Music walk, fractal geometry in music

Zhi-Yuan Su and Tzuyin Wu

Physica A: Statistical Mechanics and its Applications, 2007, vol. 380, issue C, 418-428

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.

Keywords: Music walk; Fractal; Fractional Brownian motion (fBm); Long-range correlation; Hurst exponent; Power spectrum (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:380:y:2007:i:c:p:418-428

DOI: 10.1016/j.physa.2007.02.079

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