Diminished scale
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In music, a diminished scale is a scale in which the notes of the scale ascend in alternating intervals of a whole step and a half step. Because a scale constructed in such a way has eight tones (versus seven for conventional scales), it is sometimes called an eight-tone or octatonic scale (there are other possible eight-tone scales, but the diminished is by far the most common). The latter term was first introduced by Arthur Berger in 1963. The name diminished comes from the fact that the first, third, fifth, and seventh notes of a diminished scale for a key form the diminished chord for that key. Found by Arab musicians in 800, called "Zer ef Kend", see Joseph Schillinger: The Mathematical Basis Of The Arts.
Because of the half-whole symmetry, there are only three distinct diminished scales, and 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 alternate starting points listed in parentheses, the three are:
- D♭ diminished (E, G, B♭ diminished): D♭, E♭, E, F#, G, A, B♭, C, D♭
- D diminished (F, A♭, B diminished): D, E, F, G, A♭, B♭, B, C#, D
- E♭ diminished (G♭, A, C diminished): E♭, F, F#, G#, A, B, C, D, E♭
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Diminished_scales_on_Db,_D,_and_Eb.PNG
Diminished scales on Db, D, and Eb, ascending
(Note: the flat symbol "♭" may not display properly on some browsers.)
The diminished scale may first have been used by Nikolai Rimsky-Korsakov, who describes his "discovery" in his My Musical Life, was extensively used by his student Igor Stravinsky, particularly in his famous piece The Rite of Spring, and by Alexander Scriabin.
Source
- Berger, Arthur (1963). Problems of Pitch Organization in Stravinsky. Perspectives of New Music II/I (Fall-Winter)
- van den Toorn, Pieter (1983). The Music of Igor Stravinsky. New Haven: Yale University Press.de:Verminderte Skala