Music walk, fractal geometry in music

被引：33

作者：

Su, Zhi-Yuan

Wu, Tzuyin ^{[1
]}

机构：

[1] Natl Taiwan Univ, Dept Engn Mech, Taipei 106, Taiwan

[2] Chia Nan Univ Pharm & Sci, Dept Informat Management, Tainan 717, Taiwan

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2007年 / 380卷 / 1-2期

关键词：

music walk; fractal; fractional Brownian motion (fBm); long-range correlation; Hurst exponent; power spectrum;

D O I：

10.1016/j.physa.2007.02.079

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this study, sequences of musical notes from various pieces of music are converted into one-variable random walks (here termed 'music walks'). Quantitative measurements of the properties of each musical composition are then performed by applying Hurst exponent and Fourier spectral analyses on these music-walk sequences. Our results show that music shares the similar fractal properties of a fractional Brownian motion (fBm). That is, music displays an anti-persistent trend in its tone changes (melody) over decades of musical notes; and music sequence exhibits generally the1/f(beta)-type spectrum (fractal property), with apparently two different beta values in two different temporal scales. (c) 2007 Elsevier B.V. All rights reserved.

引用

页码：418 / 428

页数：11

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