An Approach to Simultaneity in Twelve-Tone Music

Abstract

THE OVEREXTENSION and consequent weakening of the traditional tonal functions gave rise, prior to Schoenberg's formulation of his twelve-tone method, to a number of attempts to base a total musical structure upon a complex of functionally undifferentiated pitch elements. As examples, Debussy's Voiles, Scriabin's Seventh Sonata, and Roslavetz' Three Compositions for piano may be cited. Each of these works is based on sets comprising a selection of the notes of the chromatic scale. Scriabin's Seventh Sonata, for instance, is based on the following collection of seven notes and on transpositions of this collection:

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