An octatonic scale is any eight-note musical scale. However, the term most often refers to the ancohemitonic symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetrical scale is commonly called the octatonic scale (or the octatonic collection), although there are a total of 43 enharmonically non-equivalent, transpositionally non-equivalent eight-note sets.
The earliest systematic treatment of the octatonic scale was in Edmond de Polignac's unpublished treatise "Étude sur les successions alternantes de tons et demi-tons (Et sur la gamme dite majeure-mineure)" (Study of the Succession of Alternating Whole Tones and Semitones (and of the so-called Major-Minor Scale)) from c. 1879, which preceded Vito Frazzi's Scale alternate per pianoforte of 1930 by a full half-century.
Nomenclature
In Saint 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 as the Korsakovian scale (Корсаковская гамма). As early as 1911, the Russian theorist Boleslav Yavorsky described this collection of pitches as the diminished mode (уменьшённый лад), because of the stable way the diminished fifth functions in it. 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.)
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. The two modes are sometimes referred to as the half-step/whole step diminished scale and the whole step/half-step diminished scale.
Because it was associated in the early 20th century with the Dutch composer Willem Pijper, in the Netherlands, it is called the Pijper scale.
Construction
The twelve tones of the chromatic scale are covered by three disjoint diminished seventh chords. The notes from two such seventh-chords combination form an octatonic collection. Because there are three ways to select two from three, there are three octatonic scales in the twelve-tone system.
Each octatonic scale has exactly two modes: the first begins its ascent with a whole step, while the second begins its ascent with a half step (semitone). These modes are sometimes referred to as the whole step/half-step diminished scale and the half-step/whole step diminished scale, respectively.
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 below in square brackets, and return to tonic in parentheses, the three are, ascending by semitones:
C D [E] F [G] A [A] B (C) D E [F] G [G] A [B] C (D) E F [G] A [A] B [C] D (E)
It may also be represented as semitones, either starting with a whole tone (as above): , or starting with a semitone: , or labeled as set class 8‑28.
With one more scale tone than present in the western diatonic scale, it is not possible to notate music in the octatonic scale in any conventional occidental key signature, without the use of accidentals. In any conventional key signature, at least one of the semitone steps must be written as two notes with the same letter/on the same line or space on the staff. (That is, there must be at least one note that regularly appears with two different accidentals.) There are usually several equally succinct combinations of key signature and accidentals, and different composers have chosen to notate their music differently, sometimes ignoring the niceties of notation conventions designed to facilitate diatonic tonality.
Properties
Symmetry
The three octatonic collections are transpositionally and inversionally symmetric—that is, they are related by a variety of transposition and inversion operations: