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dc.contributor.authorYust, Jasonen_US
dc.contributor.editorMontiel, Marianaen_US
dc.contributor.editorPeck, Robert W.en_US
dc.date2017-11-22
dc.date.accessioned2020-01-09T21:10:27Z
dc.date.available2020-01-09T21:10:27Z
dc.date.issued2019-01-15
dc.identifier.citationJason Yust. 2019. "Geometric Generalizations of the Tonnetz and their Relation to Fourier Phase Space." Mathematical Music Theory. Hackensack, NJ: World Scientific. pp. 253 - 277. https://doi.org/10.1142/9789813235311_0013
dc.identifier.urihttps://hdl.handle.net/2144/39072
dc.description.abstractSome recent work on generalized Tonnetze has examined the topologies resulting from Richard Cohn’s common-tone based formulation, while Tymoczko has reformulated the Tonnetz as a network of voice-leading relationships and investigated the resulting geometries. This paper adopts the original common-tone based formulation and takes a geometrical approach, showing that Tonnetze can always be realized in toroidal spaces,and that the resulting spaces always correspond to one of the possible Fourier phase spaces. We can therefore use the DFT to optimize the given Tonnetz to the space (or vice-versa). I interpret two-dimensional Tonnetze as triangulations of the 2-torus into regions associated with the representatives of a single trichord type. The natural generalization to three dimensions is therefore a triangulation of the 3-torus. This means that a three-dimensional Tonnetze is, in the general case, a network of three tetrachord-types related by shared trichordal subsets. Other Tonnetze that have been proposed with bounded or otherwise non-toroidal topologies, including Tymoczko’s voice-leading Tonnetze, can be under-stood as the embedding of the toroidal Tonnetze in other spaces, or as foldings of toroidal Tonnetze with duplicated interval types.en_US
dc.format.extentpp. 253 - 277en_US
dc.publisherWorld Scientificen_US
dc.relation.ispartofMathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena
dc.titleGeometric generalizations of the Tonnetz and their relation to Fourier phase spaceen_US
dc.typeBook chapteren_US
dc.description.versionAccepted manuscripten_US
pubs.elements-sourcemanual-entryen_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-statusPublisheden_US
dc.identifier.mycv420724


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