An interval composed of 3 tones (i.e., "whole-tones") and 3 diatonic-semitones. The diminished 7th occurs naturally in every diatonic harmonic-minor scale, between the "leading-tone" (7th degree or "VII") and the "submediant" (6th degree or "VI"). Example, in the key of A-minor ("t" = tone, "s" = semitone) :
m2 M2 m2 M2 M2 m2 +2 M2
s t s t t s t+s t
G# A B C D E F G# A
|_______________________|
diminished 7th
diminished-7th = 3t + 3s = 3(t-s) + 6s
= 3(M2) + 3(m2) = 3(+1) + 6(m2)
Thus, the diminished-7th contains 3 chromatic semitones and 6 diatonic semitones. In 12-edo, the diminished-7th encompasses 9 equal semitones, which makes it enharmonically equivalent to (i.e., exactly the same size as) the major-6th -- but the diminished-7th is not properly the same as the major-6th, and in all other tunings of the diatonic scale they are different intervals.
Use of the diminished-7th on top of a diminished-triad gives rise to the diminished-7th chord, which is commonly used in major keys as well as minor.
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