Voice-leading transformation and generative theories of tonal structure

Abstract

Numerous generative approaches to explaining tonal structure and/or Schenker’s theories have been proposed since Babbitt noted a resemblance between Schenker’s analytical method and Chomskian generative grammars in 1965. One of the more challenging features of Schenker’s theory to replicate in a generative system is the interaction of counterpoint and hierarchy. Many theorists, such as Lerdahl and Jackendoff, skirt the problem by developing non-contrapuntal systems, meaning ones that do not allow for layers with conflicting hierarchical descriptions.

This article tackles the counterpoint problem by first proposing a dynamic model for tonal hierarchy, which matches the usage of basic Schenkerian symbols (slurs and beams), and differs from the representational model used by Lerdahl and Jackendoff and others. I then summarize Schenker’s argument for a contrapuntal theory of tonal structure and show that this implies a relativity of contrapuntal voices to structural level which necessitates a theory of voice-leading transformation. This concept of voice-leading transformation marks a crucial turning point in Schenker’s analytical practice leading directly to his theory of levels, and is fundamental to understanding his late theory. The article also operationalizes the idea of voice-leading transformations within a generative system, and illustrates it with short analyses of themes from Bach’sPartitasand an extended analysis of the Menuetto from Beethoven’s Op. 21 Piano Sonata. In the latter analysis the concept of voice-leading transformation facilitates the discovery of an exceptional feature in the deep middleground of the piece.