Some Formal Problems with Schenkerian Representations of Tonal Structure

Abstract

This paper is concerned with the type of data structures required for the accurate representation of tonal structure, in particular with the atomic/combinatorial nature of the non-terminal symbols within such representations. The theoretical commitments inherent in the form of Schenkerian representations will be examined, followed by a critical analysis of the consequences of these commitments for the descriptive adequacy of Schenkerian theory. Specifically, the structural phenomena examined here suggest that the form required of a successful tonal theory is a combinatorial syntax, an observation with important ramifications for the question of the computational architecture underlying our cognition of tonal music.

For an example of constituent structure trees within tonal theory, see Keiler [2].