Title:
Generalizations of the Tonnetz: tonality revisited
Authors:
Arnett, Jacob; Barth, Eric
Publisher:
Denison University
DATE ISSUED:
19-Nov-2011
PERMANENT LINK:
http://hdl.handle.net/2374.DEN/3575; http://hdl.handle.net/2374
Type:
Article
Language:
en_US
Description:
In this paper, we attempt to explore mathematical structures of tonal music from the 18th and 19th centuries. We review the known mathematical/musical structures and, noting lacking features of this geometrical construct as a useful model of tonal harmony, we propose generalizations that may be better suited to tonal music. We bring several mathematical devices to bear on the Tonnetz (or Tone Network) in new ways, including Cayley graphs and Coxeter hyperbolic representations. We conclude with three-dimensional geometric models that represent the four-note seventh chords which are ubiquitous in 18th and 19th century music.
Appears in Collections:
Proceedings: 2011 Midstates Conference for Undergraduate Research in Computer Science and Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorArnett, Jacoben
dc.contributor.authorBarth, Ericen
dc.coverage.spatialUSA - Ohio - Licking - Granvilleen_US
dc.date.accessioned2012-08-08T14:49:10Zen
dc.date.accessioned2013-12-18T22:13:24Z-
dc.date.available2012-08-08T14:49:10Zen
dc.date.available2013-12-18T22:13:24Z-
dc.date.created2011-11-19en
dc.date.issued2011-11-19en
dc.identifier.urihttp://hdl.handle.net/2374.DEN/3575en
dc.identifier.urihttp://hdl.handle.net/2374-
dc.descriptionIn this paper, we attempt to explore mathematical structures of tonal music from the 18th and 19th centuries. We review the known mathematical/musical structures and, noting lacking features of this geometrical construct as a useful model of tonal harmony, we propose generalizations that may be better suited to tonal music. We bring several mathematical devices to bear on the Tonnetz (or Tone Network) in new ways, including Cayley graphs and Coxeter hyperbolic representations. We conclude with three-dimensional geometric models that represent the four-note seventh chords which are ubiquitous in 18th and 19th century music.en_US
dc.language.isoen_USen_US
dc.publisherDenison Universityen_US
dc.relation.ispartofProceedings of the 2011 Midstates Conference on Undergraduate Research in Computer Science and Mathematicsen_US
dc.titleGeneralizations of the Tonnetz: tonality revisiteden_US
dc.typeArticleen_US
dc.contributor.institutionDenison Universityen_US
dc.contributor.repositoryDenison DRCen_US
dc.publisher.digitalDenison Universityen_US
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