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).
Vertical and horizontal lines are the expression of two opposing forces; they exist everywhere and dominate everything; their reciprocal action constitutes ‘life’. I recognized that the equilibrium of any particular aspect of nature rests on the equivalence of its opposites.Piet Mondrian
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
Bourgeois society is ruled by equivalence. It makes dissimilar things comparable by reducing them to abstract quantities. For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry.E. Jephcott, trans., p. 4 (Sourced)
Bourgeois society is ruled by equivalence. It makes dissimilar things comparable by reducing them to abstract quantities. For the Enlightenment, anything which cannot be resolved into numbers, and ultimately into one, is illusion; modern positivism consigns it to poetry.Horkheimer and Adorno (1947) Dialectic of Enlightenment, E. Jephcott, trans. 1972, p. 4
There are two ways in which the avoidance of trivialism can fail . One is to accept the classical equivalence of negation - and absolute inconsistency.Dov M. Gabbay, Franz Guenthner, in Handbook of Philosophical Logic, Volume 11, Springer, 31 March 2004, p.273
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