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Entropy of Fourier coefficients of periodic musical objects
Journal of Mathematics and Music ( IF 0.5 ) Pub Date : 2020-07-01 , DOI: 10.1080/17459737.2020.1777592
Emmanuel Amiot 1
Affiliation  

There are many ways to define and measure organization, or complexity, in music, most using the notion of informational entropy, as the opposite of organization. Some researchers prompted me to study whether it could be done from the magnitudes of Fourier coefficients of musical objects (pc-sets or rhythms) instead of addressing their atomic elements (pitches, rhythmic onsets). Indeed I found that it could be a promising new approach to measuring organization of musical material. This note only purports to expose this novel idea, leaving for future research the task of comparing it with the numerous other definitions. I also sketch the study of one relevant basis for such comparisons which has been little explored, the asymptotics of entropy of arithmetic sequences modulo n.



中文翻译:

周期性音乐对象的傅立叶系数的熵

有很多方法可以定义和衡量音乐中的组织或复杂性,大多数使用信息熵的概念作为组织的反面。一些研究人员促使我研究是否可以从音乐对象(PC 集或节奏)的傅立叶系数的大小来完成,而不是解决它们的原子元素(音高、节奏开始)。事实上,我发现它可能是一种很有前途的新方法来衡量音乐材料的组织。这篇笔记只是为了揭露这个新颖的想法,将它与众多其他定义进行比较的任务留给了未来的研究。我还概述了对此类比较的一个相关基础的研究,该基础很少被探索,即等差数列模n的熵的渐近性。

更新日期:2020-07-01
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