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A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling

Because classical music has greatly affected our life and culture in its long history, it has attracted extensive attention from researchers to understand laws behind it. Based on statistical physics, here we use a different method to investigate classical music, namely, by analyzing cumulative dist...

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Detalles Bibliográficos
Autores principales: Liu, Lu, Wei, Jianrong, Zhang, Huishu, Xin, Jianhong, Huang, Jiping
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3609771/
https://www.ncbi.nlm.nih.gov/pubmed/23544047
http://dx.doi.org/10.1371/journal.pone.0058710
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author Liu, Lu
Wei, Jianrong
Zhang, Huishu
Xin, Jianhong
Huang, Jiping
author_facet Liu, Lu
Wei, Jianrong
Zhang, Huishu
Xin, Jianhong
Huang, Jiping
author_sort Liu, Lu
collection PubMed
description Because classical music has greatly affected our life and culture in its long history, it has attracted extensive attention from researchers to understand laws behind it. Based on statistical physics, here we use a different method to investigate classical music, namely, by analyzing cumulative distribution functions (CDFs) and autocorrelation functions of pitch fluctuations in compositions. We analyze 1,876 compositions of five representative classical music composers across 164 years from Bach, to Mozart, to Beethoven, to Mendelsohn, and to Chopin. We report that the biggest pitch fluctuations of a composer gradually increase as time evolves from Bach time to Mendelsohn/Chopin time. In particular, for the compositions of a composer, the positive and negative tails of a CDF of pitch fluctuations are distributed not only in power laws (with the scale-free property), but also in symmetry (namely, the probability of a treble following a bass and that of a bass following a treble are basically the same for each composer). The power-law exponent decreases as time elapses. Further, we also calculate the autocorrelation function of the pitch fluctuation. The autocorrelation function shows a power-law distribution for each composer. Especially, the power-law exponents vary with the composers, indicating their different levels of long-range correlation of notes. This work not only suggests a way to understand and develop music from a viewpoint of statistical physics, but also enriches the realm of traditional statistical physics by analyzing music.
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spelling pubmed-36097712013-03-29 A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling Liu, Lu Wei, Jianrong Zhang, Huishu Xin, Jianhong Huang, Jiping PLoS One Research Article Because classical music has greatly affected our life and culture in its long history, it has attracted extensive attention from researchers to understand laws behind it. Based on statistical physics, here we use a different method to investigate classical music, namely, by analyzing cumulative distribution functions (CDFs) and autocorrelation functions of pitch fluctuations in compositions. We analyze 1,876 compositions of five representative classical music composers across 164 years from Bach, to Mozart, to Beethoven, to Mendelsohn, and to Chopin. We report that the biggest pitch fluctuations of a composer gradually increase as time evolves from Bach time to Mendelsohn/Chopin time. In particular, for the compositions of a composer, the positive and negative tails of a CDF of pitch fluctuations are distributed not only in power laws (with the scale-free property), but also in symmetry (namely, the probability of a treble following a bass and that of a bass following a treble are basically the same for each composer). The power-law exponent decreases as time elapses. Further, we also calculate the autocorrelation function of the pitch fluctuation. The autocorrelation function shows a power-law distribution for each composer. Especially, the power-law exponents vary with the composers, indicating their different levels of long-range correlation of notes. This work not only suggests a way to understand and develop music from a viewpoint of statistical physics, but also enriches the realm of traditional statistical physics by analyzing music. Public Library of Science 2013-03-27 /pmc/articles/PMC3609771/ /pubmed/23544047 http://dx.doi.org/10.1371/journal.pone.0058710 Text en © 2013 Liu et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Liu, Lu
Wei, Jianrong
Zhang, Huishu
Xin, Jianhong
Huang, Jiping
A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title_full A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title_fullStr A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title_full_unstemmed A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title_short A Statistical Physics View of Pitch Fluctuations in the Classical Music from Bach to Chopin: Evidence for Scaling
title_sort statistical physics view of pitch fluctuations in the classical music from bach to chopin: evidence for scaling
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3609771/
https://www.ncbi.nlm.nih.gov/pubmed/23544047
http://dx.doi.org/10.1371/journal.pone.0058710
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