{"id":1932,"date":"2019-05-15T16:18:44","date_gmt":"2019-05-15T19:18:44","guid":{"rendered":"https:\/\/www.sabra.org.br\/site\/?p=1932"},"modified":"2025-04-20T19:17:19","modified_gmt":"2025-04-20T22:17:19","slug":"matematica-e-musica","status":"publish","type":"post","link":"https:\/\/www.sabra.org.br\/site\/matematica-e-musica\/","title":{"rendered":"Matem\u00e1tica e M\u00fasica"},"content":{"rendered":"<h2>Matem\u00e1tica e M\u00fasica: Como relacionar os dois?<\/h2>\n<p>Pode ser que voc\u00ea n\u00e3o goste de <strong>matem\u00e1tica<\/strong>, mas, com certeza, voc\u00ea gosta de <strong>m\u00fasica<\/strong>. O que muitas pessoas desconhecem \u00e9 que a <strong>m\u00fasica<\/strong> tem tudo a ver com a <strong>matem\u00e1tica<\/strong>.<\/p>\n<p>Grandes matem\u00e1ticos, como Erat\u00f3stenes, Arist\u00f3xenes e Arquitas, por exemplo, desenvolveram te\u00f3ricas matem\u00e1ticas que est\u00e3o sendo utilizadas at\u00e9 o s\u00e9culo XX. Mas eles foram al\u00e9m e tamb\u00e9m eram grandes te\u00f3ricos da <strong>m\u00fasica<\/strong>.<\/p>\n<p>Mesmo que as escalas musicais tenham surgido em diferentes civiliza\u00e7\u00f5es, como a Greco-Romana, que come\u00e7ou a compor pe\u00e7as musicais por meio de um sistema que usava o alfabeto grego, foram Erat\u00f3stenes, Arist\u00f3xenes e Arquitas que se tornaram conhecidos como os respons\u00e1veis pela inven\u00e7\u00e3o das escalas.<\/p>\n<p>A raz\u00e3o \u00e1urea, que \u00e9 um n\u00famero irracional, serviu como molde para que esses pensadores pudessem criar as escalas.<\/p>\n<h2>As notas musicais como fra\u00e7\u00f5es<\/h2>\n<p>A sequ\u00eancia musical, tal como: D\u00f3; R\u00e9; Mi; F\u00e1; Sol; L\u00e1; Si e D\u00f3, foi chamada de gama pitag\u00f3rica, em respeito a Pit\u00e1goras, fil\u00f3sofo e matem\u00e1tico. Dependendo da vibra\u00e7\u00e3o de uma corda de viol\u00e3o, essas notas podem ser representadas por meio de uma fra\u00e7\u00e3o. Por exemplo:<\/p>\n<p>\u2022 D\u00f3: 1\/2<br \/>\n\u2022 R\u00e9: 8\/9<br \/>\n\u2022 Mi: 6\/81<br \/>\n\u2022 F\u00e1: 3\/4<br \/>\n\u2022 Sol: 2\/3<br \/>\n\u2022 L\u00e1: 16\/27<br \/>\n\u2022 Si: 128\/243<br \/>\n\u2022 D\u00f3: 1\/2<\/p>\n<p>Os adeptos das teorias de Pit\u00e1goras gostavam de usar n\u00fameros de dois a tr\u00eas. Isso porque, segundo eles, atrav\u00e9s desses n\u00fameros poderia ser criado qualquer outro n\u00famero. Logo, esses n\u00fameros n\u00e3o s\u00f3 faziam parte da <strong>matem\u00e1tica<\/strong>, como tamb\u00e9m da <strong>m\u00fasica<\/strong>.<\/p>\n<p>Embora as fra\u00e7\u00f5es representadas acima j\u00e1 tenham sofrido modifica\u00e7\u00f5es ao longo do tempo, continuam sendo utilizadas fra\u00e7\u00f5es para representar as notas musicais.<\/p>\n<h2><strong>Matem\u00e1tica<\/strong> facilita o aprendizado da <strong>m\u00fasica<\/strong><\/h2>\n<p>Se o objetivo \u00e9 aprender <strong>m\u00fasica<\/strong>, \u00e9 muito prov\u00e1vel que a <strong>matem\u00e1tica<\/strong> apare\u00e7a no caminho. Para os grandes estudiosos musicais, por exemplo, a <strong>matem\u00e1tica<\/strong> \u00e9 indispens\u00e1vel. Compreender a estrutura musical se torna mais f\u00e1cil, al\u00e9m de ser poss\u00edvel assimilar outras formas de se ouvir <strong>m\u00fasica<\/strong>.<\/p>\n<p>Conceitos matem\u00e1ticos que ainda hoje se utilizam na <strong>matem\u00e1tica<\/strong> s\u00e3o: \u00e1lgebra abstrata, teoria dos conjuntos e teoria dos n\u00fameros. Mesmo que sejam conceitos individuais, a <strong>matem\u00e1tica<\/strong> e <strong>m\u00fasica<\/strong> possuem liga\u00e7\u00e3o.<\/p>\n<p>Quando se observa os ritmos musicais, por exemplo, o tempo e as suas divis\u00f5es (que s\u00e3o conceitos matem\u00e1ticos) aparecem. Frequ\u00eancias, sons e timbres tamb\u00e9m possuem ra\u00edzes matem\u00e1ticas e est\u00e3o presentes na <strong>m\u00fasica<\/strong>, bem como os compassos, que s\u00e3o tempos que se repetem.<\/p>\n<h2>O c\u00e9rebro humano adora calcular e combinar sons<\/h2>\n<p>A <strong>m\u00fasica<\/strong> n\u00e3o surgiu do nada e nada mais \u00e9 que uma organiza\u00e7\u00e3o num\u00e9rica combinada. E quem interpreta isso \u00e9 o nosso c\u00e9rebro. Por isso, quem \u00e9 m\u00fasico mesmo sem querer acaba fazendo c\u00e1lculos subliminares.<\/p>\n<p>O c\u00e9rebro humano aprecia calcular. Desse modo, quanto mais se pratica mais se conhece <strong>m\u00fasica<\/strong> e se estuda, e mais se desenvolve essa capacidade. \u00c9 nesse momento que se come\u00e7a a sentir uma sensa\u00e7\u00e3o agrad\u00e1vel ao ouvir m\u00fasicas que, anteriormente, n\u00e3o faziam diferen\u00e7a.<\/p>\n<p>Por outro lado, a <strong>m\u00fasica<\/strong> pode ser uma aliada do ensino da <strong>matem\u00e1tica<\/strong>, principalmente no ensino fundamental, quando se aprende fra\u00e7\u00f5es, propor\u00e7\u00f5es e raz\u00f5es.<\/p>\n<p>Como as fra\u00e7\u00f5es est\u00e3o relacionadas \u00e0s notas musicais, a demonstra\u00e7\u00e3o disso por meio de instrumentos musicais pode fazer o aluno se interessar pela <strong>matem\u00e1tica<\/strong>.<\/p>\n<p>Se voc\u00ea gostou desse artigo, pode conhecer mais do trabalho da Sociedade Art\u00edstica Brasileira (Sabra), no site: <a href=\"https:\/\/www.sabra.org.br\/site\/\">https:\/\/www.sabra.org.br\/site\/<\/a>. A entidade mant\u00e9m a Oficina Musical de Betim (Escola de M\u00fasica), a Orquestra Sinf\u00f4nica de Betim, o Coro e a Orquestra de C\u00e2mara Lobo de Mesquita, al\u00e9m dos corais adulto e infantil, tanto em Belo Horizonte quanto em Betim.<\/p>\n<h3>Se voc\u00ea gostou deste post:<\/h3>\n<p>&#8211; siga as nossas p\u00e1ginas nas redes sociais para acompanhar as nossas atualiza\u00e7\u00f5es: estamos no <a href=\"https:\/\/www.facebook.com\/sabrabrasil\" target=\"_blank\" rel=\"noopener noreferrer\">Facebook<\/a>, no <a href=\"https:\/\/www.instagram.com\/sabrabrasil\/\" target=\"_blank\" rel=\"noopener noreferrer\">Instagram<\/a>, no <a href=\"https:\/\/www.linkedin.com\/company\/25002088\" target=\"_blank\" rel=\"noopener noreferrer\">LinkedIn<\/a>, no <a href=\"https:\/\/twitter.com\/ContatoSabra\" target=\"_blank\" rel=\"noopener noreferrer\">Twitter<\/a> e no <a href=\"https:\/\/www.youtube.com\/channel\/UCJw-kbuEvzUNdeQf20Pa-eQ\" target=\"_blank\" rel=\"noopener noreferrer\">YouTube<\/a>!<\/p>\n<p>&#8211; Conhe\u00e7a o trabalho da Sociedade Art\u00edstica Brasileira (SABRA) e todas as iniciativas culturais e sociais que ela mant\u00e9m. <a href=\"https:\/\/www.sabra.org.br\/site\/acoes\/\" target=\"_blank\" rel=\"noopener noreferrer\">Acesse nosso site!<\/a><\/p>\n<p>&#8211; entre em contato com a gente. E veja quais s\u00e3o as op\u00e7\u00f5es de ajuda na manuten\u00e7\u00e3o de nossas a\u00e7\u00f5es sociais e culturais. Basta acessar nossa p\u00e1gina <a href=\"https:\/\/www.sabra.org.br\/site\/doe-agora\/\" target=\"_blank\" rel=\"noopener noreferrer\">Doe Agora!<\/a><\/p>\n<p>&#8211; Compartilhe este texto nas suas redes sociais e ajude os seus amigos a tamb\u00e9m dominarem o assunto![\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>trabalho da sociedade art\u00edstica brasileira<br \/>\nsociedade art\u00edstica brasileira sabra<br \/>\nerat\u00f3stenes arist\u00f3xenes e arquitas<br \/>\ntrabalho da sociedade art\u00edstica<br \/>\nsociedade art\u00edstica brasileira<\/p>\n","protected":false},"author":39,"featured_media":1948,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_customify_content_layout":"","_customify_sidebar":"","_customify_page_header_display":"","_customify_disable_header":"","_customify_disable_header_top":"","_customify_disable_header_main":"","_customify_disable_header_bottom":"","_customify_disable_page_title":"","_customify_disable_content_vertical_padding":"","_customify_disable_footer_top":"","_customify_disable_footer_main":"","_customify_disable_footer_bottom":"","_customify_breadcrumb_display":"","_customify_header_transparent_display":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[15,8,1285,16,1286,11,9],"class_list":["post-1932","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog-sabra","tag-assistencia-social","tag-canto-coral","tag-escola-de-musica-sabra","tag-musicalizacao-infantil","tag-orquestra-infanto-juvenil-de-betim","tag-orquestra-sinfonica-de-betim","tag-sociedade-artistica-brasileira"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - 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Saiba como a origem da m\u00fasica \u00e9 antiga e como ela se transformou ao longo do tempo.","rel":"","context":"Em &quot;Blog SABRA&quot;","block_context":{"text":"Blog SABRA","link":"https:\/\/www.sabra.org.br\/site\/category\/blog-sabra\/"},"img":{"alt_text":"m\u00fasica-tipo-partir","src":"https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2022\/11\/a-evolucao-da-musica-pela-historia-20221007143620.jpg.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2022\/11\/a-evolucao-da-musica-pela-historia-20221007143620.jpg.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2022\/11\/a-evolucao-da-musica-pela-historia-20221007143620.jpg.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2022\/11\/a-evolucao-da-musica-pela-historia-20221007143620.jpg.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":1591,"url":"https:\/\/www.sabra.org.br\/site\/musica-na-educacao-infantil\/","url_meta":{"origin":1932,"position":5},"title":"M\u00fasica na Educa\u00e7\u00e3o Infantil","author":"M\u00e1rcio Miranda Pontes","date":"22 de outubro de 2018","format":false,"excerpt":"Motivos para inserir m\u00fasica na educa\u00e7\u00e3o infantil H\u00e1 doze anos, a Lei de Diretrizes e Bases da Educa\u00e7\u00e3o foi alterada para que a m\u00fasica se tornasse conte\u00fado obrigat\u00f3rio em toda a educa\u00e7\u00e3o b\u00e1sica. No entanto, esta importante ferramenta ainda \u00e9 um tanto negligenciada nas escolas. A educa\u00e7\u00e3o musical vai muito\u2026","rel":"","context":"Em &quot;Blog SABRA&quot;","block_context":{"text":"Blog SABRA","link":"https:\/\/www.sabra.org.br\/site\/category\/blog-sabra\/"},"img":{"alt_text":"M\u00fasica na Educa\u00e7\u00e3o Infantil","src":"https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2018\/10\/x-motivos-para-inserir-musica-na-educacao-infantil-20180705134730.jpg.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2018\/10\/x-motivos-para-inserir-musica-na-educacao-infantil-20180705134730.jpg.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2018\/10\/x-motivos-para-inserir-musica-na-educacao-infantil-20180705134730.jpg.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.sabra.org.br\/site\/wp-content\/uploads\/2018\/10\/x-motivos-para-inserir-musica-na-educacao-infantil-20180705134730.jpg.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]}],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/posts\/1932","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/comments?post=1932"}],"version-history":[{"count":0,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/posts\/1932\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/media\/1948"}],"wp:attachment":[{"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/media?parent=1932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/categories?post=1932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sabra.org.br\/site\/wp-json\/wp\/v2\/tags?post=1932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}