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Symbolic structures in music theory and composition, binary keyboards, and the Thue–Morse shift
Journal of Mathematics and Music ( IF 1.1 ) Pub Date : 2020-03-17 , DOI: 10.1080/17459737.2020.1732490
Ricardo Gómez 1 , Luis Nasser 2
Affiliation  

We address the broad idea of using mathematical models to inform music theory and composition by implementing them directly in the process of music creation. The mathematical model we will use is the Thue–Morse dynamical system. We briefly survey previously published works that were similarly motivated, and then discuss a new piece of music we composed, inspired by this symbolic dynamical system. In the course of our analysis, we also present an alternative proof of the well-know fact that the Thue–Morse subshift has topological entropy zero that motivated us to think of the map between binary sequences and musical scales as “binary keyboards.” Indeed, the binary representation allows to study musical scales through mathematical properties of the sequences that define them; here we present the set of standard Thue–Morse scales and compare them with other well-known musical scales.



中文翻译:

音乐理论和作曲中的符号结构、二进制键盘和 Thue-Morse 转变

我们通过在音乐创作过程中直接实施数学模型来解决使用数学模型为音乐理论和作曲提供信息的广泛思想。我们将使用的数学模型是Thue-Morse 动力系统。我们简要地调查了之前发表的具有类似动机的作品,然后讨论了我们创作的受这种象征性动力系统启发的新音乐。在我们的分析过程中,我们还提供了一个众所周知的事实的替代证明,即 Thue-Morse subshift 具有拓扑熵为零,这促使我们将二进制序列和音阶之间的映射视为“二进制键盘”。实际上,二进制表示允许通过定义它们的序列的数学特性来研究音阶;在这里,我们展示了一组标准的 Thue-Morse 音阶并将它们与其他著名的音阶进行比较。

更新日期:2020-03-17
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