音乐组合,tonnetz和立方和声

Maria Mannone, Eri Kitamura, Jiawei Huang, Ryo Sugawara, Y. Kitamura
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引用次数: 0

摘要

本文概述了几个世纪以来组合学和排列学在音乐中的一些应用。排列和tonnetz(声音引导和调制的空间表征)的概念可以在一个物理设备中结合在一起,这就是魔方,一个音乐版本的魔方。我们最后描述了一个立方体谐波的原型,它使用了东北大学开发的磁跟踪技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Musical combinatorics, tonnetz, and the CubeHarmonic
In this paper, we give an overview of some applications of combinatorics and permutations in music through the centuries. The concepts of permutation and tonnetz (spatial representation of voice leading and modulation) can be joined together in a physical device, the CubeHarmonic, a musical version of the Rubik's cube. We finally describe a prototype of the CubeHarmonic that uses the magnetic tracking technology developed at the Tohoku University.
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