Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited

minor 7th, minor seventh, m7


    An interval in the range of 1000 cents (¢).

    Common minor 7ths in Just Intonation are:

  • 9/5 = ~1017.596288 (~10173/5) cents
  • the Pythagorean 16/9 = ~996.0899983 (~9961/11) cents
  • the 7/4 harmonic 7th = ~968.8259065 (~9685/6) cents

    • The standard 12edo "minor 7th" is 2(10/12) = exactly 1000 cents.

    1/4-comma meantone has a true "minor 7th" of -2 generators = 225(-1/2) = ~1006.843143 cents, and also an "augmented 6th" of +10 generators = 2-55(5/2) = ~965.7842847 cents. The latter is a good approximation of the 7/4 "harmonic 7th", and in fact this closeness of approximation is probably responsible for the popularity of the various "augmented 6th chords" ("Italian", "German", "French") in "common-practice" harmony, as is renders chords which are very concordant and approach the 4:5:6:7 proportion (or subsets or variations of it).

    1/5-comma meantone has a "minor 7th" of 2(12/5) 3(-2/5) 5(-2/5) = ~1004.692514 cents, and an "augmented 6th" of 2-7 32 52 = ~976.5374295 cents.

    1/6-comma meantone has a "minor 7th" of 2(8/3) 3(-2/3) 5(-1/3) = ~1003.258761 cents, and an "augmented 6th" of 2(-25/3) 3(10/3) 5(5/3) = ~983.7061927 cents.

    [from Joe Monzo, JustMusic: A New Harmony]

Updated:

2002.09.22 - page created

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