认真对待音乐:以六和弦定理为重点的 "数学 "研究动态

Moreno Andreatta, C. Guichaoua, Nicolas Juillet
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引用次数: 0

摘要

在介绍了 "音乐 "动力学的一般框架之后,我们将重点讨论一个音乐理论问题,即米尔顿-巴比特(Milton Babbitt)的六和弦定理,该问题涉及将同调理论应用于音乐创作的一个特例。我们简要讨论了同调结构的一些历史方面及其在晶体学、频谱分析和音乐创作中的影响,即通过构建平铺整数线的节奏卡农。然后,我们介绍我们最近在一篇题为 "具有概率度量的度量空间中的新六和弦定理 "的论文中提出的巴比特结果的概率广义化,并用原创的构造和例子来说明这种新方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorems
After presenting the general framework of `mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly discuss some historical aspects of homometric structures and their ramifications in crystallography, spectral analysis and music composition via the construction of rhythmic canons tiling the integer line. We then present the probabilistic generalization of Babbitt's result we recently introduced in a paper entitled ''New hexachordal theorems in metric spaces with probability measure'' and illustrate the new approach with original constructions and examples.
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