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An octatonic scale is any eight-note musical scale. The scale most often meant by this term is one in which the notes ascend in alternating intervals of a whole step and a half step, creating a symmetric scale. In classical theory, in contradistinction to jazz theory, this scale is commonly simply called the octatonic scale (or octatonic collection), although there are forty-two other non-enharmonically equivalent, non-transpositionally equivalent eight-tone sets possible. In St. Petersburg at the turn of the 20th century, this scale had become so familiar in the circle of composers around Nikolai Rimsky-Korsakov that it was referred to there as the Korsakovian scale (Корсаковская гамма) . As early as 1911 the Russian theorist Boleslav Yavorsky described this collection of pitches as the diminished mode (уменьшенный лад), because of the stable way the diminished fifth functions in it , and in jazz theory it is called the diminished scale , or symmetric diminished scale , because it can be conceived as a combination of two interlocking diminished seventh chords, just as the augmented scale can be conceived as a combination of two interlocking augmented triads. In more recent Russian theory the term "octatonic" is not used. Instead this scale is placed among other symmetrical modes (total 11) under its historical name ''Rimsky-Korsakov scale'', or ''Rimsky-Korsakov mode'' (; ). Because it was associated in the early 20th century with the Dutch composer Willem Pijper, in the Netherlands it is called the Pijper scale . The earliest systematic treatment of the octatonic scale was Edmond de Polignac's unpublished treatise, "Etude sur les successions alternantes de tons et demi-tons (Et sur la gamme dite majeure-mineure)" from c. 1879 , which preceded Vito Frazzi's ''Scale alternate per pianoforte'' of 1930 by a full half-century . The term octatonic pitch collection was first introduced into English by Arthur Berger in 1963 . ==Construction and enumeration== The twelve tones of the chromatic scale are covered by three disjoint diminished seventh chords. The notes from exactly two such seventh-chords combination form an octatonic collection. Because there are exactly three ways to select two from three, there are exactly three octatonic scales in the twelve-tone system. Each octatonic scale has exactly two modes: the first begins its ascent with a whole step between its first two notes, while the second begins its ascent with a half step (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 . The three octatonic collections are transpositionally and inversionally symmetric—they are related by a variety of transposition and inversion operations: They are each closed under transpositions by 3, 6, or 9 semitones. A transposition by 1, 4, 7, or 10 semitones will transform the E scale into the D scale, the Db scale into the D scale, and the D scale into the E scale. Conversely, transpositions by 2, 5, 8, or 11 semitones acts in the reverse way; the E scale goes to the D scale, D to D and D to E. Thus, the set of transpositions acts on the set of diminished collections as the integers modulo 3. If the transposition is congruent to 0 mod 3 the pitch collection is unchanged and the transpositions by 1 semitone or by 2 semitones are inverse to one another. The E and D collections can be swapped by inversions around E, F, A or C (the tones common to both scales). Similarly, the D and D collections can be swapped by inversions around E, G, B, D/C and the D and E collections by inversions around D, F, A, or B. All other transformations do not change the classes (e.g. reflecting the Eb collection around E gives the E collection once again). This unfortunately means that the inversions do not act as a simple cyclic group on the set of diminished scales. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Octatonic scale」の詳細全文を読む スポンサード リンク
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