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August 12, 2014 14:39
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viable heptatonic scales
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| This is a chart of all 7 note pitch sets which have at least one mode which is a viable heptatonic scale. | |
| A viable heptatonic scale is one where: | |
| there are 7 distinct pitches. | |
| the first degree is 0 semitones. | |
| the second degree is 1, 2 or 3 semitones. | |
| the third degree is 3 or 4 semitones. | |
| the fourth degree is 5 or 6 semitones. | |
| the fifth degree is 6, 7 or 8 semitones. | |
| the sixth degree is 8 or 9 semitones. | |
| the seventh degree is 10 or 11 semitones. | |
| the first, third and fifth degree do not form a first inversion major triad, i.e. pitch set (0,3,8). Such a scale is considered mis-rooted. | |
| This definition is arbitrary, but it seems a useful one to me. | |
| The chart gives the Forte set number, the name of the scale, and a list of all its modes. | |
| For each mode, the pitch set is given; an X indicates a nonviable mode; the root seventh chord is given; | |
| an algorithm attempts to give a name for each viable mode. | |
| 1 7-35 -- diatonic -- | |
| 1 024579E M7 major | |
| 2 023579T m7 dorian | |
| 3 013578T m7 phrygian | |
| 4 024679E M7 lydian | |
| 5 024579T 7 mixolydian | |
| 6 023578T m7 minor | |
| 7 013568T m7-5 locrian | |
| 2 7-34 -- melodic minor -- | |
| 1 023579E mM7 melodic minor | |
| 2 013579T m7 phrygian M6 | |
| 3 024689E M7+5 augmented M7 | |
| 4 024679T 7 lydian dominant | |
| 5 024578T 7 mixolydian b13 | |
| 6 023568T m7-5 locrian M2 | |
| 7 013468T X m7-5 | |
| 3 7-32 -- harmonic minor -- | |
| 1 023578E mM7 harmonic minor | |
| 2 013569T m7-5 locrian M6 | |
| 3 024589E M7+5 major #5 | |
| 4 023679T m7 dorian #11 | |
| 5 014578T 7 mixolydian b9 b13 | |
| 6 034679E M7 lydian #9 | |
| 7 0134689 X dim7 | |
| 4 7-32B -- harmonic major -- | |
| 1 024578E M7 harmonic major | |
| 2 023569T m7-5 dorian b5 | |
| 3 013478T X m7 | |
| 4 023679E mM7 melodic minor #11 | |
| 5 014579T 7 mixolydian b9 | |
| 6 034689E M7+5 augmented M7 #9 | |
| 7 0135689 X dim7 | |
| 5 7-30 -- harmonic phrygian -- | |
| 1 013578E mM7 harmonic phrygian | |
| 2 02467TE X M7 | |
| 3 024589T 7+5 dominant #5 | |
| 4 023678T m7 minor #11 | |
| 5 014568T 7-5 dominant b9 b5 b13 | |
| 6 034579E M7 major #9 | |
| 7 0124689 X | |
| 6 7-33 -- whole tone + 1 -- | |
| 1 024678T 7 lydian dominant b13 | |
| 2 024568T 7-5 dominant b5 b13 | |
| 3 023468T X m7-5 | |
| 4 012468T X | |
| 5 013579E mM7 melodic phrygian | |
| 6 02468TE X M7+5 | |
| 7 024689T 7+5 augmented dominant | |
| 7 7-22 -- bhairav -- | |
| 1 014578E M7 harmonic major b9 | |
| 2 03467TE X M7 | |
| 3 0134789 X | |
| 4 023678E mM7 harmonic minor #11 | |
| 5 014569T 7-5 dominant b9 b5 | |
| 6 034589E M7+5 major #9 #5 | |
| 7 0125689 X | |
| 8 7-30B -- harmonic lydian -- | |
| 1 024678E M7 harmonic lydian | |
| 2 024569T 7-5 dominant b5 | |
| 3 023478T X m7 | |
| 4 012568T X | |
| 5 014579E M7 major b9 | |
| 6 03468TE X M7+5 | |
| 7 0135789 X | |
| 9 7-28 -- augmented dominant #9 -- a subset of messiaen's mode 6 | |
| 1 034689T 7+5 augmented dominant #9 | |
| 2 0135679 X dim7 | |
| 3 024568E M7-5 harmonic major b5 | |
| 4 023469T X m7-5 | |
| 5 012478T X | |
| 6 013679E mM7 melodic phrygian #11 | |
| 7 02568TE X | |
| 10 7-20 -- dominant #9 #5 -- | |
| 1 034589T 7+5 dominant #9 #5 | |
| 2 0125679 X | |
| 3 014568E M7-5 harmonic major b9 b5 | |
| 4 03457TE X M7 | |
| 5 0124789 X | |
| 6 013678E mM7 harmonic phrygian #11 | |
| 7 02567TE X susM7 | |
| 11 7-31 -- phrygian #11 M6 -- a subset of diminished | |
| 1 013679T m7 phrygian #11 M6 | |
| 2 025689E X | |
| 3 034679T 7 lydian dominant #9 | |
| 4 0134679 X dim7 | |
| 5 023568E dimM7 harmonic locrian M2 | |
| 6 013469T X m7-5 | |
| 7 023589E X | |
| 12 7-29 -- todi -- | |
| 1 013678T m7 phrygian #11 | |
| 2 025679E X susM7 | |
| 3 034579T 7 mixolydian #9 | |
| 4 0124679 X | |
| 5 013568E dimM7 harmonic locrian | |
| 6 02457TE X M7 | |
| 7 023589T X | |
| 13 7-29B -- major b5 -- | |
| 1 024569E M7-5 major b5 | |
| 2 023479T X m7 | |
| 3 012578T X | |
| 4 014679E M7 lydian b9 | |
| 5 03568TE X | |
| 6 0235789 X | |
| 7 013567T X m7-5 | |
| 14 7-20B -- purvi -- | |
| 1 014678E M7 harmonic lydian b9 | |
| 2 03567TE X susM7 | |
| 3 0234789 X | |
| 4 012567T X | |
| 5 014569E M7-5 major b9 b5 | |
| 6 03458TE X M7+5 | |
| 7 0125789 X | |
| 15 7-31B -- lydian dominant b9 -- a subset of diminished | |
| 1 014679T 7 lydian dominant b9 | |
| 2 035689E X | |
| 3 0235689 X dim7 | |
| 4 013467T X m7-5 | |
| 5 023569E dimM7 melodic locrian M2 | |
| 6 013479T X m7 | |
| 7 023689E X | |
| 16 7-28B -- lydian dominant b9 b13 -- a subset of messiaen's mode 6 | |
| 1 014678T 7 lydian dominant b9 b13 | |
| 2 035679E X susM7 | |
| 3 0234689 X dim7 | |
| 4 012467T X | |
| 5 013569E dimM7 melodic locrian | |
| 6 02458TE X M7+5 | |
| 7 023689T X | |
| 17 7-21B -- harmonic lydian #9 -- a subset of messiaen's mode 3 | |
| 1 034678E M7 harmonic lydian #9 | |
| 2 0134589 X | |
| 3 023478E X mM7 | |
| 4 012569T X | |
| 5 014589E M7+5 major b9 #5 | |
| 6 03478TE X M7+5 | |
| 7 0145789 X | |
| 18 7-21 -- dominant b9 #5 -- a subset of messiaen's mode 3 | |
| 1 014589T 7+5 dominant b9 #5 | |
| 2 034789E X M7+5 | |
| 3 0145689 X | |
| 4 034578E M7 harmonic major #9 | |
| 5 0124589 X | |
| 6 013478E X mM7 | |
| 7 02367TE X mM7 | |
| 19 7-27B -- augmented M7 b9 -- | |
| 1 014689E M7+5 augmented M7 b9 | |
| 2 03578TE X | |
| 3 0245789 X | |
| 4 023567T X m7-5 | |
| 5 013458T X | |
| 6 023479E X mM7 | |
| 7 012579T X | |
| 20 7-26B -- augmented dominant b9 -- a subset of messiaen's mode 3 | |
| 1 014689T 7+5 augmented dominant b9 | |
| 2 035789E X | |
| 3 0245689 X | |
| 4 023467T X m7-5 | |
| 5 012458T X | |
| 6 013479E X mM7 | |
| 7 02368TE X | |
| 21 7-19B -- major #9 b5 -- a subset of messiaen's mode 4 | |
| 1 034569E M7-5 major #9 b5 | |
| 2 0123689 X | |
| 3 012578E X | |
| 4 01467TE X M7 | |
| 5 03569TE X | |
| 6 0236789 X | |
| 7 014567T X 7-5 | |
| 22 7-18 -- harmonic major #9 b5 -- | |
| 1 034568E M7-5 harmonic major #9 b5 | |
| 2 0123589 X | |
| 3 012478E X | |
| 4 01367TE X mM7 | |
| 5 02569TE X | |
| 6 034789T X 7+5 | |
| 7 0145679 X | |
| 23 7-19 -- dominant #9 b5 -- a subset of messiaen's mode 4 | |
| 1 034569T 7-5 dominant #9 b5 | |
| 2 0123679 X | |
| 3 012568E X | |
| 4 01457TE X M7 | |
| 5 03469TE X | |
| 6 0136789 X | |
| 7 025678E X susM7 | |
| 24 7-26 -- lydian dominant #9 b13 -- a subset of messiaen's mode 3 | |
| 1 034678T 7 lydian dominant #9 b13 | |
| 2 0134579 X | |
| 3 023468E X dimM7 | |
| 4 012469T X | |
| 5 013589E X | |
| 6 02478TE X M7+5 | |
| 7 025689T X | |
| 25 7-27 -- mixolydian #9 b13 -- | |
| 1 034578T 7 mixolydian #9 b13 | |
| 2 0124579 X | |
| 3 013468E X dimM7 | |
| 4 02357TE X mM7 | |
| 5 013589T X | |
| 6 024789E X M7+5 | |
| 7 025679T X sus7 | |
| 26 7-24 -- dominant #9 b5 b13 -- | |
| 1 034568T 7-5 dominant #9 b5 b13 | |
| 2 0123579 X | |
| 3 012468E X | |
| 4 01357TE X mM7 | |
| 5 02469TE X | |
| 6 024789T X 7+5 | |
| 7 025678T X sus7 | |
| --- James McCartney 2014 |
What is the differentiation between th "T" and the "E" at he octave? Probably something obvious, but I'm not getting it. Really great resource!
T = ten semitones. minor 7th above root. Sometimes the character A is used.
E = eleven semitones. major 7th above root. Sometimes the character B is used.
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melodic minor's mode 7 fails the viability test because the 4th degree is a major 3rd (or a diminished fourth) which is not allowed by the test. It is used in jazz as the altered dominant scale since it includes b9, #9, b5, #5, and 1,3,7 of a dominant chord. Viability is mainly meant to separate normal from weird, but that does not mean the set is not useful in some way.