Parametric Interaction in Tonal Repertoires

Abstract

All theories of structure in tonal music must balance the competing claims to priority of multiple musical parameters. Most prominently, the study of tonal form has long concerned itself with how to reconcile the at times contradictory demands of thematic design and tonal structure: which is more important? With their different answers to this fundamental question, the resulting theories are as divergent as Heinrich Schenker's near-total emphasis on tonal structure and J. C. Lobe's equally single-minded interest in thematic design. A related and equally important question concerns how independent these two parameters are from one another: in different accounts they range from completely independent to strongly—even necessarily—correlated. This article argues that these two questions are not logically independent of each other, because a strong correlation between parameters precludes the judgment that one parameter is nevertheless much more important than the other. To this end, the geometric space known as the ternary plot is introduced, within which all coherent claims about the interaction of two parameters in a repertoire can be represented; the ternary plot also serves as a valuable device for comparing theories that differ in the relative importance or independence of tonal structure and thematic design. The article further argues that claims of these kinds are proper not to individual musical works but to musical repertoires, suggesting a definition of form in tonal music as always comparative and context dependent. Illustrating these claims, repertoires of Viennese string quartet minuets and piano pieces by Chopin are analyzed.