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Research article - Peer-reviewed, 2020

On features of fugue subjects. A comparison of JS Bach and later composers

Ryden, Jesper


The musical form fugue has inspired many composers, in particular writing for the organ. By quantifying a fugue subject, comparisons can be made on a statistical basis between J.S. Bach and composers from later epochs, a priori dividing works into three categories. The quantification is made by studying the following features: length, expressed in number of notes written; range (in semitones); number of pitch classes; initial interval (in semitones); number of unique intervals between successive notes; maximum interval between successive notes (in semitones). A data set of subjects from various composers was constructed. An analysis of principal components (PCA) makes possible an interpretation of the variability as well as a visualisation of all cases. Regression models for counts are introduced to investigate differences between composers, taking into account dependence on covariates. Concerning the range of the subject, a statistically significant difference was found between Bach and other composers. Furthermore, regarding the number of unique notes employed, a statistically significant difference was found between all composer categories.


principal components; generalised linear model; Poisson regression; fugue subject; range; pitch class

Published in

Journal of Mathematics and Music
2020, volume: 14, number: 1, pages: 1-20

Authors' information

Swedish University of Agricultural Sciences, Department of Energy and Technology

UKÄ Subject classification

Probability Theory and Statistics

Publication Identifiers


URI (permanent link to this page)