Properties
The twelve tones of the chromatic scale partition into three non-overlapping diminished seventh chords. A combination of any two, omitting the third, forms an octatonic collection. As there are three diminished-seventh chords that can be omitted, it follows that there are only three distinct diminished scales in the 12-tone system. Thus Olivier Messiaen considered it one of the modes of limited transposition, specifically, the second mode. A given diminished scale has only two modes: one beginning its ascent with a whole step between its first two notes, while the other begins its ascent with a half step or semitone.
Each of the three distinct scales can form differently named scales with the same sequence of tones by starting at a different point in the scale. With alternative starting points listed in parentheses, the three are:
- E♭ diminished (F♯/G♭, A, C diminished): E♭, F, F♯, G♯, A, B, C, D, E♭
- D diminished (F, A♭, B diminished): D, E, F, G, A♭, B♭, B, C♯, D
- D♭ diminished (E, G, B♭ diminished): D♭, E♭, E, F♯, G, A, B♭, C, D♭
It may also be represented as 0134679t or labeled as set class 8-28 (Schuijer 2008, p. 109).
Among the collection's remarkable features is that it is the only collection that can be disassembled into four transpositionally-related pitch pairs in six different ways, each of which features a different interval class (Cohn). For example:
- semitone: (C, C♯), (D♯, E) (F♯, G), (A, B♭)
- whole step: (C♯, D♯), (E, F♯), (G, A), (B♭, C)
- minor third:(C, E♭), (F♯, A), (C♯, E), (G, B♭)
- major third:(C, E), (F♯, B♭), (E♭, G), (A, C♯)
- perfect fourth: (C♯, F♯), (B♭, E♭), (G, C), (E, A)
- tritone: (C, F♯), (E♭, A), (C♯, G), (E, B♭)
Another remarkable feature of the diminished scale is that it contains first four notes of four minor scales separated by minor thirds. For Example: C, D, E♭, F and (enharmonically) F♯, G♯, A, B. Also E♭, F, G♭, A♭, and A, B, C, D.
The scale, "allows familiar harmonic and linear configurations such as triads and modal tetrachords to be juxtaposed unusually but within a rational framework" though the relation of the diatonic scale to the melodic and harmonic surface is thus generally oblique (Pople 1991, 2).
Read more about this topic: Octatonic Scale
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