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.
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
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