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Encyclopedia of Microtonal Music Theory

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septimal-comma

[Joe Monzo, with Kami Rousseau]

The ratio 64/63, in JustMusic prime-factor notation designated as 3-27-1, with 2,3,5,7-monzo [6 -2, 0, -1>, and an interval size of approximately 0.27 Semitones [= ~ 27.264 cents].

It is the difference between the pythagorean or 3-limit "minor 7th" of approximately 9.96 Semitones [= 16/9 = 3-2 = ~ 996.089 cents] and the "harmonic 7th" of approximately 9.69 Semitones [= 7/4 = 71 = ~ 968.825 cents].

There are many other small septimal intervals which may be called commas, such as:

However, only the first two listed fall within the range of what is properly a "comma" -- it is more appropriate to call 36/35 a "septimal diesis", and to call 225/224 a "septimal kleisma", based on their size-relationships to other intervals with those names.