Set Theory, Derivation, and Transformational Structures in Analyzing Webern’s Opus 10, Number 4

Abstract

This chapter shows how effectively transformational networks, and transformational motifs more generally, can interact with the ideas and approaches of Allen Forte's set theory. It considers a certain family of objects: a hexarchord H with characteristic subpentachord X, the complementary hexachord h with characteristic subpentachord y, and partitions of the total chromatic into H and h forms. As the music progresses, these objects are transposed or inverted more or less en masse, yielding a transformational network that organizes pertinent events over the entire piece. H, h, X, and y are all symmetrical sets. The chapter then looks at symmetrical structures: partitions of the total chromatic by trichordal derivations, an all-combinatorial hexachord Q associated with those partitions, and a characteristic symmetrical pentachord P of Q.