Octatonic scale

An octatonic scale is any eight-note musical scale. Among the most famous of these


is a scale 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, although there are


forty-two other non-enharmonically equivalent, non-transpositionally equivalent


eight-tone sets possible. In jazz theory this scale is more particularly called the


diminished scale (Campbell 2001, p. 126), or symmetric diminished scale (Hatfield


2005, p. 125), 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. 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of the octatonic scale was Edmond de Polignac's unpublished treatise, "Etude sur les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 (Kahan 2009), which preceded Vito Frazzi's Scale


alternate per pianoforte of 1930 by a full half-century (Sanguinetti 1993). The term


octatonic pitch collection was first introduced into English by Arthur Berger in 1963


(Van den Toorn 1983).


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 (non-transpositionally equivalent)


diminished scales in the 12-tone system. Thus Olivier Messiaen considered it one of


the modes of limited transposition. 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). T.






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:


Eb diminished (Fb/Gb, A, C diminished): Eb, F, F#, G#, A, B, C, D, Eb
D diminished (F, Ab, B diminished): D, E, F, G, Ab, Bb, B, C#, D
Db diminished (E, G, Bb diminished): Db, Eb, E, F#, G, A, Bb, C, Db




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, Bb)
whole step: (C#,D#), (E, F#), (G, A), (Bb, C)
minor third:(C, Eb), (F#, A), (C#, E), (G, Bb)
major third:(C, E), (F#, Bb), (Eb, G), (A, C#)
perfect fourth: (C#, F#), (Bb,Eb), (G,C), (E,A)
tritone: (C, F#), (Eb,A), (C#,G), (E, Bb)


Octatonic scales first occurred in Western music as byproducts of a series of


minor-third transpositions. Agmon locates one in the music of Scarlatti, from the


1730s. Langle's 1797 harmony treatise contains a sequential progression with a


descending octatonic bass, supporting harmonies that use all and only the notes of


an octatonic scale (p. 72, ex. 25.2). The question of when Western composers first


began to select octatonic scales as primary compositional material is difficult to


determine. One strong candidate is a recurring theme in Franz Liszt's Feux Follets,


the fifth of his first book of Etudes d'exécution transcendente (composed 1826, and


twice revised). See descending arpeggiated figures of bars 7 and 8, 10 and 11, 43,


45 through 48, 122, and 124 through 126. In turn, all three distinct octatonic scales


are used, respectively containing all, and only, the notes of each of these scales.


Jazz, Petrushka chord, Triads