标题： 认真对待音乐：聚焦六音组定理的“数学音乐”研究动态 显示英文标题

标题： Taking Music Seriously: on the Dynamics of 'Mathemusical' Research with a Focus on Hexachordal Theorems

摘要： 在介绍了“数学音乐”动力学的一般框架之后，我们专注于一个音乐理论问题，即同构理论在音乐创作中的特殊应用，也就是米尔顿·巴比特的六音组定理。 我们简要讨论了同构结构的历史方面及其在晶体学、频谱分析和通过构建覆盖整数线的节奏赋格曲在音乐创作中的影响。 然后，我们提出了我们最近在题为“带有概率测度的度量空间中的新六音组定理”的论文中引入的巴比特结果的概率推广，并通过原始构造和示例来说明新方法。 显示英文摘要

摘要： 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.