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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 . These modes are sometimes referred to as the whole step/half-step diminished scale and the half-step/whole step diminished scale, respectively. [10]
Half diminished scale: Half diminished scale on C. ... Octatonic scale: Octatonic scales on C. ... Whole tone scale on C.
The whole-tone and octatonic scales have enjoyed quite widespread use since the turn of the 20th century, particularly by Debussy (the whole-tone scale) and Stravinsky (the octatonic scale). The symmetry inherent in these modes (which means no note can be perceived as the tonic ), together with certain rhythmic devices, Messiaen described as ...
For this reason it is sometimes called a "diminished" scale, though in jazz theory this term is also applied to the octatonic scale. This interval is enharmonically equivalent to the augmented fourth found between scale degrees 1 and 4 in the Lydian mode and is also referred to as the tritone .
Sometimes called the octatonic scale because it contains eight tones, the diminished scale is composed of a series of alternating half and whole steps. There are two types of diminished scales, one starts with a half step and the other starts with a whole step. The two scales are modes of one another.
For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern W–W–H–W–W–W–H, where W stands for whole step (an interval spanning two semitones, e.g. from C to D), and H stands for half-step (e.g. from C to D ♭).
The composer Olivier Messiaen called the whole-tone scale his first mode of limited transposition. The composer and music theorist George Perle calls the whole-tone scale interval cycle 2, or C2. Since there are only two possible whole-tone-scale positions (that is, the whole-tone scale can be transposed only once), it is either C2 0 or C2 1.
The most common distance model is the 1:2, also known as the octatonic scale (set type 8-28), followed by 1:3 and 1:5, also known as set type 4-9, which is a subset of the 1:2 model. [5] Set type 4-9 has also been referred to as a "Z-Cell." [6]