用几何方法量化音色差异，拓展传统音乐理论体系
Klangfarbenakkord and Klangfarbenharmonien Metric Space Models for Music on Informational Geometry 1
- 以乐器音色为元素，用Wasserstein距离度量声音间差异
- 验证了在保留传统乐理框架下扩展音色表达的可行性
- 适合音乐信息论、声学建模与跨乐器合奏研究者
本文提出“几何和声”这一新范式，明确关注音乐音域的频谱特征。西方音乐自文艺复兴以来始终以“音高”为核心，通过五线谱记谱系统体现，并以基频如440 Hz作为代表值。本文以特定乐器的音色为基本单元，考察两声部间的Wasserstein距离及三声部以上的Wasserstein偏离度，证明在不破坏传统音乐理论整体架构的前提下，可实现对音色维度的系统性扩展。同时，以单簧管的“喉音G”为例，详细分析其在合奏中因音色脆弱性导致的双声部亲和性问题，展示了该方法在实际合奏中的应用潜力。
原文摘要 · Abstract (English)
This paper deals with the introduction of "geometric harmony", a discipline that explicitly addresses the spectral characteristics of musical gamut. The framework of Western music, from Renaissance to the present, represents sound in terms of "pitch"-as is evident from its five-line staff notation system-and employs the fundamental frequency as its representative value, 440 Hz, etc. In this paper, by taking the timbres of specific individual instruments as elements and examining the Wasserstein distance between two voices, and Wasserstein deviations between three or more voices, we demonstrate that it is possible to expand the system whilst retaining the entire framework of conventional music theory. At the same time, as an example of practical utility in ensemble playing, we provide a detailed account of the two-voices affinity of the "Throat G" on clarinet, a note known for its fragility in ensemble contexts.
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