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Encyclopedia of Microtonal Music Theory

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diminished-7th / dim7 / o7

[Joe Monzo]

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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