Self-Similarity and Compositional Strategies in the Music of Milton Babbitt

Abstract

The unfolding of a compact algebraic group into a larger structure which exhibits an isomorphic relationship with the smaller group is the essence of "self-similarity." Through the use of transformational networks which take advantage of the group properties of the forty-eight canonical operators and through the examination of the hexachordally combinatorial properties of Babbitt's row forms, this paper examines the manner in which Babbitt selects and combines rows to produce maximal diversity on the surface while optimizing internal coherence at the deeper structural levels. This study focuses on three works that cover straightforward serial structures, simple array structures and superarray structures respectively — Babbitt's three main compositional strategies.