SYMMETRY AND GOAL-DIRECTED MOTION IN MUSIC BY BÉLA BARTÓK AND GEORGE CRUMB

Abstract

Two of the most important goals for music composition during the past century were innovation and originality. In reaching for these goals, many composers abandoned tonal protocol, looking instead for new ways to generate coherence in their music. In the absence of traditional voice leading based on tonic/dominant harmony, some composers gravitated toward the use of symmetry. By symmetry I mean the projection of a series of events above and below, or forward and backward from a central axis, with a one-to-one correspondence between events on one side of the axis and those on the other. In this article, I will focus primarily on vertical symmetry in pitch space. Because horizontal symmetry often accompanies vertical symmetry, however, it cannot be set aside altogether. George Crumb's La luna está muerta, muerta… from Night of the Four Moons, for example, contains several symmetrical pitch collections, arranged in the manner of a balanced arch-form. As Ex. 1 illustrates, four pitch sets, comprising a single symmetrical interval series, occur over the course of the composition. The pitch sets in the first half of the composition, moreover, are presented in reverse order – and, hence, upside down – in the second half, transferring symmetry into the linear dimension; the events in the second half of the piece, that is, mirror those in the first half, just as the intervals above the pitch axis mirror those below it in each of the pitch collections.