An exploration of "small-ratio" musical intervals, compared to equal temperament.

intervals.txt

An exploration of "small-ratio" musical intervals, compared to equal temperament.  Each interval has
a perfect ratio before the colon, and a number of semitones with a cents (100th of a semitone) correction
approximation.

This is study for playing the Haken Continuum.


Root:    1   : 0
P2:     9/8  : 2 +3c
Fourth: 4/3  : 5 -2c
Fifth:  3/2  : 7 +2c

Major:
    Maj3:  5/4  : 4   -13c
    Maj6:  5/3  : 9   -15c
    Dom7:  7/4  : 9.5 +18c   ***
    Maj7:  15/8 : 11  -11c

Minor:
    Min3:   6/5 : 3  +15c
    Min6:   8/5 : 8  +13c
    Min7:   9/5 : 10 +17c

Neutral:
    N3:     11/9  : 3.5  -2c   (distance from 1 to N3)
            27/22 : 3.5  +4c   (distance from N3 to 5)
    N6:     18/11 : 8.5  +3c
    N7:     11/6  : 10.5 -1c   (11/9 + fifth)
            81/44 : 10.5 +6c   (27/22 + fifth)

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Major intervals (maj3, maj6, dom7, maj7) are a little smaller than equal
         (dom7 is is closer to 3/4 flat from the major scale)
Minor intervals (min3, min6, min7) are a little bigger than equal
Neutral intervals are pretty much spot-on
-------------------------------------------------------------------------

Tritone (maj3 & dom7): 7/5 : 6 -17c

Diminshed second -- complement to maj Maj7
        16/15 : 1 +12c
"Neutral" second -- complement to N7
        12/11 : 1.5 +1c
"Minor" second -- complement to min7
        10/9 : 2 -17c
"Major" second -- complement to dom7
        8/7  : 2.5 -18c
"Mindom" third -- fifth down from dom7
        7/6 : 2.5 +17c