PMID: 11607178Apr 15, 1991Paper

Self-similarity of the "1/f noise" called music

Proceedings of the National Academy of Sciences of the United States of America
K J Hsü, A Hsü

Abstract

Suggestions have been made that computer musicians should attempt to compose fractal music, and questions have been raised whether there is such a thing as fractal music. Voss and Clark observed that music is scaling, or 1/f noise, as analyzed on the basis of the amplitude (loudness) of the audio signals; they failed to find a fractal distribution of acoustic frequencies (music notes) in music. Analyzing Bach's and Mozart's compositions, we have shown that the incidence of the frequency intervals, or of the changes of acoustic frequency, has a fractal geometry. Fractal phenomena are characterized by scale-independency. The purpose of this investigation is to demonstrate the self-similarity of music and to explore its implications.

References

Feb 4, 1987·Nature·A Ellrodt, P Le Bras
Feb 4, 1987·Nature·J C HuttonM Peshavaria
Feb 1, 1990·Proceedings of the National Academy of Sciences of the United States of America·K J Hsü, A J Hsü

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Citations

Feb 23, 2012·Proceedings of the National Academy of Sciences of the United States of America·Daniel J LevitinVinod Menon
Jun 16, 2009·PloS One·Dan WuDe-Zhong Yao
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wentian Li, Dirk Holste
Nov 30, 2019·Scientific Reports·Ana Filipa Teixeira BorgesKlaus Linkenkaer-Hansen
Aug 6, 2020·Frontiers in Psychiatry·Federico E TurkheimerRobert Leech
Mar 19, 2021·Frontiers in Artificial Intelligence·Filippo Carnovalini, Antonio Rodà
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R S MendesE K Lenzi
Apr 20, 2021·Frontiers in Psychology·Mahdi MohseniChristoph Redies
Jul 14, 2021·Epilepsy & Behavior : E&B·Marjan RafieeTaufik A Valiante

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