Analyzing musical structure and performance—a statistical approach

Abstract

Musical performance theory and the theory of musical structure in general is a rapidly developing field of musicology that has wide practical implications. Due to the complex nature of music, statistics is likely to play an important role. In spite of this, up to the present, applications of statistical methods to music have been rare and mostly limited to a formal confirmation of results obtained by other methods. The present paper introduces a statistical approach to the analysis of metric, melodic and harmonic structures of a score and their inuence on musical performance. Examples by Schumann, Webern and Bach illustrate the proposed method of numerical encoding and hierarchical decomposition of score information. Application to performance data is exemplified by the analysis of tempo data for Schumann’s “Träumerei” op. 15/7. The paper demonstrates why statistics should play a major active part in performance research. The results obtained here are only a starting point and should, hopefully, stimulate a fruitful discussion between statisticians, musicologists, computer scientists and other researchers interested in the area. © 1999 Institute of Mathematical Statistics.