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

• Published in: Journal of mathematics and music (Society for Mathematics and Computation in Music) Vol. 14; no. 1; pp. 1 - 20
• Main Author: Rydén, Jesper
• Format: Journal Article
• Language: English
• Published: Baton Rouge Taylor & Francis 02.01.2020; Taylor & Francis Ltd
• Subjects: Composers; fugue subject; generalised linear model; Music; Musik; pitch class; Poisson regression; principal components; Principal components analysis; Probability Theory and Statistics; range; Regression analysis; Regression models; Sannolikhetsteori och statistik; Statistical analysis; Statistical significance
• ISSN: 1745-9737; 1745-9745; 1745-9745
• DOI: 10.1080/17459737.2019.1610193

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.