I would not want you to suppose that my rejection of Allen Forte's theory of pitch-class sets implies a rejection of the notion that there can be such a thing as a pitch-class set. It is only when one defines everything in terms of pitch-class sets that the concept becomes meaningless.
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See: Allen ForteGeorge Perle
Z-relation, or rather, "that certain pitch-class collections share the same 'interval vector' even though they are neither transpositionally nor inversionally equivalent was first pointed out by Howard Hanson in Harmonic Materials of Modern Music (New York: Appleton-Century-Crofts, 1960), p. 22, and by David Lewin in "Re: The Intervallic Content of a Collection of Notes," Journal of Music Theory 4:1 (1960). For a general criticism of Forte's concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2 (1990).
George Perle
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 eigth-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 flucuation of pitch-class content while interval content remains constant' is what the rest of us have always known as 'a transposition.'
George Perle
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
The crucial and monumental development in the art music of our century has been the qualitative change in the foundational premises of our musical language--the change from a highly chromaticized tonality whose principle functions and operations are still based on a limited selection, the seven notes of the diatonic scale, from the universal set of twelve pitch classes to a scale that comprehends the total pitch-class content of that universal set. We can point to the moment of that change with some precision. It occurs most obviously in the music of Scriabin and the Vienna circle, Schoenberg, Webern, and Berg, in 1909-1910, and very soon afterwards, though less obviously, in the music of Bartok and Stravinsky. I think it is safe to say that nothing of comparable signifigance for music has ever occurred, because the closing of the circle of fifths gives us a symmetrical collection of all twelve pitch classes that eliminates the special structural function of the perfect fifth itself, which has been the basis of every real musical system that we have hitherto known.
George Perle
“I’m star-struck when I see Paul Scholes because you never see him. On the pitch you can’t catch him. Off the pitch he disappears.”
Paul Scholes
Perle, George
Perle, Richard
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