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

IF 0.5 2区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematics and Music Pub Date : 2020-01-02 DOI:10.1080/17459737.2019.1610193

J. Rydén

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引用次数: 4

Abstract

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.

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论赋格主体的特点。巴赫与后来作曲家的比较

赋格的音乐形式激发了许多作曲家的创作灵感，尤其是为管风琴创作的作品。通过量化赋格主题，可以在统计基础上比较J.S.巴赫和后来时代的作曲家，先验地将作品分为三类。通过研究以下特征进行量化:长度，以所写音符的数量表示;音域(半音);音高类数;初始音程(半音);连续音符之间唯一音程的数目;连续音符之间的最大间隔(在半音中)构建了来自不同作曲家的主题数据集。主成分分析(PCA)使变异性的解释以及所有情况的可视化成为可能。引入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。关于主题的范围，巴赫和其他作曲家之间发现了统计学上显著的差异。此外，关于所使用的独特音符的数量，在所有作曲家类别之间发现了统计学上显著的差异。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics and Music 数学-数学跨学科应用

CiteScore

1.90

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematics and Music aims to advance the use of mathematical modelling and computation in music theory. The Journal focuses on mathematical approaches to musical structures and processes, including mathematical investigations into music-theoretic or compositional issues as well as mathematically motivated analyses of musical works or performances. In consideration of the deep unsolved ontological and epistemological questions concerning knowledge about music, the Journal is open to a broad array of methodologies and topics, particularly those outside of established research fields such as acoustics, sound engineering, auditory perception, linguistics etc.