minor 7th, minor seventh, m7

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

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]

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Updated:

2002.09.22 - page created

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