Tempo relations: Is there a psychological basis for proportional tempo theory?

Abstract

This paper is devoted to experimental research in the field of tempo performance. Epstein (1979, 1995) proposed that in a piece of music all tempo relations can be expressed by low order whole number ratios 1:1, 1:2, 2:3, and 3:4 (or the inverse). This theory relates to the Gestalt concept, in that it deals with part/whole relations and coherence of multipart pieces of music. We designed our study to look for possible underlying psychological mechanisms. The experiment addressed the question, which temporal ratios between neighboring tempi occur when subjects are asked to make arbitrary tempo modulation. Subjects were instructed to make tempo changes defined by vague terms like sma//, large, and arbitrary modulation. The finger tapping method was employed. Theoretically, a random continuum of ratios can appear. However, the results showed that tempo ratios were characterized by narrow distributions of the values. Subjects rarely responded with whole number ratios. Averaged values show that in slow down conditions (except arbitrary), the responses were close to whole number ratios; while in speed up conditions, deviations from whole number ratios were greater. We assume that results for speed up conditions were influenced by systematic temporal error. We propose that the relations between neighboring tempi may better be described in terms of categories of tempo difference.