Rydén, Jesper
- Department of Energy and Technology, Swedish University of Agricultural Sciences
Research article2020Peer reviewedOpen access
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
Journal of Mathematics and Music
2020, Volume: 14, number: 1, pages: 1-20 Publisher: TAYLOR & FRANCIS LTD
Probability Theory and Statistics
Music
DOI: https://doi.org/10.1080/17459737.2019.1610193
https://res.slu.se/id/publ/100670