A Tonnetz model for pentachords

Autores
Piovan, Luis Amadeo
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/I class. It is a generalization of the well known Öttingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.
Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina
Materia
TONNETZ
NEO-RIEMANN NETWORK
PENTACHORD
CONTEXTUAL GROUP
TESSELLATION
POINCARÉ DISK
DAVID LEWIN
CHARLES KOECHLIN
IGOR STRAVINSKY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/10112
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/10112
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A Tonnetz model for pentachordsPiovan, Luis AmadeoTONNETZNEO-RIEMANN NETWORKPENTACHORDCONTEXTUAL GROUPTESSELLATIONPOINCARÉ DISKDAVID LEWINCHARLES KOECHLINIGOR STRAVINSKYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/I class. It is a generalization of the well known Öttingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); ArgentinaTaylor & Francis Ltd2013-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/10112Piovan, Luis Amadeo; A Tonnetz model for pentachords; Taylor & Francis Ltd; Journal Of Mathematics And Music; 7; 1; 4-2013; 29-531745-9737enginfo:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/17459737.2013.769637info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1301.4255info:eu-repo/semantics/altIdentifier/doi/10.1080/17459737.2013.769637info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:01:18Zoai:ri.conicet.gov.ar:11336/10112instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:01:18.651CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Tonnetz model for pentachords
title A Tonnetz model for pentachords
spellingShingle A Tonnetz model for pentachords
Piovan, Luis Amadeo
TONNETZ
NEO-RIEMANN NETWORK
PENTACHORD
CONTEXTUAL GROUP
TESSELLATION
POINCARÉ DISK
DAVID LEWIN
CHARLES KOECHLIN
IGOR STRAVINSKY
title_short A Tonnetz model for pentachords
title_full A Tonnetz model for pentachords
title_fullStr A Tonnetz model for pentachords
title_full_unstemmed A Tonnetz model for pentachords
title_sort A Tonnetz model for pentachords
dc.creator.none.fl_str_mv Piovan, Luis Amadeo
author Piovan, Luis Amadeo
author_facet Piovan, Luis Amadeo
author_role author
dc.subject.none.fl_str_mv TONNETZ
NEO-RIEMANN NETWORK
PENTACHORD
CONTEXTUAL GROUP
TESSELLATION
POINCARÉ DISK
DAVID LEWIN
CHARLES KOECHLIN
IGOR STRAVINSKY
topic TONNETZ
NEO-RIEMANN NETWORK
PENTACHORD
CONTEXTUAL GROUP
TESSELLATION
POINCARÉ DISK
DAVID LEWIN
CHARLES KOECHLIN
IGOR STRAVINSKY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/I class. It is a generalization of the well known Öttingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.
Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina
description This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/I class. It is a generalization of the well known Öttingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.
publishDate 2013
dc.date.none.fl_str_mv 2013-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/10112
Piovan, Luis Amadeo; A Tonnetz model for pentachords; Taylor & Francis Ltd; Journal Of Mathematics And Music; 7; 1; 4-2013; 29-53
1745-9737
url http://hdl.handle.net/11336/10112
identifier_str_mv Piovan, Luis Amadeo; A Tonnetz model for pentachords; Taylor & Francis Ltd; Journal Of Mathematics And Music; 7; 1; 4-2013; 29-53
1745-9737
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.tandfonline.com/doi/abs/10.1080/17459737.2013.769637
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1301.4255
info:eu-repo/semantics/altIdentifier/doi/10.1080/17459737.2013.769637
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis Ltd
publisher.none.fl_str_mv Taylor & Francis Ltd
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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