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On features of fugue subjects. A comparison of J.S. Bach and later composers
Journal of Mathematics and Music ( IF 1.1 ) Pub Date : 2019-05-17 , DOI: 10.1080/17459737.2019.1610193
Jesper Rydén 1
Affiliation  

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.



中文翻译:

论赋格题材。JS Bach和后来的作曲家的比较

赋格曲的音乐形式激发了许多作曲家的灵感,特别是为风琴创作的作品。通过量化赋格曲主题,可以在JS Bach和后来的作曲家之间基于统计学进行比较,先验将作品分为三类。通过研究以下特征来进行量化:长度,以书写笔记的数量表示;范围(以半音为单位);音调等级数;初始间隔(以半音为单位);连续音符之间唯一间隔的数量;连续音符之间的最大间隔(以半音为单位)。构建了来自不同作曲家的主题数据集。通过对主成分(PCA)的分析,可以解释变异性并可视化所有案例。引入了计数回归模型来研究作曲家之间的差异,考虑到对协变量的依赖。关于对象的范围,在巴赫和其他作曲家之间发现了统计学上的显着差异。此外,关于所用独特音符的数量,在所有作曲者类别之间发现了统计学上的显着差异。

更新日期:2019-05-17
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