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 influence 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.