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dc.contributor.advisorBarth, Eric J., 1964-
dc.contributor.authorArnett, Jacob
dc.date.accessioned2013-01-29T19:32:22Z
dc.date.available2013-01-29T19:32:22Z
dc.date.issued2012
dc.identifier.urihttp://hdl.handle.net/10920/28205
dc.descriptionv, 20 p.en_US
dc.description.abstractIn 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 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.format.mimetypeapplication/pdf
dc.language.isoen_USen_US
dc.publisherKalamazoo Collegeen_US
dc.relation.ispartofKalamazoo College Mathematics Senior Individualized Projects Collection
dc.relation.ispartofseriesSenior Individualized Projects. Mathematics.;
dc.rightsU.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.
dc.titleGeneralizations of the Tonnetzen_US
dc.typeThesisen_US
KCollege.Access.ContactIf you are not a current Kalamazoo College student, faculty, or staff member, email dspace@kzoo.edu to request access to this thesis.


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  • Mathematics Senior Individualized Projects [249]
    This collection includes Senior Individualized Projects (SIP's) completed in the Mathematics Department. Abstracts are generally available to the public, but PDF files are available only to current Kalamazoo College students, faculty, and staff.

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