用群论解析24音微分音音乐的结构关系
Algebraic Structures in Microtonal Music
- 将24个等分音符编号，用群论描述音乐动作
- 揭示24音系统中和声与结构的代数规律
- 适合对音乐数学建模感兴趣的读者
本文探讨群论在音乐理论中的应用。西方音乐将八度均分为12个半音，可进一步将每个半音细分为两个四分音，形成24个等分音符。通过为每个音符赋值编号，可数学化地描述音乐行为。本研究分析24音微分音音乐系统，探索其中音乐与和声结构如何用群论框架解释。该工作拓展了Crans、Fiore与Satyendra的研究成果。
原文摘要 · Abstract (English)
We will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division further and split the octave into 24 equal tones by splitting each half-step in two, called a quarter-step. By assigning each of these 24 notes a number, we can discuss musical actions mathematically. In this paper, we analyze 24-tone microtonal music and explore how musical and harmonic structures in this system can be interpreted in terms of group-theoretic structures. This work extends the study by Crans, Fiore, and Satyendra.
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