The smaller of the two diatonic intervals which encompass 7 degrees of the of the diatonic scale. The minor-7th is composed of 4 tones (i.e., whole-tones) and 2 diatonic semitones, and is one chromatic semitone smaller than the major-7th.
_______ minor-7th _______
| |
C D E F G A B C
t s t t t s
M2 m2 M2 M2 M2 m2
minor-7th = 4t + 2s = 4(t-s) + 6s
= 4(M2) + 2(m2) = 4(+1) + 6(m2)
Thus, the minor-7th contains 4 chromatic semitones and 6 diatonic semitones (or equivalently, 4 augmented-primes and 6 minor-2nds). In 12-edo, the minor-7th encompasses 10 equal semitones.
Narrowing the minor-7th by one more chromatic semitone results in the diminished-7th.
Aside from the strict diatonic usage defined above, "minor-7th" may denote any interval in the range of 1000 cents.
Some minor 7ths commonly found in just intonation are:
type ratio ~cents
just minor-7th 9/5 1017.596288 (~= 10173/5)
pythagorean minor-7th 16/9 996.0899983 (~= 9961/11)
harmonic 7th 7/4 968.8259065 (~= 9685/6)
The standard 12-edo minor-7th is 2(10/12) = exactly 1000 cents.
All chain-of-5th type tunings have a true minor-7th of -2 generators (5ths), and also an augmented-6th of +10 generators. In all tunings of the meantone family, the true minor-7th is quite wider than the harmonic-7th, but in most meantones the augmented-6th is a good approximation of the harmonic-7th. 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). Here are some typical examples:
-- minor-7th (= -2 generators) -- -- augmented-6th (= +10 generators) --
meantone 2,3,5-monzo ~cents 2,3,5-monzo ~cents
1/4-comma [ 2 0 , -1/2 > 1006.843143 [- 5 0 , 5/2 > 965.7842847
1/5-comma [12/5 -2/5, -2/5 > 1004.692514 [- 7 2 , 2 > 976.5374295
1/6-comma [ 8/3 -2/3, -1/3 > 1003.258761 [-25/3 10/3, 5/3 > 983.7061927
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