Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Identifieur interne : 000039 ( Ncbi/Curation ); précédent : 000038; suivant : 000040Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Auteurs : Daniel J. Levitin [Canada] ; Parag Chordia ; Vinod MenonSource :
- Proceedings of the National Academy of Sciences of the United States of America [ 0027-8424 ] ; 2012.
Abstract
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/
Url:
DOI: 10.1073/pnas.1113828109
PubMed: 22355125
PubMed Central: 3309746
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Musical rhythm spectra from Bach to Joplin obey a 1/<italic>f</italic>
power law</title>
<author><name sortKey="Levitin, Daniel J" sort="Levitin, Daniel J" uniqKey="Levitin D" first="Daniel J." last="Levitin">Daniel J. Levitin</name>
<affiliation wicri:level="1"><nlm:aff id="aff1">Department of Psychology, School of Computer Science, and School of Music,<institution>McGill University</institution>
, Montreal, QC,<country>Canada</country>
H3A 1B1;</nlm:aff>
<country xml:lang="fr">Canada</country>
<wicri:regionArea># see nlm:aff country strict</wicri:regionArea>
</affiliation>
</author>
<author><name sortKey="Chordia, Parag" sort="Chordia, Parag" uniqKey="Chordia P" first="Parag" last="Chordia">Parag Chordia</name>
<affiliation><nlm:aff wicri:cut="; and" id="aff2">School of Music,<institution>Georgia Institute of Technology</institution>
, Atlanta,<addr-line>GA</addr-line>
30332</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Menon, Vinod" sort="Menon, Vinod" uniqKey="Menon V" first="Vinod" last="Menon">Vinod Menon</name>
<affiliation><nlm:aff id="aff3">Program in Neurosciences, Department of Psychiatry and Behavioral Sciences and Department of Neurology and Neurological Sciences,<institution>Stanford University</institution>
, Stanford,<addr-line>CA</addr-line>
94305</nlm:aff>
</affiliation>
</author>
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<idno type="doi">10.1073/pnas.1113828109</idno>
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<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Musical rhythm spectra from Bach to Joplin obey a 1/<italic>f</italic>
power law</title>
<author><name sortKey="Levitin, Daniel J" sort="Levitin, Daniel J" uniqKey="Levitin D" first="Daniel J." last="Levitin">Daniel J. Levitin</name>
<affiliation wicri:level="1"><nlm:aff id="aff1">Department of Psychology, School of Computer Science, and School of Music,<institution>McGill University</institution>
, Montreal, QC,<country>Canada</country>
H3A 1B1;</nlm:aff>
<country xml:lang="fr">Canada</country>
<wicri:regionArea># see nlm:aff country strict</wicri:regionArea>
</affiliation>
</author>
<author><name sortKey="Chordia, Parag" sort="Chordia, Parag" uniqKey="Chordia P" first="Parag" last="Chordia">Parag Chordia</name>
<affiliation><nlm:aff wicri:cut="; and" id="aff2">School of Music,<institution>Georgia Institute of Technology</institution>
, Atlanta,<addr-line>GA</addr-line>
30332</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Menon, Vinod" sort="Menon, Vinod" uniqKey="Menon V" first="Vinod" last="Menon">Vinod Menon</name>
<affiliation><nlm:aff id="aff3">Program in Neurosciences, Department of Psychiatry and Behavioral Sciences and Department of Neurology and Neurological Sciences,<institution>Stanford University</institution>
, Stanford,<addr-line>CA</addr-line>
94305</nlm:aff>
</affiliation>
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<series><title level="j">Proceedings of the National Academy of Sciences of the United States of America</title>
<idno type="ISSN">0027-8424</idno>
<idno type="eISSN">1091-6490</idno>
<imprint><date when="2012">2012</date>
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<front><div type="abstract" xml:lang="en"><p>Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/<italic>f</italic>
power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/<italic>f</italic>
<sup>β</sup>
power law across 16 subgenres and 40 composers, with β ranging from ∼0.5–1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/<italic>f</italic>
pitch spectra, demonstrated distinctive 1/<italic>f</italic>
rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/<italic>f</italic>
rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/<italic>f</italic>
spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/<italic>f</italic>
rhythms to give their compositions unique identities.</p>
</div>
</front>
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