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Z-relation, or rather, "that certain pitch-class collections share the — George Perle

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"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 Fortes concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2 (1990)."
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George Perle
George Perle
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George Perle was an American composer and music theorist. As a composer, his music was largely atonal, using methods similar to the twelve-tone technique of the Second Viennese School. This serialist style, and atonality in general, was the subject of much of his theoretical writings. His 1962 book, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern rema

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"Do we really have to look these chords up in Fortes catalog in order to find a name for them? Another theorist [Christopher Hasty] assures us that, Allen Fortes 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."
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George Perle
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"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 significance 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."
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George Perle
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"The achievement of such a change of register through a sequential progression is a familiar procedure in the music of the "common practice." The significant distinction is that where Berg subdivides the registral span into equal, i.e., cyclic, intervals, his tonal predecessors subdivide it, in changing register through sequential transference, into the unequal intervals of the diatonic scale. As I pointed out in my last lecture, however, the qualitative transformation in the language of music which we have experienced in our century has a long prehistory. Beginning with Schubert, we occasionally find normal diatonic functions questioned in changes of key that progress along the intervals of the whole-tone scale, or the diminished-7th chord, or the augmented triad. An even more radical example of a cyclic progression in a tonal composition is...from Wagner (Die Walkure, Act III)."
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George Perle
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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 Schoenbergs 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)."
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George Perle

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"I should say that when people talk about capitalism its a bit of a joke. Theres no such thing. No country, no business class, has ever been willing to subject itself to the free market, free market discipline. Free markets are for others. Like, the Third World is the Third World because they had free markets rammed down their throat. Meanwhile, the enlightened states, England, the United States, others, resorted to massive state intervention to protect private power, and still do. Thats right up to the present. I mean, the Reagan administration for example was the most protectionist in post-war American history. Virtually the entire dynamic economy in the United States is based crucially on state initiative and intervention: computers, the internet, telecommunication, automation, pharmaceutical, you just name it. Run through it, and you find massive ripoffs of the public, meaning, a system in which under one guise or another the public pays the costs and takes the risks, and profit is privatized. Thats very remote from a free market. Free market is like what India had to suffer for a couple hundred years, and most of the rest of the Third World."
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Noam Chomsky
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"I am dominated by one thing, an irresistible, burning attraction towards the abstract. The expression of human feelings and the passions of man certainly interest me deeply, but I am less concerned with expressing the motions of the soul and mind than to render visible, so to speak, the inner flashes of intuition which have something divine in their apparent insignificance and reveal magic, even divine horizons, when they are transposed into the marvellous effects of pure plastic art."
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