Sammanfattning

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.

Nyckelord

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

Publicerad i

Journal of Mathematics and Music
2020, Volym: 14, nummer: 1, sidor: 1-20
Utgivare: TAYLOR & FRANCIS LTD

SLU författare

• Rydén, Jesper

  • Institutionen för energi och teknik, Sveriges lantbruksuniversitet
    

UKÄ forskningsämne

Sannolikhetsteori och statistik
Musik


Publikationens identifierare

DOI: https://doi.org/10.1080/17459737.2019.1610193

Permanent länk till denna sida (URI)

https://res.slu.se/id/publ/100670