发表机构
The University of Tokyo; Hiroshima International University（东京大学; 广岛国际大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出几何和声学科，将乐器音色作为元素，利用Wasserstein距离与偏差扩展传统音乐理论框架，并以单簧管喉音G为例说明其在合奏中的实用价值。
AI 中文摘要
本文介绍了“几何和声”这一学科，该学科明确处理音乐音域的频谱特征。从文艺复兴时期到现在的西方音乐框架，以“音高”来表示声音，这一点从五线谱记谱体系中可见一斑，且采用基频作为代表值，如440 Hz等。本文中，我们将特定乐器的音色作为元素，研究两个声部之间的Wasserstein距离，以及三个及以上声部之间的Wasserstein偏差，证明可以在保留传统音乐理论整个框架的同时扩展该体系。同时，作为合奏演奏实用价值的实例，我们详细说明了单簧管上“喉音G”这一在合奏中以脆弱性著称的音符的两声部亲和性。
英文摘要
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.
Comments21 pages, 15 figures
