"By the time of his Fourth String Quartet, inversional symmetry had become as fundamental a premise of Bartók's harmonic language as it is of the twelve-tone music of Schoenberg, Berg, and Webern. Neither he nor they ever realized that this connection establishes a profound affinity between them in spite of the stylistic features that so obviously distinguish his music from theirs...Nowhere does he [Bartók] recognize the communality of his harmonic language with that of the twelve-tone composers that is implied in their shared premise of the harmonic equivalence of inversionally symmetrical pitch-class relations."
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As quoted in The Listening Composer (1990) by George Perle, p. 46-47, California: University of California Press. ISBN 0520069919 .Bela Bartok
By the time of his Fourth String Quartet, inversional symmetry had become as fundamental a premise of Bartók's harmonic language as it is of the twelve-tone music of Schoenberg, Berg, and Webern. Neither he nor they ever realized that this connection establishes a profound affinity between them in spite of the stylistic features that so obviously distinguish his music from theirs...Nowhere does he [Bartók] recognize the communality of his harmonic language with that of the twelve-tone composers that is implied in their shared premise of the harmonic equivalence of inversionally symmetrical pitch-class relations.
George Perle
"If...Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical partionings 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."
Alban Berg
If...[Alban] Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical partionings 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.
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
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
Bartok, Bela
Barton, Bruce Fairchild
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