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" "Collections of all twelve pitch classes can be differentiated from one another only by assigning an order to the pitch classes or by partitioning them into mutually exclusive sub-collections. The ordering principle is the basis of the twelve-tone system formulated by Schoenberg, the partitioning principle the basis of the system formulated around the same time by Hauer. In Schoenberg's compositional practice, however, the concept of a segmental pitch-class content is represented as well, as a basis for the association of paired inversionally related set forms. On the relation between Schoenberg and Hauer see Bryan R. Simms, "Who First Composed Twelve-Tone Music, Schoenberg or Hauer?" Journal of the Arnold Schoenberg Institute X/2 (November 1987).
George Perle (May 6, 1915 – January 23, 2009) was a composer and music theorist.
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If...[Alban] Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical partitionings of the major/minor system, he departs just as radically from the twelve-tone tradition that is represented in the music of Schoenberg and Webern, for whom the twelve-tone series was always an integral structure that could be transposed only as a unit, and for whom twelve-tone music always implied a constant and equivalent circulation of the totality of pitch classes.
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Do we really have to look these chords up in Forte's catalog in order to find a name for them? Another theorist [Christopher Hasty] assures us that, 'Allen Forte's perceptive interpretation...accounts for an essential quality of this mysteriously pulsating music. The eighth-note chords of the flute and clarinets form alternately, with the sustaining oboes and horns, the six-tone sonorities labeled A and B. The sonorities A and B are both representatives of the same set class (6-Z19) and are thus made up of precisely the same intervals. As Forte points out, "There is a flucuation of pitch-class content while interval content remains constant."' 'A fluctuation of pitch-class content while interval content remains constant' is what the rest of us have always known as 'a transposition.'