steps": ["34/33", "12/11", "4/3", "3/2", "17/11", "18/11", "2/1"]
},
{
"id": "hem_chrom_2",
"desc": "1:2 Hemiolic Chromatic genus 3 + 6 + 21 parts",
"stepCount": "7",
"steps": [
"50.00000",
"150.00000",
"500.00000",
"700.00000",
"750.00000",
"850.00000",
"2/1"
]
},
{
"id": "hem_chrom_11",
"desc": "11'al Hemiolic Chromatic genus with a CI of 11/9, Winnington-Ingram",
"stepCount": "7",
"steps": ["24/23", "12/11", "4/3", "3/2", "36/23", "18/11", "2/1"]
},
{
"id": "hem_chrom_13",
"desc": "13'al Hemiolic Chromatic or neutral-third genus has a CI of 16/13",
"stepCount": "7",
"steps": ["26/25", "13/12", "4/3", "3/2", "39/25", "13/8", "2/1"]
},
{
"id": "hemienn_82",
"desc": "Hemiennealimmal-72 in 612-tET tuning (strictly proper)",
"stepCount": "72",
"steps": [
"17.647059",
"31.372549",
"49.019608",
"66.666667",
"84.313725",
"98.039216",
"115.686275",
"133.333333",
"150.980392",
"164.705882",
"182.352941",
"200.000000",
"217.647059",
"231.372549",
"249.019608",
"266.666667",
"284.313725",
"298.039216",
"315.686275",
"333.333333",
"350.980392",
"364.705882",
"382.352941",
"400.000000",
"417.647059",
"431.372549",
"449.019608",
"466.666667",
"484.313725",
"498.039216",
"515.686275",
"533.333333",
"550.980392",
"564.705882",
"582.352941",
"600.000000",
"617.647059",
"631.372549",
"649.019608",
"666.666667",
"684.313725",
"698.039216",
"715.686275",
"733.333333",
"750.980392",
"764.705882",
"782.352941",
"800.000000",
"817.647059",
"831.372549",
"849.019608",
"866.666667",
"884.313725",
"898.039216",
"915.686275",
"933.333333",
"950.980392",
"964.705882",
"982.352941",
"1000.000000",
"1017.647059",
"1031.372549",
"1049.019608",
"1066.666667",
"1084.313725",
"1098.039216",
"1115.686275",
"1133.333333",
"1150.980392",
"1164.705882",
"1182.352941",
"2/1"
]
},
{
"id": "hemifamcyc",
"desc": "Hemifamity cycle of thirds scale, nearest to proper",
"stepCount": "14",
"steps": [
"85.875706",
"180.790960",
"291.525424",
"386.440678",
"402.259887",
"497.175141",
"607.909605",
"702.824859",
"788.700565",
"883.615819",
"969.491525",
"994.350282",
"1105.084746",
"2/1"
]
},
{
"id": "hemifamity_27",
"desc": "(3/2)^9 * (10/9)^3 hemifamity tempered",
"stepCount": "27",
"steps": [
"24.81614",
"110.21232",
"180.72536",
"205.92493",
"230.32672",
"291.35517",
"316.19234",
"386.89900",
"411.35967",
"472.47399",
"496.93387",
"522.04780",
"592.41413",
"607.58587",
"677.95220",
"703.06613",
"727.52601",
"788.64033",
"813.10100",
"883.80766",
"908.64483",
"969.67328",
"994.07507",
"1019.27464",
"1089.78768",
"1175.18386",
"2/1"
]
},
{
"id": "hemimute_31",
"desc": "Mutant Hemithirds[31]",
"stepCount": "31",
"steps": [
"29.7436",
"71.4685",
"113.3844",
"151.5273",
"193.1158",
"223.0172",
"265.4205",
"306.7177",
"346.0883",
"386.5111",
"417.2549",
"459.1556",
"498.7210",
"538.2865",
"580.1872",
"610.9310",
"651.3538",
"690.7244",
"732.0216",
"774.4249",
"804.3263",
"845.9148",
"884.0577",
"925.9736",
"967.6985",
"997.4421",
"1035.9848",
"1077.6340",
"1119.8081",
"1161.4573",
"2/1"
]
},
{
"id": "hemiwuer_24",
"desc": "Hemiw�rschmidt[24] in 229-tET tuning.",
"stepCount": "24",
"steps": [
"83.842795",
"120.524017",
"157.205240",
"193.886463",
"277.729258",
"314.410480",
"351.091703",
"387.772926",
"508.296943",
"544.978166",
"581.659389",
"618.340611",
"702.183406",
"738.864629",
"775.545852",
"812.227074",
"896.069869",
"932.751092",
"969.432314",
"1006.113537",
"1089.956332",
"1126.637555",
"1163.318777",
"2/1"
]
},
{
"id": "hemiwuerschmidt_19_trans_37",
"desc": "Hemiwuerschmidt[19] symmetric 2.3.7 transversal",
"stepCount": "19",
"steps": [
"49/48",
"18432/16807",
"384/343",
"8/7",
"7077888/5764801",
"147456/117649",
"3072/2401",
"16807/12288",
"823543/589824",
"1179648/823543",
"24576/16807",
"2401/1536",
"117649/73728",
"5764801/3538944",
"7/4",
"343/192",
"16807/9216",
"96/49",
"2/1"
]
},
{
"id": "hemiwuerschmidt_25_trans_37",
"desc": "Hemiwuerschmidt[25] symmetric 2.3.7 transversal",
"stepCount": "25",
"steps": [
"49/48",
"2401/2304",
"18432/16807",
"384/343",
"8/7",
"7/6",
"7077888/5764801",
"147456/117649",
"3072/2401",
"64/49",
"16807/12288",
"823543/589824",
"1179648/823543",
"24576/16807",
"49/32",
"2401/1536",
"117649/73728",
"5764801/3538944",
"12/7",
"7/4",
"343/192",
"16807/9216",
"4608/2401",
"96/49",
"2/1"
]
},
{
"id": "hemiwuerschmidt_31_trans_37",
"desc": "Hemiwuerschmidt[31] symmetric 2.3.7 transversal",
"stepCount": "31",
"steps": [
"49/48",
"2401/2304",
"884736/823543",
"18432/16807",
"384/343",
"8/7",
"7/6",
"117649/98304",
"7077888/5764801",
"147456/117649",
"3072/2401",
"64/49",
"343/256",
"16807/12288",
"823543/589824",
"1179648/823543",
"24576/16807",
"512/343",
"49/32",
"2401/1536",
"117649/73728",
"5764801/3538944",
"196608/117649",
"12/7",
"7/4",
"343/192",
"16807/9216",
"823543/442368",
"4608/2401",
"96/49",
"2/1"
]
},
{
"id": "hen_12",
"desc": "Adjusted Hahn12",
"stepCount": "12",
"steps": [
"15/14",
"8/7",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "hen_22",
"desc": "Adjusted Hahn22",
"stepCount": "22",
"steps": [
"25/24",
"15/14",
"10/9",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"25/18",
"7/5",
"35/24",
"3/2",
"100/63",
"8/5",
"5/3",
"12/7",
"7/4",
"50/27",
"15/8",
"35/18",
"2/1"
]
},
{
"id": "hept_diamond",
"desc": "Inverted-Prime Heptatonic Diamond based on Archytas's Enharmonic",
"stepCount": "25",
"steps": [
"36/35",
"28/27",
"16/15",
"9/8",
"7/6",
"6/5",
"98/81",
"56/45",
"5/4",
"32/25",
"9/7",
"4/3",
"3/2",
"14/9",
"25/16",
"8/5",
"45/28",
"81/49",
"5/3",
"12/7",
"16/9",
"15/8",
"27/14",
"35/18",
"2/1"
]
},
{
"id": "hept_diamondi",
"desc": "Prime-Inverted Heptatonic Diamond based on Archytas's Enharmonic",
"stepCount": "25",
"steps": [
"36/35",
"28/27",
"16/15",
"784/729",
"448/405",
"9/8",
"256/225",
"5/4",
"9/7",
"4/3",
"112/81",
"45/32",
"64/45",
"81/56",
"3/2",
"14/9",
"8/5",
"225/128",
"16/9",
"405/224",
"729/392",
"15/8",
"27/14",
"35/18",
"2/1"
]
},
{
"id": "hept_diamon_dp",
"desc": "Heptatonic Diamond based on Archytas's Enharmonic, 27 tones",
"stepCount": "27",
"steps": [
"36/35",
"28/27",
"16/15",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"35/27",
"4/3",
"48/35",
"112/81",
"45/32",
"64/45",
"81/56",
"35/24",
"3/2",
"54/35",
"14/9",
"8/5",
"5/3",
"12/7",
"16/9",
"15/8",
"27/14",
"35/18",
"2/1"
]
},
{
"id": "herf_istrian",
"desc": "Franz Richter Herf, Istrian scale used in \"Welle der Nacht\"op. 2",
"stepCount": "10",
"steps": [
"67/64",
"17/16",
"9/8",
"37/32",
"39/32",
"83/64",
"11/8",
"57/32",
"121/64",
"2/1"
]
},
{
"id": "heun",
"desc": "Well temperament for organ of Jan Heun (1805), 12 out of 55-tET (1/6-comma meantone)",
"stepCount": "12",
"steps": [
"87.27273",
"196.36364",
"305.45455",
"392.72727",
"501.81818",
"589.09091",
"698.18182",
"785.45455",
"894.54545",
"1003.63636",
"1090.90909",
"2/1"
]
},
{
"id": "hexagonal_13",
"desc": "Star hexagonal 13-tone scale",
"stepCount": "13",
"steps": [
"25/24",
"16/15",
"10/9",
"6/5",
"5/4",
"4/3",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "hexagonal_37",
"desc": "Star hexagonal 37-tone scale",
"stepCount": "37",
"steps": [
"25/24",
"16/15",
"27/25",
"625/576",
"10/9",
"9/8",
"256/225",
"144/125",
"75/64",
"6/5",
"100/81",
"5/4",
"32/25",
"125/96",
"4/3",
"27/20",
"25/18",
"45/32",
"64/45",
"36/25",
"40/27",
"3/2",
"192/125",
"25/16",
"8/5",
"81/50",
"5/3",
"128/75",
"125/72",
"225/128",
"16/9",
"9/5",
"1152/625",
"50/27",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "hexany_245",
"desc": "Hexany sensamagic (245/243) 2.3.7 convex closure",
"stepCount": "10",
"steps": [
"729/686",
"54/49",
"243/196",
"9/7",
"486/343",
"3/2",
"81/49",
"12/7",
"27/14",
"2/1"
]
},
{
"id": "hexany_875",
"desc": "Hexany keema (875/864) 5-limit convex closure",
"stepCount": "7",
"steps": ["25/24", "625/576", "5/4", "625/432", "3/2", "125/72", "2/1"]
},
{
"id": "hexany_1029",
"desc": "Hexany gamelismic (1029/1024) 2.5.7 convex closure",
"stepCount": "10",
"steps": [
"2560/2401",
"8/7",
"5/4",
"64/49",
"10/7",
"512/343",
"80/49",
"4096/2401",
"640/343",
"2/1"
]
},
{
"id": "hexany_1728",
"desc": "Hexany orwellismic (1728/1715) 2.3.7 convex closure",
"stepCount": "7",
"steps": [
"2592/2401",
"432/343",
"3456/2401",
"72/49",
"3/2",
"12/7",
"2/1"
]
},
{
"id": "hexany_4375",
"desc": "Hexany ragismic (4375/4374) 5-limit convex closure",
"stepCount": "12",
"steps": [
"3125/2916",
"125/108",
"5/4",
"625/486",
"25/18",
"3125/2187",
"3/2",
"125/81",
"5/3",
"1250/729",
"50/27",
"2/1"
]
},
{
"id": "hexany_5120",
"desc": "Hexany hemifamity (5120/5103) 5-limit convex closure",
"stepCount": "10",
"steps": [
"2187/2048",
"9/8",
"5/4",
"81/64",
"729/512",
"3/2",
"27/16",
"2187/1280",
"243/128",
"2/1"
]
},
{
"id": "hexany_6144",
"desc": "Hexany porwell (6144/6125) 2.5.7 convex closure",
"stepCount": "8",
"steps": [
"4375/4096",
"5/4",
"175/128",
"10/7",
"6125/4096",
"25/16",
"875/512",
"2/1"
]
},
{
"id": "hexany_65625",
"desc": "Hexany porwell (65625/65536) 5-limit convex closure",
"stepCount": "11",
"steps": [
"140625/131072",
"9375/8192",
"75/64",
"5/4",
"46875/32768",
"375/256",
"3/2",
"28125/16384",
"1875/1024",
"15/8",
"2/1"
]
},
{
"id": "hexany_cl",
"desc": "Hexany Cluster 1",
"stepCount": "12",
"steps": [
"9/8",
"144/125",
"6/5",
"5/4",
"4/3",
"27/20",
"36/25",
"3/2",
"8/5",
"9/5",
"48/25",
"2/1"
]
},
{
"id": "hexany_cl_2",
"desc": "Composed of 1.3.5.45, 1.3.5.75, 1.3.5.9, and 1.3.5.25 hexanies",
"stepCount": "11",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"3/2",
"25/16",
"8/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "hexany_tetr",
"desc": "Complex 12 of p. 115, a hexany based on Archytas's Enharmonic",
"stepCount": "6",
"steps": ["36/35", "16/15", "9/7", "4/3", "48/35", "2/1"]
},
{
"id": "hexany_trans",
"desc": "Complex 1 of p. 115, a hexany based on Archytas's Enharmonic",
"stepCount": "6",
"steps": ["28/27", "16/15", "35/27", "4/3", "112/81", "2/1"]
},
{
"id": "hexany_trans_2",
"desc": "Complex 2 of p. 115, a hexany based on Archytas's Enharmonic",
"stepCount": "6",
"steps": ["28/27", "16/15", "4/3", "48/35", "64/45", "2/1"]
},
{
"id": "hexany_trans_3",
"desc": "Complex 9 of p. 115, a hexany based on Archytas's Enharmonic",
"stepCount": "6",
"steps": ["28/27", "16/15", "5/4", "9/7", "4/3", "2/1"]
},
{
"id": "hexany_u_2",
"desc": "Hexany union = genus [335577] minus two corners",
"stepCount": "25",
"steps": [
"21/20",
"16/15",
"15/14",
"35/32",
"8/7",
"7/6",
"6/5",
"5/4",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"8/5",
"5/3",
"12/7",
"7/4",
"64/35",
"28/15",
"15/8",
"40/21",
"2/1"
]
},
{
"id": "hexany_union",
"desc": "The union of all of the pitches of the 1.3.5.7 hexany on each tone as 1/1",
"stepCount": "19",
"steps": [
"21/20",
"15/14",
"8/7",
"7/6",
"6/5",
"5/4",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"8/5",
"5/3",
"12/7",
"7/4",
"28/15",
"40/21",
"2/1"
]
},
{
"id": "hexany_urot",
"desc": "Aggregate rotations of 1.3.5.7 hexany, 1.3 = 1/1",
"stepCount": "24",
"steps": [
"49/48",
"15/14",
"35/32",
"10/9",
"8/7",
"7/6",
"5/4",
"245/192",
"21/16",
"4/3",
"49/36",
"10/7",
"35/24",
"3/2",
"49/32",
"14/9",
"5/3",
"245/144",
"12/7",
"7/4",
"15/8",
"40/21",
"35/18",
"2/1"
]
},
{
"id": "hexany_1",
"desc": "Two out of 1 3 5 7 hexany on 1.3",
"stepCount": "6",
"steps": ["7/6", "5/4", "35/24", "5/3", "7/4", "2/1"]
},
{
"id": "hexany_2",
"desc": "Hexany Cluster 2",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"125/96",
"4/3",
"25/18",
"3/2",
"25/16",
"5/3",
"15/8",
"2"
]
},
{
"id": "hexany_3",
"desc": "Hexany Cluster 3",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"6/5",
"5/4",
"4/3",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"48/25",
"2"
]
},
{
"id": "hexany_4",
"desc": "Hexany Cluster 4",
"stepCount": "12",
"steps": [
"25/24",
"9/8",
"6/5",
"5/4",
"4/3",
"36/25",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2"
]
},
{
"id": "hexany_5",
"desc": "Hexany Cluster 5",
"stepCount": "12",
"steps": [
"9/8",
"6/5",
"5/4",
"4/3",
"3/2",
"25/16",
"8/5",
"5/3",
"9/5",
"15/8",
"48/25",
"2"
]
},
{
"id": "hexany_6",
"desc": "Hexany Cluster 6, periodicity block 125/108 and 135/128",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"9/8",
"6/5",
"5/4",
"4/3",
"3/2",
"25/16",
"8/5",
"5/3",
"15/8",
"2/1"
]
},
{
"id": "hexany_7",
"desc": "Hexany Cluster 7",
"stepCount": "12",
"steps": [
"25/24",
"6/5",
"5/4",
"4/3",
"25/18",
"3/2",
"25/16",
"8/5",
"5/3",
"9/5",
"15/8",
"2"
]
},
{
"id": "hexany_8",
"desc": "Hexany Cluster 8",
"stepCount": "12",
"steps": [
"25/24",
"6/5",
"5/4",
"125/96",
"4/3",
"3/2",
"25/16",
"8/5",
"5/3",
"15/8",
"48/25",
"2"
]
},
{
"id": "hexany_10",
"desc": "1.3.5.9 Hexany and Lou Harrison's Joyous 6. Second key is Harrison's Solemn 6 (1962)",
"stepCount": "6",
"steps": ["9/8", "5/4", "3/2", "5/3", "15/8", "2/1"]
},
{
"id": "hexany_11",
"desc": "1.3.7.9 Hexany on 1.3",
"stepCount": "6",
"steps": ["9/8", "7/6", "21/16", "3/2", "7/4", "2/1"]
},
{
"id": "hexany_12",
"desc": "3.5.7.9 Hexany on 3.9",
"stepCount": "6",
"steps": ["10/9", "7/6", "35/27", "14/9", "5/3", "2/1"]
},
{
"id": "hexany_13",
"desc": "1.3.5.11 Hexany on 1.11",
"stepCount": "6",
"steps": ["12/11", "5/4", "15/11", "3/2", "20/11", "2/1"]
},
{
"id": "hexany_14",
"desc": "5.11.13.15 Hexany (5.15), used in The Giving, by Stephen J. Taylor",
"stepCount": "6",
"steps": ["11/10", "13/10", "22/15", "26/15", "143/75", "2/1"]
},
{
"id": "hexany_15",
"desc": "1.3.5.15 2)4 hexany (1.15 tonic) degenerate, symmetrical pentatonic",
"stepCount": "5",
"steps": ["5/4", "4/3", "3/2", "8/5", "2/1"]
},
{
"id": "hexany_16",
"desc": "1.3.9.27 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["9/8", "4/3", "3/2", "16/9", "2/1"]
},
{
"id": "hexany_17",
"desc": "1.5.25.125 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["5/4", "32/25", "25/16", "8/5", "2/1"]
},
{
"id": "hexany_18",
"desc": "1.7.49.343 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["8/7", "64/49", "49/32", "7/4", "2/1"]
},
{
"id": "hexany_19",
"desc": "1.5.7.35 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["8/7", "5/4", "8/5", "7/4", "2/1"]
},
{
"id": "hexany_20",
"desc": "3.5.7.105 Hexany",
"stepCount": "6",
"steps": ["16/15", "7/6", "32/21", "5/3", "16/9", "2/1"]
},
{
"id": "hexany_21",
"desc": "3.5.9.135 Hexany",
"stepCount": "6",
"steps": ["16/15", "32/27", "3/2", "5/3", "16/9", "2/1"]
},
{
"id": "hexany_21_a",
"desc": "3.5.9.135 Hexany + 4/3. Is Didymos Diatonic tetrachord on 1/1 and inv. on 3/2",
"stepCount": "7",
"steps": ["16/15", "32/27", "4/3", "3/2", "5/3", "16/9", "2/1"]
},
{
"id": "hexany_22",
"desc": "1.11.121.1331 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["128/121", "11/8", "16/11", "121/64", "2/1"]
},
{
"id": "hexany_23",
"desc": "1.3.11.33 Hexany, degenerate pentatonic form",
"stepCount": "5",
"steps": ["4/3", "11/8", "16/11", "3/2", "2/1"]
},
{
"id": "hexany_24",
"desc": "1.5.11.55 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["5/4", "11/8", "16/11", "8/5", "2/1"]
},
{
"id": "hexany_25",
"desc": "1.7.11.77 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["8/7", "11/8", "16/11", "7/4", "2/1"]
},
{
"id": "hexany_26",
"desc": "1.9.11.99 Hexany, a degenerate pentatonic form",
"stepCount": "5",
"steps": ["9/8", "11/8", "16/11", "16/9", "2/1"]
},
{
"id": "hexany_49",
"desc": "1.3.21.49 2)4 hexany (1.21 tonic)",
"stepCount": "6",
"steps": ["8/7", "7/6", "3/2", "49/32", "7/4", "2/1"]
},
{
"id": "hexanys_valentino",
"desc": "hexanys tempered in 13-limit POTE-tuned valentino",
"stepCount": "12",
"steps": [
"155.91598",
"203.24381",
"389.78995",
"467.74794",
"593.03376",
"701.62190",
"857.53788",
"904.86571",
"966.12603",
"1091.41185",
"1169.36984",
"2/1"
]
},
{
"id": "hexanys",
"desc": "Hexanys 1 3 5 7 9",
"stepCount": "12",
"steps": [
"35/32",
"9/8",
"5/4",
"21/16",
"45/32",
"3/2",
"105/64",
"27/16",
"7/4",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "hexanys_2",
"desc": "Hexanys 1 3 7 11 13",
"stepCount": "12",
"steps": [
"77/64",
"13/8",
"7/4",
"33/32",
"91/64",
"3/2",
"231/128",
"39/32",
"11/8",
"21/16",
"143/128",
"2/1"
]
},
{
"id": "hexlesfip_22",
"desc": "15-limit, 10 cent lesfip; no consonances smaller than 12/11",
"stepCount": "22",
"steps": [
"67.41223",
"114.48561",
"180.70061",
"202.39331",
"271.28742",
"317.69466",
"383.58017",
"430.21027",
"498.97723",
"564.73749",
"586.63832",
"634.05267",
"701.39382",
"769.17317",
"816.03021",
"882.40327",
"904.36815",
"997.57100",
"1018.96163",
"1085.57540",
"1131.59971",
"2/1"
]
},
{
"id": "hexlesfip_22_seed",
"desc": "Scale square of 5-limit diamond plus {27/16, 45/32, 75/64}",
"stepCount": "22",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"25/18",
"45/32",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "hexy_miraculous",
"desc": "hexy in 13-limit POTE-tuned miraculous",
"stepCount": "12",
"steps": [
"84.21945",
"200.96668",
"266.02221",
"382.76944",
"499.51666",
"583.73612",
"700.48334",
"817.23056",
"882.28610",
"966.50555",
"1083.25278",
"2/1"
]
},
{
"id": "hexy",
"desc": "Maximized 9-limit harmony containing a hexany",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"28/15",
"2/1"
]
},
{
"id": "hexymarv",
"desc": "Marvel-tempered hexy, 197-tET",
"stepCount": "12",
"steps": [
"85.27919",
"201.01523",
"268.02030",
"383.75635",
"499.49239",
"584.77157",
"700.50761",
"816.24365",
"883.24873",
"968.52792",
"1084.26396",
"2/1"
]
},
{
"id": "hi_19_marv",
"desc": "inverted smithgw_hahn19 in 1/4 kleismic tempering",
"stepCount": "19",
"steps": [
"46.84250",
"115.58705",
"184.33159",
"8/7",
"6/5",
"384.38583",
"431.22833",
"499.97288",
"584.44007",
"615.55993",
"700.02712",
"768.77167",
"815.61417",
"5/3",
"931.20121",
"999.94576",
"1084.41295",
"40/21",
"2/1"
]
},
{
"id": "higgs",
"desc": "From Greg Higgs announcement of the formation of an Internet Tuning list",
"stepCount": "7",
"steps": ["3/2", "8/5", "21/13", "34/21", "13/8", "5/3", "2/1"]
},
{
"id": "highschool_9",
"desc": "Nine note Highschool scale, Fokker block 135/128 and 27/25",
"stepCount": "9",
"steps": ["9/8", "6/5", "5/4", "4/3", "3/2", "8/5", "5/3", "15/8", "2/1"]
},
{
"id": "highschool_1_rodan",
"desc": "12highschool1 tempered in 13-limit POTE-tuned rodan",
"stepCount": "12",
"steps": [
"82.76793",
"206.89283",
"317.25007",
"386.19634",
"496.55359",
"579.32152",
"703.44641",
"813.80366",
"882.74993",
"965.51786",
"1089.64275",
"2/1"
]
},
{
"id": "highschool_1",
"desc": "First 12-note Highschool scale",
"stepCount": "12",
"steps": [
"21/20",
"9/8",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "highschool_2_miracle",
"desc": "12highschool2 tempered in 11-limit POTE-tuned miracle",
"stepCount": "12",
"steps": [
"116.63274",
"199.59291",
"316.22566",
"383.57080",
"500.20354",
"616.83629",
"699.79646",
"816.42920",
"883.77434",
"966.73451",
"1083.36726",
"2/1"
]
},
{
"id": "highschool_2",
"desc": "Second 12-note Highschool scale",
"stepCount": "12",
"steps": [
"15/14",
"9/8",
"6/5",
"5/4",
"4/3",
"10/7",
"3/2",
"8/5",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "highschool_3",
"desc": "Third 12-note Highschool scale, inverse is fourth Highschool scale",
"stepCount": "12",
"steps": [
"16/15",
"8/7",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "hijaz_pentachord_7_limit",
"desc": "Hijaz pentachord 90:96:112:120:135",
"stepCount": "4",
"steps": ["16/15", "56/45", "4/3", "3/2"]
},
{
"id": "hijaz_pentachord_13_limit_a",
"desc": "Hijaz pentachord 12:13:15:16:18",
"stepCount": "4",
"steps": ["13/12", "5/4", "4/3", "3/2"]
},
{
"id": "hijaz_pentachord_13_limit_b",
"desc": "Hijaz pentachord 78:84:96:104:117",
"stepCount": "4",
"steps": ["14/13", "16/13", "4/3", "3/2"]
},
{
"id": "hijaz_pentachord_67_limit",
"desc": "Hijaz pentachord 54:58:67:72:81",
"stepCount": "4",
"steps": ["29/27", "67/54", "4/3", "3/2"]
},
{
"id": "hijaz_tetrachord_7_limit",
"desc": "Hijaz tetrachord 45:48:56:60",
"stepCount": "3",
"steps": ["16/15", "56/45", "4/3"]
},
{
"id": "hijaz_tetrachord_11_limit",
"desc": "Hijaz tetrachord 33:36:42:44",
"stepCount": "3",
"steps": ["12/11", "14/11", "4/3"]
},
{
"id": "hijaz_tetrachord_13_limit_a",
"desc": "Hijaz tetrachord 12:13:15:16",
"stepCount": "3",
"steps": ["13/12", "5/4", "4/3"]
},
{
"id": "hijaz_tetrachord_13_limit_b",
"desc": "Hijaz tetrachord 39:42:48:52",
"stepCount": "3",
"steps": ["14/13", "16/13", "4/3"]
},
{
"id": "hijaz_tetrachord_67_limit",
"desc": "Hijaz tetrachord 54:58:67:72",
"stepCount": "3",
"steps": ["29/27", "67/54", "4/3"]
},
{
"id": "hilim_13",
"desc": "13 patent val epimorphic 2.11.13.17.19 scale",
"stepCount": "13",
"steps": [
"17/16",
"19/17",
"13/11",
"16/13",
"17/13",
"11/8",
"16/11",
"17/11",
"13/8",
"22/13",
"34/19",
"32/17",
"2/1"
]
},
{
"id": "hinsz_gr",
"desc": "Reconstructed Hinsz temperament, organ Pelstergasthuiskerk Groningen. Ortgies,2002",
"stepCount": "12",
"steps": [
"84.35999",
"192.18000",
"32/27",
"8192/6561",
"4/3",
"582.40499",
"696.09000",
"786.31499",
"888.26999",
"16/9",
"4096/2187",
"2/1"
]
},
{
"id": "hipkins",
"desc": "Hipkins' Chromatic",
"stepCount": "7",
"steps": ["256/243", "8/7", "4/3", "3/2", "128/81", "12/7", "2/1"]
},
{
"id": "hirajoshi",
"desc": "Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.112",
"stepCount": "5",
"steps": ["185.00000", "337.00000", "683.00000", "790.00000", "2/1"]
},
{
"id": "hirajoshi_2",
"desc": "Japanese pentatonic koto scale, theoretical. Helmholz/Ellis p.519, nr.110",
"stepCount": "5",
"steps": ["9/8", "6/5", "3/2", "8/5", "2/1"]
},
{
"id": "hirajoshi_3",
"desc": "Observed Japanese pentatonic koto scale. Helmholtz/Ellis p.519, nr.111",
"stepCount": "5",
"steps": ["193.00000", "357.00000", "719.00000", "801.00000", "1199.00000"]
},
{
"id": "hirashima",
"desc": "Tatsushi Hirashima, temperament of chapel organ of Kobe Shoin Women's Univ.",
"stepCount": "12",
"steps": [
"100.97814",
"193.15686",
"304.88814",
"5/4",
"503.42157",
"599.02314",
"696.57843",
"802.93314",
"889.73528",
"1006.84314",
"1082.89214",
"2/1"
]
},
{
"id": "hjelmstad_blues",
"desc": "Paul Hjelmstad's \"blues\"scale, TL 27-05-2005",
"stepCount": "6",
"steps": ["7/6", "4/3", "49/36", "3/2", "7/4", "2/1"]
},
{
"id": "hjelmstad_boogie",
"desc": "Paul Hjelmstad's \"Boogie Woogie\"scale, TL 20-3-2006",
"stepCount": "10",
"steps": [
"9/8",
"5/4",
"21/16",
"45/32",
"3/2",
"27/16",
"7/4",
"15/8",
"63/32",
"2/1"
]
},
{
"id": "hjelmstad_conv",
"desc": "Convex closure in breed plane of hjelmboogie.scl",
"stepCount": "10",
"steps": [
"7/6",
"49/40",
"4/3",
"49/36",
"10/7",
"3/2",
"49/30",
"7/4",
"40/21",
"2/1"
]
},
{
"id": "ho_mai_nhi",
"desc": "Ho Mai Nhi (Nam Hue) dan tranh scale, Vietnam",
"stepCount": "5",
"steps": ["11/10", "4/3", "3/2", "33/20", "2/1"]
},
{
"id": "hochgartz",
"desc": "Michael Hochgartz, modified 1/5-comma meantone temperament",
"stepCount": "12",
"steps": [
"83.57620",
"195.30749",
"292.96123",
"390.61497",
"502.34626",
"585.92246",
"697.65374",
"788.26871",
"892.96123",
"997.65374",
"15/8",
"2/1"
]
},
{
"id": "hofmann_chrom",
"desc": "Hofmann's Chromatic",
"stepCount": "7",
"steps": ["100/99", "10/9", "4/3", "3/2", "50/33", "5/3", "2/1"]
},
{
"id": "hofmann_1",
"desc": "Hofmann's Enharmonic #1, Dorian mode",
"stepCount": "7",
"steps": ["256/255", "16/15", "4/3", "3/2", "128/85", "8/5", "2/1"]
},
{
"id": "hofmann_2",
"desc": "Hofmann's Enharmonic #2, Dorian mode",
"stepCount": "7",
"steps": ["136/135", "16/15", "4/3", "3/2", "68/45", "8/5", "2/1"]
},
{
"id": "holder",
"desc": "William Holder's equal beating meantone temperament (1694). 3/2 beats 2.8 Hz",
"stepCount": "12",
"steps": [
"81.47300",
"193.58600",
"307.40100",
"388.26700",
"502.67100",
"583.93200",
"695.76800",
"777.52600",
"890.00900",
"1004.17700",
"1085.27900",
"2/1"
]
},
{
"id": "holder_2",
"desc": "Holder's irregular e.b. temperament with improved Eb and G#",
"stepCount": "12",
"steps": [
"81.473 cents",
"193.586 cents",
"307.401 cents",
"388.267 cents",
"502.671 cents",
"583.932 cents",
"695.768 cents",
"780.479 cents",
"890.009 cents",
"1004.813 cents",
"1085.279 cents",
"2/1"
]
},
{
"id": "honkyoku",
"desc": "Honkyoku tuning for shakuhachi",
"stepCount": "9",
"steps": [
"75.00000",
"400.00000",
"500.00000",
"575.00000",
"700.00000",
"775.00000",
"1000.00000",
"1075.00000",
"2/1"
]
},
{
"id": "horwell_22",
"desc": "Horwell[22] hobbit in 995-tET tuning",
"stepCount": "22",
"steps": [
"42.21106",
"112.16080",
"154.37186",
"231.55779",
"273.76884",
"343.71859",
"385.92965",
"428.14070",
"498.09045",
"540.30151",
"610.25126",
"659.69849",
"701.90955",
"771.85930",
"814.07035",
"884.02010",
"926.23116",
"975.67839",
"1045.62814",
"1087.83920",
"1157.78894",
"2/1"
]
},
{
"id": "hppshq",
"desc": "Hedgehog-pajarous-pajara-suprapyth-hedgepig-quasisoup superwakalix",
"stepCount": "22",
"steps": [
"56/55",
"15/14",
"10/9",
"9/8",
"7/6",
"60/49",
"5/4",
"9/7",
"4/3",
"135/98",
"10/7",
"16/11",
"3/2",
"14/9",
"45/28",
"5/3",
"12/7",
"7/4",
"90/49",
"40/21",
"27/14",
"2/1"
]
},
{
"id": "hulen_33",
"desc": "Peter Hulen's ratiotonic temperament, E = 1/1",
"stepCount": "33",
"steps": [
"65/64",
"33/32",
"135/128",
"35/32",
"143/128",
"9/8",
"75/64",
"77/64",
"39/32",
"5/4",
"81/64",
"165/128",
"21/16",
"169/128",
"11/8",
"45/32",
"91/64",
"3/2",
"195/128",
"49/32",
"99/64",
"25/16",
"13/8",
"105/64",
"27/16",
"55/32",
"7/4",
"225/128",
"117/64",
"15/8",
"121/64",
"63/32",
"2/1"
]
},
{
"id": "hummel",
"desc": "Johann Nepomuk Hummel's quasi-equal temperament (1829)",
"stepCount": "12",
"steps": [
"99.92334",
"199.30420",
"299.48618",
"399.10984",
"499.52284",
"599.36333",
"699.98259",
"800.01661",
"899.50138",
"999.78224",
"1099.49871",
"2/1"
]
},
{
"id": "hummel_2",
"desc": "Johann Nepomuk Hummel's temperament according to the second bearing plan, also John Marsh's quasi-equal temperament (1840)",
"stepCount": "12",
"steps": [
"100.28085",
"199.99733",
"300.49862",
"400.42196",
"499.80282",
"599.98479",
"699.60846",
"800.02146",
"899.86195",
"1000.48121",
"1100.51523",
"2/1"
]
},
{
"id": "huntington_7",
"desc": "Huntington[7] 2.5.7.13 subgroup scale in 400-tET tuning",
"stepCount": "7",
"steps": [
"129.00000",
"357.00000",
"486.00000",
"615.00000",
"843.00000",
"972.00000",
"2/1"
]
},
{
"id": "huntington_10",
"desc": "Huntington[10] 2.5.7.13 subgroup scale in 400-tET tuning",
"stepCount": "10",
"steps": [
"129.00000",
"258.00000",
"387.00000",
"486.00000",
"615.00000",
"744.00000",
"843.00000",
"972.00000",
"1101.00000",
"2/1"
]
},
{
"id": "huseyni_pentachord_13_limit",
"desc": "Huseyni pentachord 66:72:78:88:99",
"stepCount": "4",
"steps": ["12/11", "13/11", "4/3", "3/2"]
},
{
"id": "huseyni_pentachord_19_limit",
"desc": "Huseyni pentachord 96:105:114:128:144",
"stepCount": "4",
"steps": ["35/32", "19/16", "4/3", "3/2"]
},
{
"id": "huseyni_pentachord_23_limit",
"desc": "Huseyni pentachord 42:46:50:56:63",
"stepCount": "4",
"steps": ["23/21", "25/21", "4/3", "3/2"]
},
{
"id": "huseyni_pentachord_71_limit",
"desc": "Huseyni pentachord 60:66:71:80:90",
"stepCount": "4",
"steps": ["11/10", "71/60", "4/3", "3/2"]
},
{
"id": "husmann",
"desc": "Tetrachord division according to Husmann",
"stepCount": "6",
"steps": ["256/243", "9/8", "32/27", "19683/16384", "81/64", "4/3"]
},
{
"id": "huzzam_pentachord_61_limit",
"desc": "Huzzam pentachord 114:122:138:150:171",
"stepCount": "4",
"steps": ["61/57", "23/19", "25/19", "3/2"]
},
{
"id": "huzzam_pentachord_79_limit",
"desc": "Huzzam pentachord 60:64:72:79:90",
"stepCount": "4",
"steps": ["16/15", "6/5", "79/60", "3/2"]
},
{
"id": "huzzam",
"desc": "Arab Huzzam on C, Julien J. Weiss",
"stepCount": "7",
"steps": ["9/8", "16/13", "4/3", "3/2", "8/5", "15/8", "2/1"]
},
{
"id": "hyper_enh",
"desc": "13/10 HyperEnharmonic. This genus is at the limit of usable tunings",
"stepCount": "7",
"steps": ["80/79", "40/39", "4/3", "3/2", "120/79", "20/13", "2/1"]
},
{
"id": "hyper_enh_2",
"desc": "Hyperenharmonic genus from Kathleen Schlesinger's enharmonic Phrygian Harmonia",
"stepCount": "7",
"steps": ["48/47", "24/23", "4/3", "3/2", "72/47", "36/23", "2/1"]
},
{
"id": "hypo_chrom",
"desc": "Hypolydian Chromatic Tonos",
"stepCount": "12",
"steps": [
"20/19",
"40/37",
"10/9",
"4/3",
"10/7",
"40/27",
"20/13",
"8/5",
"80/49",
"5/3",
"40/23",
"2/1"
]
},
{
"id": "hypo_diat",
"desc": "Hypolydian Diatonic Tonos",
"stepCount": "12",
"steps": [
"10/9",
"20/17",
"5/4",
"4/3",
"10/7",
"40/27",
"20/13",
"5/3",
"40/23",
"20/11",
"40/21",
"2/1"
]
},
{
"id": "hypo_enh",
"desc": "Hypolydian Enharmonic Tonos",
"stepCount": "12",
"steps": [
"40/39",
"80/77",
"20/19",
"4/3",
"10/7",
"40/27",
"20/13",
"80/51",
"160/101",
"8/5",
"16/9",
"2/1"
]
},
{
"id": "hypod_chrom",
"desc": "Hypodorian Chromatic Tonos",
"stepCount": "12",
"steps": [
"16/15",
"32/29",
"8/7",
"16/13",
"4/3",
"32/23",
"16/11",
"32/21",
"64/41",
"8/5",
"16/9",
"2/1"
]
},
{
"id": "hypod_chrom_2",
"desc": "Schlesinger's Chromatic Hypodorian Harmonia",
"stepCount": "7",
"steps": ["16/15", "8/7", "4/3", "16/11", "32/21", "8/5", "2/1"]
},
{
"id": "hypod_chrom_2_inv",
"desc": "Inverted Schlesinger's Chromatic Hypodorian Harmonia",
"stepCount": "7",
"steps": ["5/4", "21/16", "11/8", "3/2", "7/4", "15/8", "2/1"]
},
{
"id": "hypod_chromenh",
"desc": "Schlesinger's Hypodorian Harmonia in a mixed chromatic-enharmonic genus",
"stepCount": "7",
"steps": ["32/31", "16/15", "4/3", "16/11", "32/21", "8/5", "2/1"]
},
{
"id": "hypod_chrominv",
"desc": "A harmonic form of Kathleen Schlesinger's Chromatic Hypodorian Inverted",
"stepCount": "7",
"steps": ["17/16", "9/8", "11/8", "3/2", "25/16", "13/8", "2/1"]
},
{
"id": "hypod_diat",
"desc": "Hypodorian Diatonic Tonos",
"stepCount": "12",
"steps": [
"16/15",
"8/7",
"16/13",
"32/25",
"4/3",
"32/23",
"16/11",
"8/5",
"32/19",
"16/9",
"32/17",
"2/1"
]
},
{
"id": "hypod_diat_2",
"desc": "Schlesinger's Hypodorian Harmonia, a subharmonic series through 13 from 16",
"stepCount": "8",
"steps": ["16/15", "16/13", "4/3", "32/23", "16/11", "8/5", "16/9", "2/1"]
},
{
"id": "hypod_diatcon",
"desc": "A Hypodorian Diatonic with its own trite synemmenon replacing paramese",
"stepCount": "7",
"steps": ["16/15", "16/13", "4/3", "32/23", "8/5", "16/9", "2/1"]
},
{
"id": "hypod_diatinv",
"desc": "Inverted Schlesinger's Hypodorian Harmonia, a harmonic series from 8 from 16",
"stepCount": "9",
"steps": [
"9/8",
"5/4",
"11/8",
"23/16",
"3/2",
"13/8",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "hypod_enh",
"desc": "Hypodorian Enharmonic Tonos",
"stepCount": "12",
"steps": [
"32/31",
"64/61",
"16/15",
"32/27",
"4/3",
"32/23",
"16/11",
"64/43",
"128/85",
"32/21",
"64/37",
"2/1"
]
},
{
"id": "hypod_enhinv",
"desc": "Inverted Schlesinger's Enharmonic Hypodorian Harmonia",
"stepCount": "7",
"steps": ["21/16", "43/32", "11/8", "3/2", "15/8", "31/16", "2/1"]
},
{
"id": "hypod_enhinv_2",
"desc": "A harmonic form of Schlesinger's Hypodorian enharmonic inverted",
"stepCount": "7",
"steps": ["33/32", "17/16", "11/8", "3/2", "49/32", "25/16", "2/1"]
},
{
"id": "hypodorian_pis",
"desc": "Diatonic Perfect Immutable System in the Hypodorian Tonos",
"stepCount": "15",
"steps": [
"12/11",
"6/5",
"4/3",
"3/2",
"8/5",
"24/13",
"2/1",
"48/23",
"24/11",
"12/5",
"8/3",
"3/1",
"24/7",
"48/13",
"4/1"
]
},
{
"id": "hypol_chrom",
"desc": "Schlesinger's Hypolydian Harmonia in the chromatic genus",
"stepCount": "8",
"steps": ["20/19", "10/9", "4/3", "10/7", "20/13", "8/5", "5/3", "2/1"]
},
{
"id": "hypol_chrominv",
"desc": "Inverted Schlesinger's Chromatic Hypolydian Harmonia",
"stepCount": "8",
"steps": ["6/5", "5/4", "13/10", "7/5", "3/2", "9/5", "19/10", "2/1"]
},
{
"id": "hypol_chrominv_2",
"desc": "harmonic form of Schlesinger's Chromatic Hypolydian inverted",
"stepCount": "7",
"steps": ["21/20", "11/10", "13/10", "7/5", "3/2", "8/5", "2/1"]
},
{
"id": "hypol_chrominv_3",
"desc": "A harmonic form of Schlesinger's Chromatic Hypolydian inverted",
"stepCount": "7",
"steps": ["21/20", "11/10", "13/10", "3/2", "8/5", "17/10", "2/1"]
},
{
"id": "hypol_diat",
"desc": "Schlesinger's Hypolydian Harmonia, a subharmonic series through 13 from 20",
"stepCount": "8",
"steps": ["10/9", "5/4", "4/3", "10/7", "20/13", "5/3", "20/11", "2/1"]
},
{
"id": "hypol_diatcon",
"desc": "A Hypolydian Diatonic with its own trite synemmenon replacing paramese",
"stepCount": "7",
"steps": ["10/9", "5/4", "4/3", "20/13", "5/3", "20/11", "2/1"]
},
{
"id": "hypol_diatinv",
"desc": "Inverted Schlesinger's Hypolydian Harmonia, a harmonic series from 10 from 20",
"stepCount": "8",
"steps": ["11/10", "6/5", "13/10", "7/5", "3/2", "8/5", "9/5", "2/1"]
},
{
"id": "hypol_enh",
"desc": "Schlesinger's Hypolydian Harmonia in the enharmonic genus",
"stepCount": "8",
"steps": ["40/39", "20/19", "4/3", "10/7", "20/13", "8/5", "5/3", "2/1"]
},
{
"id": "hypol_enhinv",
"desc": "Inverted Schlesinger's Enharmonic Hypolydian Harmonia",
"stepCount": "8",
"steps": ["5/4", "51/40", "13/10", "7/5", "3/2", "19/10", "39/20", "2/1"]
},
{
"id": "hypol_enhinv_2",
"desc": "A harmonic form of Schlesinger's Hypolydian enharmonic inverted",
"stepCount": "7",
"steps": ["41/40", "21/20", "13/10", "7/5", "29/20", "3/2", "2/1"]
},
{
"id": "hypol_enhinv_3",
"desc": "A harmonic form of Schlesinger's Hypolydian enharmonic inverted",
"stepCount": "7",
"steps": ["41/40", "21/20", "13/10", "3/2", "31/20", "8/5", "2/1"]
},
{
"id": "hypol_pent",
"desc": "Schlesinger's Hypolydian Harmonia in the pentachromatic genus",
"stepCount": "8",
"steps": ["25/24", "10/9", "4/3", "10/7", "20/13", "100/63", "5/3", "2/1"]
},
{
"id": "hypol_tri",
"desc": "Schlesinger's Hypolydian Harmonia in the first trichromatic genus",
"stepCount": "8",
"steps": ["30/29", "15/14", "4/3", "10/7", "20/13", "30/19", "60/37", "2/1"]
},
{
"id": "hypol_tri_2",
"desc": "Schlesinger's Hypolydian Harmonia in the second trichromatic genus",
"stepCount": "8",
"steps": ["30/29", "10/9", "4/3", "10/7", "20/13", "30/19", "5/3", "8/1"]
},
{
"id": "hypolydian_pis",
"desc": "The Diatonic Perfect Immutable System in the Hypolydian Tonos",
"stepCount": "15",
"steps": [
"14/13",
"7/6",
"14/11",
"7/5",
"14/9",
"7/4",
"28/15",
"2/1",
"28/13",
"7/3",
"28/11",
"14/5",
"28/9",
"7/2",
"4/1"
]
},
{
"id": "hypop_chrom",
"desc": "Hypophrygian Chromatic Tonos",
"stepCount": "12",
"steps": [
"18/17",
"12/11",
"9/8",
"9/7",
"18/13",
"36/25",
"3/2",
"36/23",
"8/5",
"18/11",
"9/5",
"2/1"
]
},
{
"id": "hypop_chromenh",
"desc": "Schlesinger's Hypophrygian Harmonia in a mixed chromatic-enharmonic genus",
"stepCount": "7",
"steps": ["36/35", "18/17", "18/13", "3/2", "36/23", "18/11", "2/1"]
},
{
"id": "hypop_chrominv",
"desc": "Inverted Schlesinger's Chromatic Hypophrygian Harmonia",
"stepCount": "7",
"steps": ["11/9", "23/18", "4/3", "13/9", "16/9", "17/9", "2/1"]
},
{
"id": "hypop_chrominv_2",
"desc": "A harmonic form of Schlesinger's Chromatic Hypophrygian inverted",
"stepCount": "7",
"steps": ["19/18", "10/9", "4/3", "13/9", "14/9", "5/3", "2/1"]
},
{
"id": "hypop_diat",
"desc": "Hypophrygian Diatonic Tonos",
"stepCount": "12",
"steps": [
"9/8",
"36/31",
"6/5",
"9/7",
"18/13",
"36/25",
"3/2",
"18/11",
"12/7",
"9/5",
"36/19",
"2/1"
]
},
{
"id": "hypop_diat_2",
"desc": "Schlesinger's Hypophrygian Harmonia",
"stepCount": "8",
"steps": ["9/8", "6/5", "18/13", "36/25", "3/2", "18/11", "9/5", "2/1"]
},
{
"id": "hypop_diat_2_inv",
"desc": "Inverted Schlesinger's Hypophrygian Harmonia, a harmonic series from 9 from 18",
"stepCount": "8",
"steps": ["10/9", "11/9", "4/3", "25/18", "13/9", "5/3", "16/9", "2/1"]
},
{
"id": "hypop_diatcon",
"desc": "A Hypophrygian Diatonic with its own trite synemmenon replacing paramese",
"stepCount": "7",
"steps": ["9/8", "6/5", "18/13", "36/25", "18/11", "9/5", "2/1"]
},
{
"id": "hypop_enh",
"desc": "Hypophrygian Enharmonic Tonos",
"stepCount": "12",
"steps": [
"36/35",
"24/23",
"18/17",
"6/5",
"18/13",
"36/25",
"3/2",
"72/47",
"48/31",
"36/23",
"9/5",
"2/1"
]
},
{
"id": "hypop_enhinv",
"desc": "Inverted Schlesinger's Enharmonic Hypophrygian Harmonia",
"stepCount": "7",
"steps": ["23/18", "47/36", "4/3", "13/9", "17/9", "35/18", "2/1"]
},
{
"id": "hypop_enhinv_2",
"desc": "A harmonic form of Schlesinger's Hypophrygian enharmonic inverted",
"stepCount": "7",
"steps": ["37/36", "19/18", "4/3", "13/9", "3/2", "14/9", "2/1"]
},
{
"id": "hypophryg_pis",
"desc": "The Diatonic Perfect Immutable System in the Hypophrygian Tonos",
"stepCount": "15",
"steps": [
"13/12",
"13/11",
"13/10",
"13/9",
"13/8",
"26/15",
"2/1",
"52/25",
"13/6",
"26/11",
"13/5",
"26/9",
"13/4",
"26/7",
"4/1"
]
},
{
"id": "iivv_17",
"desc": "17-limit IIVV",
"stepCount": "21",
"steps": [
"33/32",
"17/16",
"13/12",
"9/8",
"7/6",
"39/32",
"5/4",
"21/16",
"4/3",
"11/8",
"45/32",
"17/12",
"3/2",
"51/32",
"13/8",
"5/3",
"27/16",
"7/4",
"11/6",
"15/8",
"2/1"
]
},
{
"id": "ikosany",
"desc": "Convex closure of Eikosany in 385/384-tempering, 140-tET tuning",
"stepCount": "31",
"steps": [
"51.428571",
"60.000000",
"77.142857",
"111.428571",
"137.142857",
"257.142857",
"265.714286",
"291.428571",
"317.142857",
"342.857143",
"368.571429",
"377.142857",
"462.857143",
"497.142857",
"522.857143",
"557.142857",
"574.285714",
"582.857143",
"634.285714",
"702.857143",
"754.285714",
"762.857143",
"814.285714",
"840.000000",
"874.285714",
"960.000000",
"994.285714",
"1020.000000",
"1071.428571",
"1080.000000",
"2/1"
]
},
{
"id": "ikosany_7",
"desc": "Seven-limit tuning of ikosany.scl",
"stepCount": "31",
"steps": [
"36/35",
"28/27",
"729/700",
"16/15",
"27/25",
"81/70",
"7/6",
"32/27",
"6/5",
"243/200",
"216/175",
"56/45",
"729/560",
"4/3",
"27/20",
"112/81",
"243/175",
"7/5",
"36/25",
"3/2",
"54/35",
"14/9",
"8/5",
"81/50",
"224/135",
"243/140",
"16/9",
"9/5",
"324/175",
"28/15",
"2/1"
]
},
{
"id": "indian_12",
"desc": "North Indian Gamut, modern Hindustani gamut out of 22 or more shrutis",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"45/32",
"3/2",
"8/5",
"27/16",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "indian_12_c",
"desc": "Carnatic gamut. Kuppuswami: Carnatic music and the Tamils, p. v",
"stepCount": "12",
"steps": [
"18/17",
"9/8",
"6/5",
"54/43",
"4/3",
"24/17",
"3/2",
"27/17",
"27/16",
"9/5",
"81/43",
"2/1"
]
},
{
"id": "indian_a",
"desc": "One observed indian mode",
"stepCount": "7",
"steps": [
"183.00000",
"342.00000",
"533.00000",
"685.00000",
"871.00000",
"1074.00000",
"2/1"
]
},
{
"id": "indian_b",
"desc": "Observed Indian mode",
"stepCount": "7",
"steps": [
"183.00000",
"271.00000",
"534.00000",
"686.00000",
"872.00000",
"983.00000",
"2/1"
]
},
{
"id": "indian_c",
"desc": "Observed Indian mode",
"stepCount": "7",
"steps": [
"111.00000",
"314.00000",
"534.00000",
"686.00000",
"828.00000",
"1017.00000",
"2/1"
]
},
{
"id": "indian_d",
"desc": "Indian D (Ellis, correct)",
"stepCount": "7",
"steps": [
"174.00000",
"350.00000",
"477.00000",
"697.00000",
"908.00000",
"1070.00000",
"2/1"
]
},
{
"id": "indian_e",
"desc": "Observed Indian mode",
"stepCount": "7",
"steps": [
"90.00000",
"366.00000",
"493.00000",
"707.00000",
"781.00000",
"1080.00000",
"2/1"
]
},
{
"id": "indian_g",
"desc": "Shruti/Mathieu's Magic Mode scale in 94-tET (Schismic, Garibaldi) temperament",
"stepCount": "22",
"steps": [
"89.36170",
"114.89362",
"178.72340",
"204.25532",
"293.61702",
"319.14894",
"382.97872",
"408.51064",
"497.87234",
"523.40426",
"587.23404",
"612.76596",
"702.12766",
"791.48936",
"817.02128",
"880.85106",
"906.38298",
"995.74468",
"1021.27660",
"1085.10638",
"1110.63830",
"2/1"
]
},
{
"id": "indian_rat",
"desc": "Indian Raga, From Fortuna, after Helmholtz, ratios by JC",
"stepCount": "22",
"steps": [
"34/33",
"35/33",
"12/11",
"9/8",
"22/19",
"35/29",
"5/4",
"40/31",
"4/3",
"11/8",
"17/12",
"16/11",
"3/2",
"17/11",
"35/22",
"59/36",
"27/16",
"7/4",
"38/21",
"15/8",
"60/31",
"2/1"
]
},
{
"id": "indian_rot",
"desc": "Rotated North Indian Gamut",
"stepCount": "12",
"steps": [
"25/24",
"16/15",
"75/64",
"5/4",
"4/3",
"3/2",
"25/16",
"8/5",
"5/3",
"15/8",
"125/64",
"2/1"
]
},
{
"id": "indian_ayyar",
"desc": "Carnatic sruti system, C.Subrahmanya Ayyar, 1976. alt:21/20 25/16 63/40 40/21",
"stepCount": "22",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"27/16",
"7/4",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "indian_dk",
"desc": "Raga Darbari Kanada",
"stepCount": "9",
"steps": ["9/8", "7/6", "6/5", "4/3", "3/2", "14/9", "8/5", "16/9", "2/1"]
},
{
"id": "indian_ellis",
"desc": "Ellis's Indian Chromatic, theoretical #74 of App.XX, p.517 of Helmholtz",
"stepCount": "22",
"steps": [
"36/35",
"18/17",
"12/11",
"9/8",
"36/31",
"6/5",
"36/29",
"9/7",
"4/3",
"26/19",
"52/37",
"13/9",
"52/35",
"26/17",
"52/33",
"13/8",
"52/31",
"26/15",
"52/29",
"13/7",
"52/27",
"2/1"
]
},
{
"id": "indian_hahn",
"desc": "Indian shrutis Paul Hahn proposal",
"stepCount": "22",
"steps": [
"25/24",
"16/15",
"10/9",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"4/3",
"27/20",
"45/32",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "indian_hrdaya_1",
"desc": "From Hrdayakautaka of Hrdaya Narayana (17th c) Bhatkande's interpretation",
"stepCount": "12",
"steps": [
"27/25",
"9/8",
"6/5",
"54/43",
"4/3",
"162/113",
"3/2",
"18/11",
"27/16",
"9/5",
"81/43",
"2/1"
]
},
{
"id": "indian_hrdaya_2",
"desc": "From Hrdayakautaka of Hrdaya Narayana (17th c) Levy's interpretation",
"stepCount": "12",
"steps": [
"27/25",
"9/8",
"6/5",
"24/19",
"4/3",
"36/25",
"3/2",
"18/11",
"12/7",
"9/5",
"36/19",
"2/1"
]
},
{
"id": "indian_invrot",
"desc": "Inverted and rotated North Indian gamut",
"stepCount": "12",
"steps": [
"128/125",
"16/15",
"6/5",
"5/4",
"32/25",
"4/3",
"3/2",
"8/5",
"128/75",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "indian_magrama",
"desc": "Indian mode Ma-grama (Sa Ri Ga Ma Pa Dha Ni Sa)",
"stepCount": "7",
"steps": ["9/8", "5/4", "45/32", "3/2", "27/16", "15/8", "2/1"]
},
{
"id": "indian_mystical_22",
"desc": "Srinivasan Nambirajan, 11-limit shruti scale",
"stepCount": "23",
"steps": [
"12/11",
"11/10",
"10/9",
"9/8",
"8/7",
"7/6",
"6/5",
"11/9",
"5/4",
"9/7",
"4/3",
"11/8",
"7/5",
"10/7",
"3/2",
"11/7",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "indian_newbengali",
"desc": "Modern Bengali scale,S.M. Tagore: The mus. scales of the Hindus,Calcutta 1884",
"stepCount": "22",
"steps": [
"49.00000",
"99.00000",
"151.00000",
"9/8",
"259.00000",
"6/5",
"374.00000",
"435.00000",
"4/3",
"543.00000",
"45/32",
"637.00000",
"685.00000",
"736.00000",
"787.00000",
"841.00000",
"896.00000",
"952.00000",
"1011.00000",
"1070.00000",
"1135.00000",
"2/1"
]
},
{
"id": "indian_old_2_ellis",
"desc": "Ellis Old Indian Chrom2, Helmholtz, p. 517. This is a 4 cent appr. to #73",
"stepCount": "22",
"steps": [
"32/31",
"17/16",
"12/11",
"9/8",
"7/6",
"29/24",
"5/4",
"31/24",
"4/3",
"11/8",
"17/12",
"16/11",
"3/2",
"17/11",
"27/17",
"18/11",
"27/16",
"7/4",
"29/16",
"15/8",
"29/15",
"2/1"
]
},
{
"id": "indian_oldellis",
"desc": "Ellis Old Indian Chromatic, Helmholtz, p. 517. This is a 0.5 cent appr. to #73",
"stepCount": "22",
"steps": [
"51.00000",
"35/33",
"153.00000",
"9/8",
"264.66700",
"325.33300",
"5/4",
"442.00000",
"4/3",
"549.00000",
"600.00000",
"651.00000",
"3/2",
"753.00000",
"35/22",
"855.00000",
"27/16",
"966.66700",
"1027.33300",
"15/8",
"1144.00000",
"2/1"
]
},
{
"id": "indian_raja",
"desc": "A folk scale from Rajasthan, India",
"stepCount": "6",
"steps": ["9/8", "5/4", "4/3", "3/2", "15/8", "2/1"]
},
{
"id": "indian_sagrama",
"desc": "Indian mode Sa-grama (Sa Ri Ga Ma Pa Dha Ni Sa), inverse of Didymus' diatonic",
"stepCount": "7",
"steps": ["9/8", "5/4", "4/3", "3/2", "27/16", "15/8", "2/1"]
},
{
"id": "indian_sarana",
"desc": "26 saranas (shrutis) by Acharekar and Acharya Brihaspati, 1/1=240 or 270 Hz",
"stepCount": "26",
"steps": [
"25/24",
"256/243",
"16/15",
"800/729",
"10/9",
"2560/2187",
"32/27",
"6/5",
"5/4",
"320/243",
"4/3",
"27/20",
"45/32",
"40/27",
"3/2",
"25/16",
"128/81",
"8/5",
"400/243",
"5/3",
"1280/729",
"16/9",
"9/5",
"15/8",
"160/81",
"2/1"
]
},
{
"id": "indian_sarana_2",
"desc": "26 saranas by Vidhyadhar Oak, 1/1=240 Hz",
"stepCount": "26",
"steps": [
"256/243",
"16/15",
"10/9",
"9/8",
"2560/2187",
"32/27",
"100/81",
"5/4",
"81/64",
"320/243",
"4/3",
"45/32",
"64/45",
"40/27",
"3/2",
"128/81",
"8/5",
"5/3",
"27/16",
"1280/729",
"16/9",
"50/27",
"15/8",
"243/128",
"160/81",
"2/1"
]
},
{
"id": "indian_srutiharm",
"desc": "B. Chaitanya Deva's sruti harmonium and S. Ramanathan's sruti vina, 1973. B.C. Deva, The Music of India, 1981, p. 109-110",
"stepCount": "22",
"steps": [
"86.57974",
"110.54184",
"191.88995",
"203.20525",
"296.51143",
"312.46762",
"390.11445",
"415.24165",
"512.25493",
"526.34918",
"599.63988",
"621.92119",
"708.28493",
"798.55929",
"826.32309",
"891.95186",
"907.03896",
"1005.57624",
"1026.73211",
"1098.80578",
"1118.85891",
"2/1"
]
},
{
"id": "indian_srutivina",
"desc": "Raja S.M. Tagore's sruti vina, measured by Ellis and Hipkins, 1886. 1/1=241.2",
"stepCount": "22",
"steps": [
"45.338 cents",
"111.193 cents",
"169.436 cents",
"222.630 cents",
"267.486 cents",
"316.000 cents",
"389.182 cents",
"436.121 cents",
"505.565 cents",
"544.256 cents",
"583.127 cents",
"640.588 cents",
"712.450 cents",
"749.156 cents",
"806.854 cents",
"855.262 cents",
"916.783 cents",
"953.997 cents",
"1012.565 cents",
"1076.939 cents",
"1136.401 cents",
"1219.981 cents"
]
},
{
"id": "indian_vina",
"desc": "Observed South Indian tuning of a vina, Ellis",
"stepCount": "12",
"steps": [
"97.00000",
"195.00000",
"312.00000",
"397.00000",
"515.00000",
"596.00000",
"692.00000",
"782.00000",
"883.00000",
"997.00000",
"1092.00000",
"1207.00000"
]
},
{
"id": "indian_vina_2",
"desc": "Observed tuning of old vina in Tanjore Palace, Ellis and Hipkins. 1/1=210.7 Hz",
"stepCount": "24",
"steps": [
"99.00000",
"195.00000",
"288.00000",
"382.00000",
"478.00000",
"571.00000",
"675.00000",
"774.00000",
"869.00000",
"959.00000",
"1054.00000",
"1148.00000",
"1254.00000",
"1353.00000",
"1444.00000",
"1543.00000",
"1650.00000",
"1741.00000",
"1838.00000",
"1934.00000",
"2032.00000",
"2121.00000",
"2220.00000",
"2324.00000"
]
},
{
"id": "indian_vina_3",
"desc": "Tuning of K.S. Subramanian's vina (1983)",
"stepCount": "12",
"steps": [
"256/243",
"9/8",
"32/27",
"5/4",
"4/3",
"45/32",
"3/2",
"128/81",
"27/16",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "indian",
"desc": "Indian shruti scale",
"stepCount": "22",
"steps": [
"256/243",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"81/64",
"4/3",
"27/20",
"45/32",
"729/512",
"3/2",
"128/81",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"243/128",
"2/1"
]
},
{
"id": "indian_2_sm",
"desc": "Shruti/Mathieu's Magic Mode scale in 289-equal (schismic) temperament",
"stepCount": "22",
"steps": [
"91.34948",
"112.11073",
"182.69896",
"203.46021",
"294.80969",
"315.57093",
"386.15917",
"406.92042",
"498.26990",
"519.03114",
"589.61938",
"610.38062",
"701.73010",
"793.07958",
"813.84083",
"884.42907",
"905.19031",
"996.53979",
"1017.30104",
"1087.88927",
"1108.65052",
"2/1"
]
},
{
"id": "indian_2",
"desc": "Indian shruti scale with tritone 64/45 schisma lower (Mr.Devarajan, Madurai)",
"stepCount": "22",
"steps": [
"256/243",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"81/64",
"4/3",
"27/20",
"45/32",
"64/45",
"3/2",
"128/81",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"243/128",
"2/1"
]
},
{
"id": "indian_3",
"desc": "Indian shruti scale with 32/31 and 31/16 and tritone schisma lower",
"stepCount": "22",
"steps": [
"32/31",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"81/64",
"4/3",
"27/20",
"45/32",
"64/45",
"3/2",
"128/81",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"31/16",
"2/1"
]
},
{
"id": "indian_4",
"desc": "Indian shruti scale according to Firoze Framjee: Text book of Indian music",
"stepCount": "22",
"steps": [
"135/128",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"512/405",
"4/3",
"45/32",
"64/45",
"40/27",
"3/2",
"405/256",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"256/135",
"2/1"
]
},
{
"id": "indian_5",
"desc": "23 Shrutis, Amit Mitra, 1/1 no. 12:2, Table C.",
"stepCount": "23",
"steps": [
"256/243",
"16/15",
"10/9",
"9/8",
"32/27",
"6/5",
"5/4",
"81/64",
"4/3",
"27/20",
"45/32",
"64/45",
"40/27",
"3/2",
"128/81",
"8/5",
"5/3",
"27/16",
"16/9",
"9/5",
"15/8",
"243/128",
"2/1"
]
},
{
"id": "indian_6",
"desc": "Shrutis calculated by generation method, Amit Mitra, 1/1 no. 12:2, Table B.",
"stepCount": "77",
"steps": [
"81/80",
"128/125",
"250/243",
"648/625",
"25/24",
"256/243",
"135/128",
"16/15",
"27/25",
"625/576",
"10/9",
"9/8",
"256/225",
"144/125",
"125/108",
"75/64",
"32/27",
"6/5",
"243/200",
"625/512",
"768/625",
"100/81",
"5/4",
"512/405",
"81/64",
"32/25",
"625/486",
"162/125",
"125/96",
"320/243",
"675/512",
"4/3",
"27/20",
"512/375",
"864/625",
"25/18",
"45/32",
"64/45",
"729/512",
"36/25",
"625/432",
"729/500",
"375/256",
"40/27",
"3/2",
"243/160",
"192/125",
"125/81",
"972/625",
"25/16",
"128/81",
"405/256",
"8/5",
"81/50",
"625/384",
"1024/625",
"400/243",
"5/3",
"27/16",
"128/75",
"216/125",
"125/72",
"225/128",
"16/9",
"9/5",
"729/400",
"1152/625",
"50/27",
"15/8",
"256/135",
"243/128",
"48/25",
"625/324",
"243/125",
"125/64",
"160/81",
"2/1"
]
},
{
"id": "indium_17",
"desc": "Indium[17] 2.5/3.7/3.11/3 subgroup scale in 31\\253 tuning",
"stepCount": "17",
"steps": [
"123.32016",
"147.03557",
"270.35573",
"294.07115",
"417.39130",
"441.10672",
"564.42688",
"588.14229",
"611.85771",
"735.17787",
"758.89328",
"882.21344",
"905.92885",
"1029.24901",
"1052.96443",
"1176.28458",
"2/1"
]
},
{
"id": "indra_31",
"desc": "Indra[31] (540/539, 1375/1372) hobbit in 296-tET",
"stepCount": "31",
"steps": [
"32.43243",
"85.13514",
"117.56757",
"150.00000",
"198.64865",
"235.13514",
"267.56757",
"316.21622",
"348.64865",
"381.08108",
"433.78378",
"466.21622",
"498.64865",
"551.35135",
"583.78378",
"616.21622",
"648.64865",
"701.35135",
"733.78378",
"766.21622",
"818.91892",
"851.35135",
"883.78378",
"932.43243",
"964.86486",
"1001.35135",
"1050.00000",
"1082.43243",
"1114.86486",
"1167.56757",
"2/1"
]
},
{
"id": "interbartolo_1",
"desc": "Graziano Interbartolo & Paolo Venturino Bach temperament nr.1 (2006)",
"stepCount": "12",
"steps": [
"135/128",
"193.15686",
"298.37062",
"5/4",
"503.42157",
"45/32",
"696.57843",
"795.27467",
"889.73529",
"1001.46657",
"15/8",
"2/1"
]
},
{
"id": "interbartolo_2",
"desc": "Graziano Interbartolo & Paolo Venturino Bach temperament nr.2 (2006)",
"stepCount": "12",
"steps": [
"256/243",
"192.18000",
"298.04500",
"8192/6561",
"503.91000",
"1024/729",
"696.09000",
"794.13500",
"888.26999",
"1001.95500",
"4096/2187",
"2/1"
]
},
{
"id": "interbartolo_3",
"desc": "Graziano Interbartolo & Paolo Venturino Bach temperament nr.3 (2006)",
"stepCount": "12",
"steps": [
"256/243",
"193.15686",
"297.71938",
"5/4",
"503.42157",
"45/32",
"696.57843",
"793.97219",
"889.73529",
"1001.46657",
"15/8",
"2/1"
]
},
{
"id": "ionic",
"desc": "Ancient greek Ionic",
"stepCount": "7",
"steps": ["9/8", "5/4", "4/3", "3/2", "5/3", "9/5", "2"]
},
{
"id": "iran_diat",
"desc": "Iranian Diatonic from Dariush Anooshfar, Safi-a-ddin Armavi's scale from 125 ET",
"stepCount": "7",
"steps": [
"220.80000",
"441.60000",
"489.60000",
"710.40000",
"931.20000",
"979.20000",
"2/1"
]
},
{
"id": "iranian_pentachord_7_limit",
"desc": "Iranian pentachord 42:45:48:56:63",
"stepCount": "9",
"steps": [
"64/63",
"9/8",
"6/5",
"9/7",
"3/2",
"27/16",
"9/5",
"27/14",
"2/1"
]
},
{
"id": "iraq",
"desc": "Iraq 8-tone scale, Ellis",
"stepCount": "8",
"steps": [
"394/355",
"8192/6561",
"4/3",
"623/421",
"591/355",
"16/9",
"513/260",
"2/1"
]
},
{
"id": "isfahan_5",
"desc": "Isfahan (IG #2, DF #8), from Rouanet",
"stepCount": "5",
"steps": ["13/12", "7/6", "5/4", "4/3", "2/1"]
},
{
"id": "islamic",
"desc": "Islamic Genus (DF#7), from Rouanet",
"stepCount": "5",
"steps": ["13/12", "7/6", "91/72", "4/3", "2/1"]
},
{
"id": "italian",
"desc": "Italian organ temperament, G.C. Klop (1974), 1/12 P.comma, also d'Alembert/Rousseau (1752/67)",
"stepCount": "12",
"steps": [
"84.35999",
"192.18000",
"288.26999",
"8192/6561",
"496.09000",
"584.35999",
"696.09000",
"784.35999",
"888.26999",
"992.18000",
"1084.35999",
"2/1"
]
},
{
"id": "iter_1",
"desc": "McLaren style, IE= 2.414214, PD=5, SD=0",
"stepCount": "6",
"steps": ["94/93", "39/38", "214/201", "57/49", "85/59", "1525.86396"]
},
{
"id": "iter_2",
"desc": "Iterated 1 + SQR(2) Scale, IE=2.414214, PD=5, SD=1",
"stepCount": "8",
"steps": [
"94/93",
"39/38",
"214/201",
"57/49",
"85/59",
"157/88",
"91/45",
"169/70"
]
},
{
"id": "iter_3",
"desc": "Iterated 27/16 Scale, analog of Hexachord, IE=27/16, PD=3, SD=2",
"stepCount": "10",
"steps": [
"126/113",
"137/114",
"152/121",
"79/61",
"664/487",
"169/115",
"82/53",
"193/121",
"158/97",
"27/16"
]
},
{
"id": "iter_4",
"desc": "Iterated 5/2 scale, IE=5/2, PD=4, SD=3",
"stepCount": "17",
"steps": [
"216/211",
"123/116",
"209/196",
"57/53",
"67/61",
"22/19",
"128/109",
"343/286",
"110/87",
"88/61",
"133/89",
"115/73",
"142/79",
"123/67",
"307/162",
"201/98",
"5/2"
]
},
{
"id": "iter_5",
"desc": "Iterated 5/3 scale, analog of Hexachord, IE=5/3, PD=3, SD=2",
"stepCount": "10",
"steps": [
"67/60",
"125/104",
"103/82",
"141/109",
"125/92",
"136/93",
"235/153",
"242/153",
"221/137",
"5/3"
]
},
{
"id": "iter_6",
"desc": "Iterated binary 1+SQR(2) scale, IE= 2.414214, G=2, PD=4, SD=2",
"stepCount": "11",
"steps": [
"56/53",
"115/103",
"91/73",
"54/41",
"135/97",
"101/65",
"85/49",
"153/79",
"88/43",
"253/117",
"169/70"
]
},
{
"id": "iter_7",
"desc": "Iterated 27/16 scale, analog of Hexachord, IE=27/16, PD=3, SD=2",
"stepCount": "10",
"steps": [
"79/74",
"106/93",
"179/152",
"174/143",
"126/97",
"147/106",
"114/77",
"205/134",
"49/31",
"27/16"
]
},
{
"id": "iter_8",
"desc": "Iterated 27/16 scale, analog of Hexachord, IE=27/16, PD=2, SD=2",
"stepCount": "9",
"steps": [
"106/93",
"179/152",
"174/143",
"126/97",
"147/106",
"114/77",
"205/134",
"49/31",
"27/16"
]
},
{
"id": "iter_9",
"desc": "Iterated 27/16 Scale, analog of Hexachord, IE=27/16, PD=2, SD=12",
"stepCount": "5",
"steps": ["106/93", "126/97", "114/77", "49/31", "27/16"]
},
{
"id": "iter_10",
"desc": "Iterated 5/2 scale, IE=5/2, PD=4, SD=3",
"stepCount": "17",
"steps": [
"359/339",
"194/173",
"91/80",
"607/526",
"19/16",
"127/101",
"339/262",
"241/181",
"141/100",
"117/74",
"72/43",
"211/119",
"167/84",
"178/87",
"40/19",
"136/61",
"5/2"
]
},
{
"id": "iter_11",
"desc": "Binary 5/3 Scale #2",
"stepCount": "10",
"steps": [
"110.54484",
"221.08968",
"276.36210",
"331.63452",
"442.17936",
"552.72420",
"663.26903",
"718.54145",
"773.81387",
"5/3"
]
},
{
"id": "iter_12",
"desc": "Binary 5/3 Scale #4",
"stepCount": "9",
"steps": [
"221.08968",
"276.36210",
"331.63452",
"442.17936",
"552.72420",
"663.26903",
"718.54145",
"773.81387",
"5/3"
]
},
{
"id": "iter_13",
"desc": "Binary 5/3 Scale #6",
"stepCount": "5",
"steps": ["221.08968", "442.17936", "663.26903", "773.81387", "5/3"]
},
{
"id": "iter_14",
"desc": "Binary Divided 3/1 Scale #2",
"stepCount": "11",
"steps": [
"118.87219",
"237.74438",
"475.48875",
"594.36094",
"713.23313",
"950.97750",
"1188.72188",
"1426.46625",
"1545.33844",
"1664.21063",
"3/1"
]
},
{
"id": "iter_15",
"desc": "Binary Division Scale",
"stepCount": "10",
"steps": [
"150.00000",
"300.00000",
"375.00000",
"450.00000",
"600.00000",
"750.00000",
"900.00000",
"975.00000",
"1050.00000",
"2/1"
]
},
{
"id": "iter_16",
"desc": "Binary Division Scale 4+2",
"stepCount": "11",
"steps": [
"75.00000",
"150.00000",
"300.00000",
"375.00000",
"450.00000",
"600.00000",
"750.00000",
"900.00000",
"975.00000",
"1050.00000",
"2/1"
]
},
{
"id": "iter_17",
"desc": "Binary E Scale #2",
"stepCount": "17",
"steps": [
"108.20213",
"216.40426",
"243.45479",
"270.50532",
"324.60638",
"432.80851",
"486.90958",
"541.01064",
"649.21277",
"865.61702",
"973.81915",
"1082.02128",
"1298.42554",
"1352.52660",
"1406.62766",
"1514.82979",
"1731.23405"
]
},
{
"id": "iter_18",
"desc": "Binary E Scale #4",
"stepCount": "10",
"steps": [
"216.40426",
"432.80851",
"541.01064",
"649.21277",
"865.61702",
"1082.02128",
"1298.42554",
"1406.62766",
"1514.82979",
"1731.23405"
]
},
{
"id": "iter_19",
"desc": "Binary Kidjel Ratio scale #2, IE=16/3",
"stepCount": "16",
"steps": [
"362.25562",
"407.53758",
"452.81953",
"543.38344",
"724.51125",
"815.07516",
"905.63906",
"1086.76687",
"1449.02250",
"1630.15031",
"1811.27812",
"2173.53375",
"2264.09766",
"2354.66156",
"2535.78937",
"16/3"
]
},
{
"id": "iter_20",
"desc": "Binary PHI Scale #2",
"stepCount": "11",
"steps": [
"52.06814",
"104.13629",
"208.27258",
"260.34072",
"312.40886",
"416.54515",
"520.68144",
"624.81773",
"676.88587",
"728.95401",
"833.09030"
]
},
{
"id": "iter_21",
"desc": "Binary PHI Scale 5+2 #2",
"stepCount": "12",
"steps": [
"26.03407",
"52.06814",
"104.13629",
"208.27258",
"260.34072",
"312.40886",
"416.54515",
"520.68144",
"624.81773",
"676.88587",
"728.95401",
"833.09030"
]
},
{
"id": "iter_22",
"desc": "Binary PI Scale #2",
"stepCount": "16",
"steps": [
"247.72442",
"278.68997",
"309.65552",
"371.58663",
"495.44884",
"557.37994",
"619.31105",
"743.17326",
"990.89768",
"1114.75989",
"1238.62210",
"1486.34652",
"1548.27762",
"1610.20873",
"1734.07094",
"1981.79536"
]
},
{
"id": "iter_23",
"desc": "Binary SQR(3) Scale #2",
"stepCount": "16",
"steps": [
"118.87219",
"133.73121",
"148.59023",
"178.30828",
"237.74437",
"267.46242",
"297.18047",
"356.61656",
"475.48875",
"534.92484",
"594.36094",
"713.23312",
"742.95117",
"772.66922",
"832.10531",
"950.97750"
]
},
{
"id": "iter_24",
"desc": "Binary SQR(5) Scale #2",
"stepCount": "16",
"steps": [
"174.14461",
"195.91268",
"217.68076",
"261.21691",
"348.28921",
"391.82537",
"435.36152",
"522.43382",
"696.57843",
"783.65073",
"870.72304",
"1044.86764",
"1088.40379",
"1131.93995",
"1219.01225",
"1393.15686"
]
},
{
"id": "iter_25",
"desc": "Binary SQR(7) Scale #2",
"stepCount": "16",
"steps": [
"210.55162",
"236.87057",
"263.18952",
"315.82743",
"421.10324",
"473.74114",
"526.37905",
"631.65486",
"842.20648",
"947.48229",
"1052.75810",
"1263.30971",
"1315.94762",
"1368.58552",
"1473.86133",
"1684.41295"
]
},
{
"id": "iter_26",
"desc": "E Scale",
"stepCount": "17",
"steps": [
"54/53",
"41/39",
"19/18",
"50/47",
"51/47",
"63/55",
"22/19",
"13/11",
"91/73",
"13/9",
"76/51",
"74/47",
"31/17",
"80/43",
"25/13",
"19/9",
"87/32"
]
},
{
"id": "iter_27",
"desc": "Iterated Kidjel Ratio Scale, IE=16/3, PD=3, SD=3",
"stepCount": "16",
"steps": [
"91/90",
"89/88",
"79/78",
"101/99",
"35/33",
"426/401",
"61/57",
"89/80",
"219/160",
"424/307",
"201/140",
"136/77",
"137/77",
"101/55",
"113/52",
"16/3"
]
},
{
"id": "iter_28",
"desc": "McLaren 3-Division Scale",
"stepCount": "5",
"steps": ["74/73", "226/217", "87/77", "75/52", "3/1"]
},
{
"id": "iter_29",
"desc": "Iterated Binary Division of the Octave, IE=2, PD=6, SD=0",
"stepCount": "7",
"steps": ["93/92", "140/137", "118/113", "217/199", "44/37", "99/70", "2/1"]
},
{
"id": "iter_30",
"desc": "Iterated E-scale, IE= 2.71828, PD=5, SD=0",
"stepCount": "6",
"steps": ["148/147", "55/54", "103/98", "79/69", "536/371", "193/71"]
},
{
"id": "iter_31",
"desc": "Iterated Kidjel Ratio Scale, IE=16/3, PD=3, SD=0",
"stepCount": "4",
"steps": ["91/90", "35/33", "219/160", "16/3"]
},
{
"id": "iter_32",
"desc": "Iterated PHI scale, IE= 1.61803339, PD=8, SD=0",
"stepCount": "9",
"steps": [
"98/97",
"61/60",
"151/147",
"165/158",
"59/55",
"149/133",
"131/109",
"206/153",
"144/89"
]
},
{
"id": "iter_33",
"desc": "Iterated PI Scale, IE= 3.14159, PD=4, SD=0",
"stepCount": "5",
"steps": ["86/85", "138/133", "137/122", "131/91", "311/99"]
},
{
"id": "iter_34",
"desc": "Iterated SQR(3) scale, IE= 1.73205, PD=8, SD=0",
"stepCount": "9",
"steps": [
"147/146",
"86/85",
"149/146",
"202/195",
"135/127",
"279/251",
"239/199",
"92/67",
"97/56"
]
},
{
"id": "iter_35",
"desc": "Iterated SQR(5) scale, IE= 2.23607, PD=6, SD=0",
"stepCount": "7",
"steps": [
"155/154",
"70/69",
"158/153",
"72/67",
"74/63",
"225/157",
"161/72"
]
},
{
"id": "iter_36",
"desc": "Iterated SQR(7) scale, IE= 2.64575, PD=5, SD=0",
"stepCount": "6",
"steps": ["133/132", "51/50", "176/167", "131/114", "13/9", "127/48"]
},
{
"id": "ives",
"desc": "Charles Ives' stretched major scale, \"Scrapbook\"pp. 108-110",
"stepCount": "7",
"steps": [
"250.00000",
"500.00000",
"625.00000",
"875.00000",
"1125.00000",
"1375.00000",
"1500.00000"
]
},
{
"id": "ives_2_a",
"desc": "Speculation by Joe Monzo for Ives' other stretched scale",
"stepCount": "7",
"steps": [
"258.33333",
"516.66667",
"645.83333",
"904.16667",
"1162.50000",
"1420.83333",
"1550.00000"
]
},
{
"id": "ives_2_b",
"desc": "Alt. speculation by Joe Monzo for Ives' other stretched scale",
"stepCount": "7",
"steps": [
"241.66667",
"483.33333",
"604.16667",
"845.83333",
"1087.50000",
"1329.16667",
"1450.00000"
]
},
{
"id": "jademohaporc",
"desc": "Jade-mohajira-porcupine wakalix",
"stepCount": "7",
"steps": ["12/11", "11/9", "4/3", "3/2", "18/11", "11/6", "2/1"]
},
{
"id": "janke_1",
"desc": "Reiner Janke, Temperatur I (1998)",
"stepCount": "12",
"steps": [
"95.00000",
"198.00000",
"297.00000",
"396.00000",
"499.00000",
"594.00000",
"699.00000",
"796.00000",
"897.00000",
"998.00000",
"1095.00000",
"2/1"
]
},
{
"id": "janke_2",
"desc": "Reiner Janke, Temperatur II",
"stepCount": "12",
"steps": [
"95.00000",
"196.00000",
"297.00000",
"394.00000",
"499.00000",
"594.00000",
"698.00000",
"796.00000",
"895.00000",
"998.00000",
"1093.00000",
"2/1"
]
},
{
"id": "janke_3",
"desc": "Reiner Janke, Temperatur III",
"stepCount": "12",
"steps": [
"94.00000",
"196.00000",
"296.00000",
"393.00000",
"499.00000",
"593.00000",
"698.00000",
"795.00000",
"894.00000",
"998.00000",
"1092.00000",
"2/1"
]
},
{
"id": "janke_4",
"desc": "Reiner Janke, Temperatur IV",
"stepCount": "12",
"steps": [
"92.00000",
"196.00000",
"298.00000",
"392.00000",
"500.00000",
"591.00000",
"698.00000",
"794.00000",
"894.00000",
"999.00000",
"1091.00000",
"2/1"
]
},
{
"id": "janke_5",
"desc": "Reiner Janke, Temperatur V",
"stepCount": "12",
"steps": [
"90.00000",
"196.00000",
"294.00000",
"392.00000",
"498.00000",
"588.00000",
"698.00000",
"792.00000",
"894.00000",
"996.00000",
"1090.00000",
"2/1"
]
},
{
"id": "janke_6",
"desc": "Reiner Janke, Temperatur VI",
"stepCount": "12",
"steps": [
"91.00000",
"196.00000",
"297.00000",
"392.00000",
"501.00000",
"589.00000",
"698.00000",
"794.00000",
"894.00000",
"999.00000",
"1090.00000",
"2/1"
]
},
{
"id": "janke_7",
"desc": "Reiner Janke, Temperatur VII",
"stepCount": "12",
"steps": [
"89.00000",
"195.00000",
"300.00000",
"391.00000",
"502.00000",
"586.00000",
"698.00000",
"793.00000",
"893.00000",
"1004.00000",
"1089.00000",
"2/1"
]
},
{
"id": "jemblung_1",
"desc": "Scale of bamboo gamelan jemblung from Kalijering, slendro-like. 1/1=590 Hz",
"stepCount": "5",
"steps": ["230.44036", "442.89125", "684.25910", "947.73875", "2/1"]
},
{
"id": "jemblung_2",
"desc": "Bamboo gamelan jemblung at Royal Batavia Society. 1/1=504 Hz",
"stepCount": "5",
"steps": ["237.17491", "528.68711", "697.36895", "945.11000", "2/1"]
},
{
"id": "ji_5_coh",
"desc": "Differential fully coherent pentatonic scale",
"stepCount": "5",
"steps": ["7/6", "4/3", "35/24", "41/24", "2/1"]
},
{
"id": "ji_7",
"desc": "7-limit rational interpretation of 7-tET. OdC",
"stepCount": "7",
"steps": ["10/9", "128/105", "4/3", "3/2", "105/64", "9/5", "2/1"]
},
{
"id": "ji_7_a",
"desc": "Superparticular approximation to 7-tET. Op de Coul, 1998",
"stepCount": "7",
"steps": ["11/10", "11/9", "4/3", "3/2", "18/11", "9/5", "2/1"]
},
{
"id": "ji_8_coh",
"desc": "Differentially coherent 8-tone scale with subharmonic 40",
"stepCount": "8",
"steps": ["43/40", "6/5", "51/40", "7/5", "31/20", "67/40", "73/40", "2/1"]
},
{
"id": "ji_9",
"desc": "Pseudo-equal 7-limit 9-tET",
"stepCount": "9",
"steps": [
"2592/2401",
"7/6",
"432/343",
"49/36",
"72/49",
"343/216",
"12/7",
"2401/1296",
"2/1"
]
},
{
"id": "ji_9_coh",
"desc": "Differentially coherent 9-tone scale with subharmonic 30",
"stepCount": "9",
"steps": [
"16/15",
"7/6",
"19/15",
"41/30",
"22/15",
"8/5",
"26/15",
"28/15",
"2/1"
]
},
{
"id": "ji_10_coh",
"desc": "Differentially coherent 10-tone scale with subharmonic 48",
"stepCount": "10",
"steps": [
"13/12",
"55/48",
"5/4",
"4/3",
"17/12",
"3/2",
"5/3",
"7/4",
"89/48",
"2/1"
]
},
{
"id": "ji_10_coh_2",
"desc": "Other diff. coherent 10-tone scale with subharmonic 30",
"stepCount": "10",
"steps": [
"7/6",
"6/5",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"9/5",
"11/6",
"2/1"
]
},
{
"id": "ji_10_i_4",
"desc": "7-limit scale with mean variety four",
"stepCount": "10",
"steps": [
"16/15",
"8/7",
"128/105",
"4/3",
"10/7",
"32/21",
"8/5",
"128/75",
"64/35",
"2/1"
]
},
{
"id": "ji_11",
"desc": "3 and 7 prime rational interpretation of 11-tET. OdC 2000",
"stepCount": "11",
"steps": [
"343/324",
"9/8",
"98/81",
"9/7",
"49/36",
"72/49",
"14/9",
"81/49",
"16/9",
"648/343",
"2/1"
]
},
{
"id": "ji_12",
"desc": "Basic JI with 7-limit tritone. Robert Rich: Geometry",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"6/5",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "ji_12_a",
"desc": "7-limit 12-tone scale",
"stepCount": "12",
"steps": [
"16/15",
"9/8",
"7/6",
"5/4",
"4/3",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "ji_12_b",
"desc": "alternate 7-limit 12-tone scale",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"7/6",
"5/4",
"21/16",
"7/5",
"3/2",
"8/5",
"12/7",
"7/4",
"15/8",
"2/1"
]
},
{
"id": "ji_12_coh",
"desc": "Differentially coherent 12-tone scale with subharmonic 60",
"stepCount": "12",
"steps": [
"16/15",
"67/60",
"6/5",
"19/15",
"4/3",
"7/5",
"3/2",
"8/5",
"5/3",
"53/30",
"28/15",
"2/1"
]
},
{
"id": "ji_13",
"desc": "5-limit 12-tone symmetrical scale with two tritones",
"stepCount": "13",
"steps": [
"16/15",
"9/8",
"32/27",
"5/4",
"4/3",
"45/32",
"64/45",
"3/2",
"8/5",
"27/16",
"16/9",
"15/8",
"2/1"
]
},
{
"id": "ji_15_coh",
"desc": "Differentially coherent 15-tone scale with subharmonic 88",
"stepCount": "15",
"steps": [
"93/88",
"12/11",
"101/88",
"53/44",
"14/11",
"29/22",
"61/44",
"16/11",
"67/44",
"35/22",
"73/44",
"7/4",
"20/11",
"21/11",
"2/1"
]
},
{
"id": "ji_17",
"desc": "3 and 7 prime rational interpretation of 17-tET. OdC",
"stepCount": "17",
"steps": [
"28/27",
"243/224",
"9/8",
"32/27",
"896/729",
"9/7",
"4/3",
"112/81",
"81/56",
"3/2",
"14/9",
"729/448",
"27/16",
"16/9",
"448/243",
"27/14",
"2/1"
]
},
{
"id": "ji_17_a",
"desc": "3, 5 and 11 prime rational interpretation of 17-tET, OdC",
"stepCount": "17",
"steps": [
"25/24",
"27/25",
"9/8",
"32/27",
"27/22",
"32/25",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"44/27",
"27/16",
"16/9",
"50/27",
"48/25",
"2/1"
]
},
{
"id": "ji_17_b",
"desc": "Alt. 3, 5 and 11 prime rational interpretation of 17-tET, OdC",
"stepCount": "17",
"steps": [
"25/24",
"12/11",
"9/8",
"32/27",
"11/9",
"32/25",
"4/3",
"11/8",
"16/11",
"3/2",
"25/16",
"18/11",
"27/16",
"16/9",
"11/6",
"48/25",
"2/1"
]
},
{
"id": "ji_18",
"desc": "11-limit approximation of 18-tET",
"stepCount": "18",
"steps": [
"80/77",
"27/25",
"55/49",
"7/6",
"40/33",
"63/50",
"55/42",
"49/36",
"99/70",
"72/49",
"55/36",
"100/63",
"33/20",
"12/7",
"98/55",
"50/27",
"77/40",
"2/1"
]
},
{
"id": "ji_19",
"desc": "5-limit 19-tone scale, subset of genus [3333555]",
"stepCount": "19",
"steps": [
"25/24",
"135/128",
"16/15",
"9/8",
"75/64",
"6/5",
"5/4",
"4/3",
"27/20",
"45/32",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"225/128",
"9/5",
"15/8",
"2/1"
]
},
{
"id": "ji_20",
"desc": "3 and 7 prime rational interpretation of 20-tET. OdC",
"stepCount": "20",
"steps": [
"28/27",
"2187/2048",
"54/49",
"8/7",
"32/27",
"896/729",
"81/64",
"4/3",
"49/36",
"729/512",
"72/49",
"3/2",
"128/81",
"729/448",
"27/16",
"7/4",
"49/27",
"4096/2187",
"27/14",
"2/1"
]
},
{
"id": "ji_21",
"desc": "7-limit 21-tone just scale, Op de Coul, 2001",
"stepCount": "21",
"steps": [
"28/27",
"16/15",
"10/9",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"4/3",
"7/5",
"10/7",
"3/2",
"14/9",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "ji_22",
"desc": "5-limit 22-tone scale (Zarlino?)",
"stepCount": "22",
"steps": [
"25/24",
"16/15",
"27/25",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"125/96",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"125/72",
"9/5",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "ji_29",
"desc": "3,5,11-prime rational interpretation of 29-tET, OdC",
"stepCount": "29",
"steps": [
"128/125",
"256/243",
"27/25",
"11/10",
"9/8",
"144/125",
"32/27",
"40/33",
"99/80",
"81/64",
"125/96",
"4/3",
"15/11",
"45/32",
"64/45",
"22/15",
"3/2",
"192/125",
"128/81",
"160/99",
"33/20",
"27/16",
"125/72",
"16/9",
"20/11",
"50/27",
"243/128",
"125/64",
"2/1"
]
},
{
"id": "ji_30",
"desc": "11-limit rational interpretation of 30-tET",
"stepCount": "30",
"steps": [
"45/44",
"21/20",
"15/14",
"35/32",
"9/8",
"55/48",
"33/28",
"6/5",
"315/256",
"63/50",
"9/7",
"675/512",
"27/20",
"2048/1485",
"99/70",
"1485/1024",
"40/27",
"1024/675",
"14/9",
"100/63",
"512/315",
"5/3",
"56/33",
"96/55",
"16/9",
"64/35",
"28/15",
"40/21",
"88/45",
"2/1"
]
},
{
"id": "ji_31",
"desc": "A just 7-limit 31-tone scale",
"stepCount": "31",
"steps": [
"128/125",
"25/24",
"16/15",
"35/32",
"9/8",
"8/7",
"7/6",
"6/5",
"128/105",
"5/4",
"32/25",
"21/16",
"4/3",
"48/35",
"7/5",
"10/7",
"35/24",
"3/2",
"32/21",
"25/16",
"8/5",
"105/64",
"5/3",
"12/7",
"7/4",
"16/9",
"64/35",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "ji_121",
"desc": "13-limit detempering of 121-tET",
"stepCount": "121",
"steps": [
"100/99",
"64/63",
"50/49",
"40/39",
"36/35",
"28/27",
"25/24",
"22/21",
"21/20",
"35/33",
"16/15",
"15/14",
"14/13",
"13/12",
"12/11",
"35/32",
"11/10",
"10/9",
"39/35",
"28/25",
"9/8",
"25/22",
"8/7",
"55/48",
"15/13",
"64/55",
"7/6",
"75/64",
"13/11",
"25/21",
"105/88",
"6/5",
"63/52",
"40/33",
"11/9",
"16/13",
"26/21",
"56/45",
"5/4",
"44/35",
"63/50",
"14/11",
"32/25",
"9/7",
"35/27",
"13/10",
"55/42",
"21/16",
"33/25",
"4/3",
"75/56",
"35/26",
"27/20",
"15/11",
"48/35",
"11/8",
"18/13",
"39/28",
"7/5",
"45/32",
"64/45",
"10/7",
"56/39",
"13/9",
"16/11",
"35/24",
"22/15",
"40/27",
"49/33",
"112/75",
"3/2",
"50/33",
"32/21",
"55/36",
"20/13",
"54/35",
"14/9",
"25/16",
"11/7",
"63/40",
"35/22",
"8/5",
"45/28",
"21/13",
"13/8",
"18/11",
"33/20",
"104/63",
"5/3",
"117/70",
"42/25",
"22/13",
"75/44",
"12/7",
"55/32",
"26/15",
"96/55",
"7/4",
"44/25",
"16/9",
"25/14",
"70/39",
"9/5",
"20/11",
"64/35",
"11/6",
"24/13",
"13/7",
"28/15",
"15/8",
"49/26",
"40/21",
"21/11",
"25/13",
"27/14",
"35/18",
"39/20",
"49/25",
"63/32",
"99/50",
"2/1"
]
},
{
"id": "ji_311",
"desc": "41-limit transversal of 311-tET",
"stepCount": "311",
"steps": [
"289/288",
"170/169",
"133/132",
"100/99",
"85/84",
"70/69",
"64/63",
"55/54",
"49/48",
"45/44",
"40/39",
"37/36",
"34/33",
"32/31",
"30/29",
"28/27",
"27/26",
"25/24",
"24/23",
"23/22",
"22/21",
"21/20",
"20/19",
"19/18",
"37/35",
"18/17",
"17/16",
"33/31",
"16/15",
"31/29",
"15/14",
"29/27",
"14/13",
"41/38",
"27/25",
"13/12",
"25/23",
"37/34",
"12/11",
"35/32",
"23/21",
"56/51",
"11/10",
"32/29",
"21/19",
"31/28",
"10/9",
"49/44",
"29/26",
"19/17",
"28/25",
"46/41",
"9/8",
"35/31",
"26/23",
"17/15",
"25/22",
"33/29",
"57/50",
"8/7",
"55/48",
"31/27",
"23/20",
"15/13",
"37/32",
"22/19",
"29/25",
"57/49",
"7/6",
"76/65",
"34/29",
"27/23",
"20/17",
"33/28",
"13/11",
"32/27",
"19/16",
"25/21",
"31/26",
"55/46",
"91/76",
"6/5",
"65/54",
"35/29",
"29/24",
"23/19",
"17/14",
"28/23",
"39/32",
"11/9",
"38/31",
"27/22",
"16/13",
"37/30",
"21/17",
"26/21",
"31/25",
"46/37",
"81/65",
"5/4",
"114/91",
"49/39",
"34/27",
"29/23",
"24/19",
"19/15",
"33/26",
"14/11",
"37/29",
"23/18",
"32/25",
"77/60",
"9/7",
"40/31",
"31/24",
"22/17",
"48/37",
"13/10",
"30/23",
"17/13",
"38/29",
"21/16",
"25/19",
"29/22",
"33/25",
"45/34",
"65/49",
"117/88",
"4/3",
"147/110",
"75/56",
"51/38",
"35/26",
"31/23",
"27/20",
"23/17",
"19/14",
"34/25",
"15/11",
"41/30",
"26/19",
"48/35",
"11/8",
"40/29",
"29/21",
"18/13",
"25/18",
"32/23",
"39/28",
"88/63",
"7/5",
"80/57",
"38/27",
"31/22",
"24/17",
"17/12",
"44/31",
"27/19",
"57/40",
"10/7",
"63/44",
"33/23",
"23/16",
"36/25",
"13/9",
"42/29",
"29/20",
"16/11",
"35/24",
"19/13",
"41/28",
"22/15",
"25/17",
"28/19",
"31/21",
"37/25",
"46/31",
"52/35",
"76/51",
"112/75",
"220/147",
"3/2",
"176/117",
"95/63",
"68/45",
"50/33",
"41/27",
"35/23",
"32/21",
"29/19",
"26/17",
"23/15",
"20/13",
"37/24",
"17/11",
"48/31",
"31/20",
"14/9",
"81/52",
"25/16",
"36/23",
"58/37",
"11/7",
"41/26",
"30/19",
"19/12",
"46/29",
"27/17",
"51/32",
"91/57",
"8/5",
"77/48",
"37/23",
"29/18",
"21/13",
"34/21",
"60/37",
"13/8",
"44/27",
"31/19",
"18/11",
"41/25",
"23/14",
"28/17",
"33/20",
"48/29",
"58/35",
"108/65",
"5/3",
"147/88",
"77/46",
"52/31",
"37/22",
"32/19",
"27/16",
"22/13",
"39/23",
"17/10",
"46/27",
"29/17",
"65/38",
"12/7",
"55/32",
"31/18",
"19/11",
"45/26",
"26/15",
"33/19",
"54/31",
"96/55",
"7/4",
"100/57",
"58/33",
"37/21",
"30/17",
"23/13",
"39/22",
"16/9",
"41/23",
"25/14",
"34/19",
"52/29",
"88/49",
"9/5",
"56/31",
"38/21",
"29/16",
"20/11",
"51/28",
"31/17",
"64/35",
"11/6",
"68/37",
"35/19",
"24/13",
"37/20",
"63/34",
"13/7",
"41/22",
"28/15",
"58/31",
"15/8",
"62/33",
"32/17",
"17/9",
"70/37",
"36/19",
"19/10",
"40/21",
"21/11",
"44/23",
"23/12",
"25/13",
"52/27",
"27/14",
"29/15",
"31/16",
"33/17",
"37/19",
"39/20",
"45/23",
"49/25",
"55/28",
"63/32",
"69/35",
"91/46",
"99/50",
"135/68",
"169/85",
"299/150",
"2/1"
]
},
{
"id": "jioct_12",
"desc": "12-tone JI version of Messiaen's octatonic scale, Erlich & Par�zek",
"stepCount": "12",
"steps": [
"25/24",
"27/25",
"125/108",
"6/5",
"5/4",
"25/18",
"36/25",
"3/2",
"5/3",
"125/72",
"9/5",
"2/1"
]
},
{
"id": "jira_1",
"desc": "Martin Jira, �closed� temperament (2000)",
"stepCount": "12",
"steps": [
"94.13500",
"196.09000",
"296.09000",
"392.18000",
"4/3",
"594.13500",
"698.04500",
"794.13500",
"894.13500",
"16/9",
"1094.13500",
"2/1"
]
},
{
"id": "jira_2",
"desc": "Martin Jira, �open� temperament (2000)",
"stepCount": "12",
"steps": [
"88.26999",
"196.09000",
"32/27",
"392.18000",
"4/3",
"592.18000",
"698.04500",
"790.22500",
"894.13500",
"16/9",
"1094.13500",
"2/1"
]
},
{
"id": "jobin_bach",
"desc": "Emile Jobin, WTC temperament after Bach's signet",
"stepCount": "12",
"steps": [
"86.80214",
"193.15686",
"292.42357",
"5/4",
"4/3",
"584.84714",
"696.57843",
"788.75714",
"889.73529",
"994.37857",
"1082.89214",
"2/1"
]
},
{
"id": "johnson_7",
"desc": "Aaron Johnson, 7-tET approximation",
"stepCount": "7",
"steps": [
"1157625/1048576",
"342.56773",
"11025/8192",
"685.47311",
"105/64",
"121550625/67108864",
"2/1"
]
},
{
"id": "johnson_44",
"desc": "Aaron Johnson, 44-tET approximation",
"stepCount": "44",
"steps": [
"64/63",
"4096/3969",
"262144/250047",
"16777216/15752961",
"1073741824/992436543",
"163.58455",
"190.84864",
"218.11273",
"245.37683",
"272.64092",
"300.28497",
"327.54906",
"354.81315",
"382.07725",
"409.34134",
"436.60543",
"463.86952",
"491.13361",
"518.39770",
"545.66180",
"572.92589",
"600.18998",
"627.45407",
"654.71816",
"681.98226",
"709.24635",
"736.51044",
"763.77453",
"791.03862",
"818.30271",
"845.56681",
"872.83090",
"900.09499",
"927.35908",
"954.62317",
"981.88727",
"1009.15136",
"1036.41545",
"992436543/536870912",
"15752961/8388608",
"250047/131072",
"3969/2048",
"63/32",
"2/1"
]
},
{
"id": "johnson_eb",
"desc": "Aaron Johnson, \"1/4-comma tempered\"equal beating C-G-D-A-E plus just thirds",
"stepCount": "12",
"steps": [
"71/68",
"19/17",
"508/425",
"5/4",
"568/425",
"95/68",
"127/85",
"25/16",
"142/85",
"152/85",
"127/68",
"2/1"
]
},
{
"id": "johnson_ratwell",
"desc": "Aaron Johnson, rational well-temperament with five 24/19's",
"stepCount": "12",
"steps": [
"19/18",
"103/92",
"32/27",
"361/288",
"4/3",
"38/27",
"208/139",
"19/12",
"129/77",
"16/9",
"152/81",
"2/1"
]
},
{
"id": "johnson_temp",
"desc": "Aaron Johnson, temperament with just 5/4, 24/19 and 19/15",
"stepCount": "12",
"steps": [
"89.64491",
"193.15750",
"293.06616",
"5/4",
"497.68872",
"588.53494",
"696.57875",
"30/19",
"889.73625",
"995.37744",
"1087.42497",
"2/1"
]
},
{
"id": "johnson_secor_rwt",
"desc": "Johnson/Secor proportional-beating well-temperament with five 24/19s.",
"stepCount": "12",
"steps": [
"19/18",
"3629/3240",
"32/27",
"361/288",
"4/3",
"38/27",
"431/288",
"19/12",
"2413/1440",
"16/9",
"152/81",
"2/1"
]
},
{
"id": "johnston_6_qt_row",
"desc": "11-limit 'prime row' from Ben Johnston's \"6th Quartet\"",
"stepCount": "12",
"steps": [
"25/24",
"10/9",
"75/64",
"5/4",
"75/56",
"25/18",
"55/36",
"25/16",
"5/3",
"75/44",
"15/8",
"35/18"
]
},
{
"id": "johnston_6_qt",
"desc": "11-limit complete system from Ben Johnston's \"6th Quartet\"",
"stepCount": "61",
"steps": [
"225/224",
"55/54",
"45/44",
"28/27",
"25/24",
"35/33",
"15/14",
"88/81",
"10/9",
"9/8",
"25/22",
"55/48",
"225/196",
"7/6",
"75/64",
"32/27",
"25/21",
"98/81",
"40/33",
"11/9",
"100/81",
"5/4",
"225/176",
"35/27",
"55/42",
"4/3",
"75/56",
"110/81",
"15/11",
"112/81",
"25/18",
"45/32",
"10/7",
"35/24",
"225/154",
"40/27",
"121/81",
"3/2",
"50/33",
"55/36",
"14/9",
"25/16",
"128/81",
"45/28",
"44/27",
"5/3",
"75/44",
"140/81",
"225/128",
"16/9",
"25/14",
"20/11",
"11/6",
"50/27",
"225/121",
"15/8",
"77/81",
"40/21",
"35/18",
"160/81",
"2/1"
]
},
{
"id": "johnston_21",
"desc": "Johnston 21-note just enharmonic scale",
"stepCount": "21",
"steps": [
"25/24",
"27/25",
"9/8",
"75/64",
"6/5",
"5/4",
"32/25",
"125/96",
"4/3",
"25/18",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"125/72",
"9/5",
"15/8",
"48/25",
"125/64",
"2/1"
]
},
{
"id": "johnston_22",
"desc": "Johnston 22-note 7-limit scale from end of string quartet nr. 4",
"stepCount": "22",
"steps": [
"28/27",
"16/15",
"10/9",
"8/7",
"7/6",
"6/5",
"5/4",
"9/7",
"21/16",
"27/20",
"45/32",
"81/56",
"3/2",
"14/9",
"8/5",
"5/3",
"12/7",
"7/4",
"9/5",
"15/8",
"27/14",
"2/1"
]
},
{
"id": "johnston_25",
"desc": "Johnston 25-note just enharmonic scale",
"stepCount": "25",
"steps": [
"25/24",
"135/128",
"16/15",
"10/9",
"9/8",
"75/64",
"6/5",
"5/4",
"81/64",
"32/25",
"4/3",
"27/20",
"45/32",
"36/25",
"3/2",
"25/16",
"8/5",
"5/3",
"27/16",
"225/128",
"16/9",
"9/5",
"15/8",
"48/25",
"2/1"
]
},
{
"id": "johnston_81",
"desc": "Johnston 81-note 5-limit scale of Sonata for Microtonal Piano",
"stepCount": "81",
"steps": [
"81/80",
"128/125",
"250/243",
"648/625",
"25/24",
"256/243",
"135/128",
"16/15",
"2187/2048",
"27/25",
"2187/2000",
"800/729",
"1125/1024",
"10/9",
"9/8",
"729/640",
"144/125",
"125/108",
"729/625",
"75/64",
"32/27",
"1215/1024",
"6/5",
"243/200",
"625/512",
"100/81",
"5/4",
"81/64",
"32/25",
"162/125",
"125/96",
"320/243",
"4/3",
"27/20",
"512/375",
"2187/1600",
"864/625",
"25/18",
"1024/729",
"45/32",
"64/45",
"729/512",
"36/25",
"729/500",
"375/256",
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