Music Walk, Fractal Geometry in Music

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Title:	Music Walk, Fractal Geometry in Music
Authors:	Zhi-Yuan Su Tzuyin Wu
Contributors:	資訊管理系
Keywords:	Music walk Fractal Fractional Brownian motion (fBm) Long-range correlation Hurst exponent Power spectrum
Date:	2007-07
Issue Date:	2010-01-11 11:12:42 (UTC+8)
Abstract:	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 the 1/fβ-type spectrum (fractal property), with apparently two different β values in two different temporal scales.
Relation:	Physica A: Statistical Mechanics and its Applications 380(1) ： p.418-428
Appears in Collections:	[Dept. of Information Management] Periodical Articles

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