On The Mathematics of Musical Measures and Their Relation to Geometry

The musical measures have been of primary importance throughout the history of music, because it is thanks to this tool that music is written and through it is performed and disseminated, however, those who study music formally understand the musical measures as only a tool to write and represent mu...

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Autores:
Lugos Abarca, Josué Alexis
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
spa
OAI Identifier:
oai:repository.eafit.edu.co:10784/33448
Acceso en línea:
https://hdl.handle.net/10784/33448
Palabra clave:
Musical measures
geometry
equations
rhythmic figures
areas of geometric figures
Compases musicales
geometría
ecuaciones
figuras rítmicas
áreas de figuras geométricas
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License
Copyright © 2023 Josué Alexis Lugos Abarca
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spelling Centro Universitario de Música FermattaLugos Abarca, Josué Alexis20232024-02-19T18:43:26Z20232024-02-19T18:43:26Z2346-48792346-4738https://hdl.handle.net/10784/3344810.17230/ricercare.2023.16.2The musical measures have been of primary importance throughout the history of music, because it is thanks to this tool that music is written and through it is performed and disseminated, however, those who study music formally understand the musical measures as only a tool to write and represent music, therefore, in this article we investigate the musical measures from another perspective: through mathematics, we will look for expressions that are able to describe the musical measures and thus find a new way to study them, in the second part, as a consequence, a possible analog to the Pythagorean theorem is constructed, which gives us the basis to begin to develop part of the geometry from the unique use of musical variables such as tempo, the rhythmic break, the time of a song and the number of measures.Los compases musicales han sido de suma importancia durante toda la historia de la música, pues es gracias a esta herramienta que se escribe la música y que a través de ella se ejecuta y se divulga, no obstante, aquellos quienes estudian la música de manera formal entendemos los compases musicales como sólo una herramienta para escribir y representar la música, por tanto, dentro de este artículo se investigan los compases musicales desde otra perspectiva: mediante las matemáticas, se buscaran expresiones que sean capaces de describir los compases musicales y así hallar una nueva forma de estudiarlos, en segunda parte, como consecuencia, se construye un posible análogo al teorema de Pitágoras lo que nos da las bases para empezar a desarrollar parte de la geometría a partir del uso único de variables musicales como el tempo, el quebrado rítmico, el tiempo de una canción y del número de compases.application/pdfspaUniversidad EAFIThttps://publicaciones.eafit.edu.co/index.php/ricercare/article/view/7497https://publicaciones.eafit.edu.co/index.php/ricercare/article/view/7497Copyright © 2023 Josué Alexis Lugos AbarcaopenAccessLibre accesohttp://purl.org/coar/access_right/c_abf2Ricercare, No. 16 (2023)On The Mathematics of Musical Measures and Their Relation to GeometrySobre la matemática de los compases musicales y su relación con la geometríaarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Musical measuresgeometryequationsrhythmic figuresareas of geometric figuresCompases musicalesgeometríaecuacionesfiguras rítmicasáreas de figuras geométricasRicercare162758ORIGINALon-the-mathematics-of-musical.pdfTexto completoapplication/pdf3737758https://repository.eafit.edu.co/bitstreams/d511706f-5efc-4d90-a77a-8a9b8a755943/downloadcb50bb01246fe77646e60c8afa698ff8MD51THUMBNAILminaitura-ricercare_Mesa de trabajo 1.jpgCarátulaimage/jpeg182034https://repository.eafit.edu.co/bitstreams/0d67df3c-484c-476d-a1cf-b95d57f37bfc/downloada0d2ce2dd3fc2bd2c5aa7702f779f7ceMD5210784/33448oai:repository.eafit.edu.co:10784/334482024-02-21 11:31:43.602open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv On The Mathematics of Musical Measures and Their Relation to Geometry
dc.title.spa.fl_str_mv Sobre la matemática de los compases musicales y su relación con la geometría
title On The Mathematics of Musical Measures and Their Relation to Geometry
spellingShingle On The Mathematics of Musical Measures and Their Relation to Geometry
Musical measures
geometry
equations
rhythmic figures
areas of geometric figures
Compases musicales
geometría
ecuaciones
figuras rítmicas
áreas de figuras geométricas
title_short On The Mathematics of Musical Measures and Their Relation to Geometry
title_full On The Mathematics of Musical Measures and Their Relation to Geometry
title_fullStr On The Mathematics of Musical Measures and Their Relation to Geometry
title_full_unstemmed On The Mathematics of Musical Measures and Their Relation to Geometry
title_sort On The Mathematics of Musical Measures and Their Relation to Geometry
dc.creator.fl_str_mv Lugos Abarca, Josué Alexis
dc.contributor.author.spa.fl_str_mv Lugos Abarca, Josué Alexis
dc.contributor.spa.fl_str_mv Centro Universitario de Música Fermatta
dc.subject.keyword.eng.fl_str_mv Musical measures
geometry
equations
rhythmic figures
areas of geometric figures
topic Musical measures
geometry
equations
rhythmic figures
areas of geometric figures
Compases musicales
geometría
ecuaciones
figuras rítmicas
áreas de figuras geométricas
dc.subject.keyword.spa.fl_str_mv Compases musicales
geometría
ecuaciones
figuras rítmicas
áreas de figuras geométricas
description The musical measures have been of primary importance throughout the history of music, because it is thanks to this tool that music is written and through it is performed and disseminated, however, those who study music formally understand the musical measures as only a tool to write and represent music, therefore, in this article we investigate the musical measures from another perspective: through mathematics, we will look for expressions that are able to describe the musical measures and thus find a new way to study them, in the second part, as a consequence, a possible analog to the Pythagorean theorem is constructed, which gives us the basis to begin to develop part of the geometry from the unique use of musical variables such as tempo, the rhythmic break, the time of a song and the number of measures.
publishDate 2023
dc.date.issued.none.fl_str_mv 2023
dc.date.available.none.fl_str_mv 2024-02-19T18:43:26Z
dc.date.accessioned.none.fl_str_mv 2024-02-19T18:43:26Z
dc.date.none.fl_str_mv 2023
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
publishedVersion
info:eu-repo/semantics/publishedVersion
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.spa.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 2346-4879
2346-4738
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10784/33448
dc.identifier.doi.none.fl_str_mv 10.17230/ricercare.2023.16.2
identifier_str_mv 2346-4879
2346-4738
10.17230/ricercare.2023.16.2
url https://hdl.handle.net/10784/33448
dc.language.iso.none.fl_str_mv spa
language spa
dc.relation.isversionof.none.fl_str_mv https://publicaciones.eafit.edu.co/index.php/ricercare/article/view/7497
dc.relation.uri.none.fl_str_mv https://publicaciones.eafit.edu.co/index.php/ricercare/article/view/7497
dc.rights.eng.fl_str_mv Copyright © 2023 Josué Alexis Lugos Abarca
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.accessrights.eng.fl_str_mv openAccess
dc.rights.acceso.spa.fl_str_mv Libre acceso
rights_invalid_str_mv Copyright © 2023 Josué Alexis Lugos Abarca
openAccess
Libre acceso
http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad EAFIT
dc.source.spa.fl_str_mv Ricercare, No. 16 (2023)
institution Universidad EAFIT
bitstream.url.fl_str_mv https://repository.eafit.edu.co/bitstreams/d511706f-5efc-4d90-a77a-8a9b8a755943/download
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repository.name.fl_str_mv Repositorio Institucional Universidad EAFIT
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