<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1665-2436</journal-id>
<journal-title><![CDATA[Revista latinoamericana de investigación en matemática educativa]]></journal-title>
<abbrev-journal-title><![CDATA[Relime]]></abbrev-journal-title>
<issn>1665-2436</issn>
<publisher>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-24362023000100013</article-id>
<article-id pub-id-type="doi">10.12802/relime.23.2611</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Enseñanza interdisciplinaria música-matemática: la guitarra y su rol protagónico en el desarrollo histórico de la música occidental]]></article-title>
<article-title xml:lang="en"><![CDATA[Interdisciplinary Music-Mathematics teaching: The guitar and its leading role in the historical development of western music]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Espinoza Ramírez]]></surname>
<given-names><![CDATA[Lianggi]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vergara Gómez]]></surname>
<given-names><![CDATA[Andrea]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Católica del Maule  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<volume>26</volume>
<numero>1</numero>
<fpage>13</fpage>
<lpage>46</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362023000100013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362023000100013&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362023000100013&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El temperamento igual es la afinación estándar de instrumentos en Occidente y ha delineado nuestra actual manera de concebir la música. El propósito de esta investigación es explorar cómo los conocimientos puestos en uso y significados asociados al surgimiento histórico del temperamento igual en instrumentos antecesores a la guitarra pueden contribuir a un enfoque interdisciplinario para el aprendizaje de la matemática y la música. Para esto se realizó un análisis interpretativo del contenido del libro Armonía universal de Mersenne de 1637, y se estudió el proceso de génesis y desarrollo en el siglo XVI de los saberes presentes en este libro. Los resultados revelan que es posible repensar la enseñanza de algunos contenidos geométricos a nivel escolar, como el teorema de Euclides y la progresión geométrica, a partir del problema de la división proporcional del mástil de la guitarra. Se revela, además, que la noción de autosimilitud permitiría generar propuestas didácticas interdisciplinarias, que propicien una vinculación transversal entre la Matemática y la Música.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Equal temperament is the standard tuning for instruments in the West and has shaped our current way of thinking about music. The purpose of this research is to explore how the knowledge put to use and the meanings associated with the historical emergence of equal temperament, in instruments that preceded the guitar, can contribute to an interdisciplinary approach to learning mathematics and music. For this, an interpretative analysis of the content of the book Mersenne&#8217;s Universal Harmony of 1637 was carried out, and the process of genesis and development in the 16th century of the knowledge present in this book was studied. The results reveal that it is possible to rethink the teaching of some geometric contents at school level, such as Euclid&#8217;s theorem and geometric progression, based on the problem of the proportional division of the guitar neck. We also conclude that the notion of self-similarity would allow the generation of interdisciplinary didactic proposals that foster a transversal link between Mathematics and Music.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O temperamento igual é a afinação padrão para instrumentos no Ocidente e moldou nossa maneira atual de pensar sobre música. O objetivo desta pesquisa é explorar como o conhecimento posto em prática e os significados associados ao surgimento histórico do temperamento igualitário, em instrumentos que antecederam o violão, podem contribuir para uma abordagem interdisciplinar da aprendizagem da matemática e da música. Para isso, realizou-se uma análise interpretativa do conteúdo do livro A Harmonia Universal de Mersenne de 1637, e estudou-se o processo de gênese e desenvolvimento no século XVI do conhecimento presente neste livro. Os resultados revelam que é possível repensar o ensino de alguns conteúdos geométricos no nível escolar, como o teorema de Euclides e a progressão geométrica, a partir do problema da divisão proporcional do braço do violão. Concluímos também que a noção de auto-semelhança permitiria a geração de propostas didáticas interdisciplinares que fomentassem um vínculo transversal entre a Matemática e a Música.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé Le tempérament égal est l&#8217;accordage standard des instruments en Occident et a façonné notre façon actuelle de penser la musique. Le but de cette recherche est d&#8217;explorer comment les connaissances mises en &#339;uvre et les significations associées à l&#8217;émergence historique du tempérament égal, dans les instruments qui ont précédé la guitare, peuvent contribuer à une approche interdisciplinaire de l&#8217;apprentissage des mathématiques et de la musique. Pour cela, une analyse interprétative du contenu du livre L&#8217;Harmonie universelle de Mersenne de 1637 a été réalisée, et le processus de genèse et de développement au XVIe siècle des connaissances présentes dans ce livre a été étudié. Les résultats révèlent qu&#8217;il est possible de repenser l&#8217;enseignement de certains contenus géométriques au niveau scolaire, comme le théorème d&#8217;Euclide et la progression géométrique, à partir du problème de la division proportionnelle du manche de la guitare. Nous concluons également que la notion d&#8217;auto-similarité permettrait de générer des propositions didactiques interdisciplinaires favorisant un lien transversal entre les mathématiques et la musique.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Temperamento igual]]></kwd>
<kwd lng="es"><![CDATA[Relación Música-Matemática]]></kwd>
<kwd lng="es"><![CDATA[Guitarra]]></kwd>
<kwd lng="es"><![CDATA[Autosimilitud]]></kwd>
<kwd lng="en"><![CDATA[Equal temperament]]></kwd>
<kwd lng="en"><![CDATA[Music-Math relationship]]></kwd>
<kwd lng="en"><![CDATA[Guitar]]></kwd>
<kwd lng="en"><![CDATA[Self-similarity]]></kwd>
<kwd lng="pt"><![CDATA[Temperamento igual]]></kwd>
<kwd lng="pt"><![CDATA[Relação Música-Matemática]]></kwd>
<kwd lng="pt"><![CDATA[Violão]]></kwd>
<kwd lng="pt"><![CDATA[Autossimilaridade]]></kwd>
<kwd lng="fr"><![CDATA[Tempérament égal]]></kwd>
<kwd lng="fr"><![CDATA[Relation Musique-Mathématiques]]></kwd>
<kwd lng="fr"><![CDATA[Guitare]]></kwd>
<kwd lng="fr"><![CDATA[Autosimilitude]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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