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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

A musical scale with 8 tones per octave is called an octatonic scale.

octatonic diminished scale

In the familiar 12-edo tuning, there are 3 possible octatonic scales of the diminished family, all of them composed of interlaced pairs of "diminished-7th" chords. The intervals between degrees in these scales are alternating Large (L) and (s) steps (which in this tuning are synonymous with tone and semitone, respectively).

In the diagram below, integers which designate the degrees of 12-edo (where C = 0) are given under the letter-names. In the case of "black-key" notes, the letter-names are arbitrarily chosen (i.e., in 12edo, C#=Db etc., so either could be used). L = 2 degrees, s = 1 degree.

  L  s  L  s  L  s  L  s

C  D  Eb F  F# G# A  B  (C)
0  2  3  5  6  8  9  11

C# D# E  F# G  A  Bb C  (C#)
1  3  4  6  7  9  10 0

D  E  F  G  G# A# B  C# (D)
2  4  5  7  8  10 11 1

These 12-edo octatonic scales may also be thought of as being composed of two identical disjunct tetrachords, a tritone apart, separated by a "semitone of disjunction".

s     > semitone of disjunction
L     \
   A   \
s       tetrachord
   G#  /
L     /
s     > semitone of disjunction
L     \
   Eb  \
s       tetrachord
   D   /
L     /
. . . . . . . . .

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