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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]
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 ...
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.
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."
Piano line in the intro is octatonic, bass synth adds a ninth tone. Adi Morag "Octabones" (1999) Orbital; Oolaa from the Green Album. Suraj Synthesist Khayaal , a lil fantasy [16] [17] Gilad Hochman; Closer for two alto saxophones (2022) Polarizations for solo viola (2023) Dream Theater; The Dark eternal night [18]
This leads to scales with translational symmetry which include the octatonic scale (also known as the symmetric diminished scale; its mirror image is known as the inverse symmetric diminished scale [citation needed]) and the two-semitone tritone scale:
The Symphony for Organ and Orchestra established Copland as a serious modern composer. Musicologist Gayle Murchison posits that his use of the octatonic and whole-tone scales, polyrhythmic ostinato figures, and dissonant counterpoint proves his mastery of the modernist harmonic, rhythmic, and melodic techniques of the 1920s. [5]
Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.