On the relationship between tempo and quantitative metric, melodic, and harmonic information in Chopin's Prélude Op. 28 No. 4: A statistical analysis of 30 performances

We investigate the relationship between analytical information extracted from the score of Chopin's Prélude Op. 28 No. 4 and tempo curves obtained from 30 recordings by well-known pianists. The score-related information consists of metric, melodic, and harmonic weight functions. A hierarchic regression approach is used. The statistical analysis yields strong evidence for the approximate validity of an operator defined in terms of hierarchically decomposed weight functions, as originally introduced by G. Mazzola and J. Beran in 1997 ("Rational Composition of Performance." In: Regulation of Creative Processes in Music, edited by W. Auhagen and R. Kopiez, Staatliches Institut für Musikforschung, Berlin, pp. 37-67) in the context of Schumann's Träumerei. Further analysis based on these findings reveals some typical features of the performances.