MozartV1, Main, Exploration, bibRecord, 000286

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

Identifieur interne : 000286 ( Main/Exploration ); précédent : 000285; suivant : 000287

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

Auteurs : Lu Liu ; Jianrong Wei ; Huishu Zhang ; Jianhong Xin ; Jiping Huang

Source :

PLoS ONE ; 2013.

RBID : PMC:3609771

English descriptors

KwdEn :
- Humans, Music, Physical Phenomena, Pitch Perception (physiology), Statistics as Topic.
MESH :
- physiology : Pitch Perception.
- Humans, Music, Physical Phenomena, Statistics as Topic.

Abstract

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.

Url:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3609771

DOI: 10.1371/journal.pone.0058710
PubMed: 23544047
PubMed Central: 3609771

Affiliations:

Le document en format XML

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

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

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Abstract

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