“频谱和谐”：迈向音色与语音的统一——马勒与勋伯格梦想的解决
"Spectral Harmony" Towards the Unification of Timbre and Speech: Resolution of the Young Mahler Schoenberg Dream
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中文总结 AI 辅助
本文提出基于信息几何和巴拿赫空间的频谱序列化方法，统一音色与语音，解决勋伯格三大历史问题，并公开工具于GitHub。
中文摘要 AI 辅助
在本文中，我们提出了一种由古斯塔夫·马勒和阿诺德·勋伯格在19世纪末至20世纪初设想的频谱序列化方法，该方法能够实现基于音乐结构的音色选择。基于信息几何，我们评估了多声部音色频谱之间的Wasserstein距离，如我们之前的论文所示，该距离以包含三个或更多音符的频谱和弦的二阶矩（以平方赫兹表示）来表达。通过将这些量嵌入巴拿赫空间，我们从音色角度分析了理查·施特劳斯、马勒、阿尔班·贝尔格和安东·韦伯恩作品中的特定段落，展示了同一和弦如何因配器不同而表现出不同的亲和力与发散性。以哇哇弱音器为例，我们提出了一个在同一巴拿赫空间中处理乐器音色和语音的模型，并尝试量化“元音三角形”（以赫兹为单位）。这些努力构成了对勋伯格历史三大问题——序列主义、音色旋律和念唱——的部分但综合的解决方案，这些问题在马勒和勋伯格有生之年，以及包括诺诺、布列兹和施托克豪森在内的战后一代作曲家中，都未能完全解决。我们旨在从音色角度重新审视整个音乐思维，并为诠释、演奏和作曲开辟新的可能性。所有工具均在GitHub上公开提供，以便任何人都能复现和扩展这些分析。
英文摘要
In this article, we present a method of spectral serialization envisioned by G. Mahler and A. Schoenberg between the late 19th and early 20th centuries that enables the selection of timbres rooted in musical structure. Based on information geometry, we evaluate the Wasserstein distance between polyphonic timbre spectra, as demonstrated in our previous paper, in terms of the second moment of spectral chords comprising three or more notes, expressed in squared hertz. By embedding these quantities in a Banach space, we analyze specific passages from works by R. Strauss, Mahler, A. Berg, and A. Webern from the perspective of timbre, showing how the same chord exhibits different affinities and divergences depending on orchestration. Taking the wah wah mute as an example, we propose a model that treats instrumental timbre and speech within the same Banach space, and we attempt to quantify the "vowel triangle" in Hz. These efforts constitute a partial but integrated solution to the historical three problems of Schoenberg. Serialism, Klangfarbenmelodie, and Sprechgesang which neither Mahler nor Schoenberg in their lifetimes, nor the postwar generation of composers including Nono, Boulez, and Stockhausen, was able to resolve fully. We aim to reconsider musical thought as a whole from the perspective of timbre and to open new possibilities for interpretation, performance, and composition. All tools are publicly available on GitHub, so that anyone can reproduce and extend these analyses.
发表机构
- The University of Tokyo（东京大学）
- Hiroshima International University（广岛国际大学）
机构由 AI 辅助整理，请以论文原文为准。
