Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited

Septimal Comma


    The ratio 64/63, in JustMusic prime-factor notation designated as 3271, with an interval size of approximately 0.27 Semitones [= ~ 27.264 cents].

    It is the difference between the Pythagorean or 3-Limit "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:

    50/49 [= 527-2 = ~ 34.976 cents]
    49/48 [= 3-172 = ~ 35.697 cents]
    36/35 [= 325-17-1 = ~ 48.770 cents]
    225/224 [= 32527-1 = ~ 7.712 cents]

    although it has been suggested that the last ratio listed would more appropriately be called a kleisma, because it is quite a bit smaller than other commas and close in size to a kleisma.

    [from Joe Monzo, JustMusic: A New Harmony]

    [with thanks to Kami Rousseau]

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