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dc.contributor.authorPopoff, Alexandreen_US
dc.contributor.authorYust, Jasonen_US
dc.date.accessioned2021-03-19T14:30:37Z
dc.date.available2021-03-19T14:30:37Z
dc.identifier.citationAlexandre Popoff, Jason Yust. "Meter networks: a categorical framework for metrical analysis." Journal of Mathematics and Music, pp. 1 - 22. https://doi.org/10.1080/17459737.2020.1836687
dc.identifier.issn1745-9737
dc.identifier.issn1745-9745
dc.identifier.urihttps://hdl.handle.net/2144/42286
dc.description.abstractThis paper develops a framework based on category theory which unifies the simultaneous consideration of timepoints, metrical relations, and meter inclusion founded on the category Rel of sets and binary relations. Metrical relations are defined as binary relations on the set of timepoints, and the subsequent use of the monoid they generate and of the corresponding functor to Rel allows us to define meter networks, i.e. networks of timepoints (or sets of timepoints) related by metrical relations. We compare this to existing theories of metrical conflict, such as those of Harald Krebs and Richard Cohn, and illustrate that these tools help to more effectively combine displacement and grouping dissonance and reflect analytical claims concerning nineteenth-century examples of complex hemiola and twentieth-century polymeter. We show that meter networks can be transformed into each other through meter network morphisms, which allows us to describe both meter displacements and meter inclusions. These networks are applied to various examples from the nineteenth and twentieth century.en_US
dc.format.extentp. 1 - 22en_US
dc.languageen
dc.language.isoen_US
dc.publisherInforma UK Limiteden_US
dc.relation.ispartofJournal of Mathematics and Music
dc.subjectApplied mathematicsen_US
dc.subjectPerforming arts and creative writingen_US
dc.subjectMeteren_US
dc.subjectMetrical layeren_US
dc.subjectHemiolaen_US
dc.subjectTransformational networksen_US
dc.subjectBinary relationsen_US
dc.subjectCategory theoryen_US
dc.titleMeter networks: a categorical framework for metrical analysisen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1080/17459737.2020.1836687
pubs.elements-sourcecrossrefen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Fine Artsen_US
pubs.organisational-groupBoston University, College of Fine Arts, School of Musicen_US
pubs.publication-statusPublished onlineen_US
dc.date.online2020-11-22
dc.identifier.mycv589839


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