Sets, Scales, and Symmetries: The Pitch-Structural Basis of George Crumb's "Makrokosmos" I and II

Abstract

Pitch-structural materials in George Crumb's Makrokosmos I and II include four basic trichordal set types from which larger sets are generated through various symmetrical dispositions of pcs. The largest collections correspond to whole-tone, pentatonic, and octatonic scale types. These materials are assimilated into a tightly interwoven complex of pc sets which offers not only a variety of pitch-structural units but also the potential for rigorously controlled interaction within the system. The primary materials are developed principally through symmetrical organizational schemes within which certain pc relationships function motivically in both local and long-range constructions. The resulting reticulated structures are illustrated in detailed analyses of “Primeval Sounds: Genesis I” from Volume I and “Voices from ‘Corona Borealis’” from Volume II.

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