{"id":4447,"date":"2017-03-03T13:39:10","date_gmt":"2017-03-03T12:39:10","guid":{"rendered":"http:\/\/serveiseducatius.xtec.cat\/tarragones\/?p=4447"},"modified":"2019-04-30T10:21:29","modified_gmt":"2019-04-30T08:21:29","slug":"agarita","status":"publish","type":"post","link":"https:\/\/serveiseducatius.xtec.cat\/tarragones\/general\/agarita\/","title":{"rendered":"Les matem\u00e0tiques en la m\u00fasica"},"content":{"rendered":"<p><em><strong><span style=\"color: #808080;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-6424\" src=\"http:\/\/serveiseducatius.xtec.cat\/tarragones\/wp-content\/uploads\/usu549\/2017\/03\/Ins-Gaud\u00ed-Alexis-Garita.jpg\" alt=\"Ins Gaud\u00ed - Alexis Garita\" width=\"177\" height=\"236\" \/>T\u00edtol:<\/span> <\/strong><\/em><strong>Les matem\u00e0tiques en la m\u00fasica<\/strong><br \/>\n<em><strong><span style=\"color: #808080;\">Autor:<\/span> <\/strong><\/em><strong>Alexis Garita Mart\u00ednez<\/strong><br \/>\n<span style=\"color: #808080;\"><em><strong>Tutora: <\/strong><\/em><\/span>Sandra Perona Ventaja<br \/>\n<span style=\"color: #808080;\"><em><strong>Modalitat: <\/strong><\/em><\/span>Ci\u00e8ncies i tecnologia: Cientificot\u00e8cnic<br \/>\n<span style=\"color: #808080;\"><em><strong>\u00c0rea curricular: <\/strong><\/em><\/span>M\u00fasica i matem\u00e0tiques<br \/>\n<span style=\"color: #808080;\"><em><strong>Centre: <\/strong><\/em><\/span>Ins Gaud\u00ed<br \/>\n<em><strong><span style=\"color: #808080;\">Localitat:<\/span>\u00a0<\/strong><\/em>Reus<\/p>\n<p style=\"text-align: justify;\">Aquest treball tracta sobre les matem\u00e0tiques que podem trobar a la m\u00fasica.<\/p>\n<p style=\"text-align: justify;\">El treball ha estat estructurat d\u2019una manera molt clara, parlant de les quatre vessants m\u00e9s evidents que considero que t\u00e9 la m\u00fasica (relacionables amb les matem\u00e0tiques): l\u2019altura, el temps i el timbre dels sons, com a visi\u00f3 m\u00e9s concreta, i com a visi\u00f3 general, la forma musical. Tots aquests punts els relaciono directament amb les matem\u00e0tiques, de diferents formes, segons el contingut de la vessant musical.<\/p>\n<p style=\"text-align: justify;\">M\u2019agradaria destacar que la visi\u00f3 matem\u00e0tica de la m\u00fasica que he intentat il\u00b7lustrar en el treball, no \u00e9s ni molt menys semblant a la visi\u00f3 real que tinc de la m\u00fasica, ja que per sobre de tot la considero el que \u00e9s: un art. Per tant, m\u2019agradaria que es tingu\u00e9s en compte que el que exposo en aquest treball no \u00e9s exactament el que considero realment com a m\u00fasica, sin\u00f3 que simplement intento mostrar la vessant matem\u00e0tica que t\u00e9, que no \u00e9s ni molt menys la \u00fanica que t\u00e9.<\/p>\n<h6><strong>Objectius:<\/strong><\/h6>\n<p style=\"text-align: justify;\">Establir com es troben les matem\u00e0tiques dintre de la m\u00fasica i quina \u00e9s la relaci\u00f3 que hi ha en quatre \u00e0mbits concrets de la m\u00fasica amb les matem\u00e0tiques: l\u2019\u00e0mbit de l\u2019altura, el temps i el timbre del so i de la m\u00fasica, i l\u2019\u00e0mbit de la forma musical, i a m\u00e9s, poder arribar a facilitar una mica l\u2019observaci\u00f3 de la complexitat que pot arribar a tenir la m\u00fasica en molts casos i tots els aspectes que s\u2019hi concentren.<\/p>\n<h6><strong>Hip\u00f2tesis:<\/strong><\/h6>\n<p>Les matem\u00e0tiques es troben relacionades amb la m\u00fasica en diversos \u00e0mbits seus, de maneres diferents.<\/p>\n<h6><strong>El proc\u00e9s:<\/strong><\/h6>\n<ul>\n<li>Definici\u00f3 de l\u2019objectiu i concreci\u00f3 del tema<\/li>\n<li>Estudi de diferents \u00e0mbits que relacionen les matem\u00e0tiques amb la m\u00fasica<\/li>\n<li>An\u00e0lisi de les quatre vessants musicals que vull relacionar amb les matem\u00e0tiques<\/li>\n<li>Estudi de la hist\u00f2ria de la m\u00fasica i del seu vincle al llarg del temps amb les matem\u00e0tiques<\/li>\n<li>Realitzaci\u00f3 de la part pr\u00e0ctica: an\u00e0lisi de 4 obres de diferents autors en funci\u00f3 de la Proporci\u00f3 \u00c0uria i composici\u00f3 d\u2019una petita pe\u00e7a e funci\u00f3 de la Proporci\u00f3 \u00c0uria<a href=\"http:\/\/serveiseducatius.xtec.cat\/tarragones\/wp-content\/uploads\/usu549\/2017\/03\/violi.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-6133 aligncenter\" src=\"http:\/\/serveiseducatius.xtec.cat\/tarragones\/wp-content\/uploads\/usu549\/2017\/03\/violi.jpg\" alt=\"violi\" width=\"440\" height=\"293\" srcset=\"https:\/\/serveiseducatius.xtec.cat\/tarragones\/wp-content\/uploads\/usu549\/2017\/03\/violi.jpg 440w, https:\/\/serveiseducatius.xtec.cat\/tarragones\/wp-content\/uploads\/usu549\/2017\/03\/violi-300x200.jpg 300w\" sizes=\"auto, (max-width: 440px) 100vw, 440px\" \/><\/a><\/li>\n<\/ul>\n<h6><strong>Conclusions:<\/strong><\/h6>\n<ul>\n<li style=\"text-align: justify;\">Conclusi\u00f3 1: la relaci\u00f3 entre l\u2019altura dels sons musicals i les matem\u00e0tiques \u00e9s que, havent estudiat diversos sistemes d\u2019afinaci\u00f3, prenent les freq\u00fc\u00e8ncies dels sons podem realitzar moltes relacions matem\u00e0tiques que permeten directament tenir coneixement sobre l\u2019afinaci\u00f3 musical de forma te\u00f2rica, en paper.<\/li>\n<li style=\"text-align: justify;\">Conclusi\u00f3 2: la relaci\u00f3 entre el ritme musical, la vessant m\u00e9s anal\u00edtica o num\u00e8rica de la m\u00fasica, i les matem\u00e0tiques, s\u00f3n purament els n\u00fameros, els valors establerts a cada figura musical, que despr\u00e9s es transforma en el fet de contar. Aquesta relaci\u00f3 es plasma en el pla musical per a la seva posterior interpretaci\u00f3.<\/li>\n<li style=\"text-align: justify;\">Conclusi\u00f3 3: la relaci\u00f3 que podem observar entre la vessant musical del timbre del so amb les matem\u00e0tiques \u00e9s que est\u00e0 \u00edntimament relacionat amb els harm\u00f2nics, que a la vegada s\u00f3n ells la relaci\u00f3 matem\u00e0tica (i f\u00edsica), per totes les demostracions i c\u00e0lculs que es poden fer amb ells.<\/li>\n<li style=\"text-align: justify;\">Conclusi\u00f3 4: la relaci\u00f3 que trobem en la forma musical i les matem\u00e0tiques es pot dividir en dues parts. Primer, \u00e9s una matem\u00e0tica que podem aplicar a patrons o subjectes musicals, que serveix m\u00e9s aviat per a la composici\u00f3, i s\u00f3n canvis o transformacions que prenem de la geometria cl\u00e0ssica i que apliquem a la m\u00fasica per a crear patrons musicals diferents. La segona, \u00e9s pr\u00f2piament la relaci\u00f3 que hi ha entre la forma musical i les matem\u00e0tiques, i est\u00e0 relacionada directament amb el nombre d\u2019or: \u00e9s una divisi\u00f3 concreta de les obres musicals que col\u00b7loca el punt culminant de l\u2019obra en relaci\u00f3 a la Proporci\u00f3 \u00c0uria.<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" style=\"border: 1px solid #CCC; border-width: 1px; margin-bottom: 5px; max-width: 100%;\" src=\"\/\/www.slideshare.net\/slideshow\/embed_code\/key\/qHxsU8il7Llu2N\" width=\"595\" height=\"485\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" allowfullscreen=\"allowfullscreen\"> <\/iframe><\/p>\n<h6><strong>Bibliografia:<\/strong><\/h6>\n<ul>\n<li>\u00a0ARBON\u00c9S, Javier i MILRUD, Pablo, La armon\u00eda es num\u00e9rica. M\u00fasica y matem\u00e1ticas, 2011, Barcelona, Ed. RBA<\/li>\n<li>CALVO-MANZANO, Antonio, Ac\u00fastica f\u00edsico-musical, 1991, Madrid, Ed. Real Musical<\/li>\n<li>COMELLAS, Jos\u00e9 Luis, Historia sencilla de la m\u00fasica, 2006, Madrid, Ed. RIALP<\/li>\n<li>LIVIO, Mario, La Proporci\u00f3n \u00c1urea: la historia del n\u00famero \u03c6, 2006, Barcelona, Ed. Ariel<\/li>\n<li>IMSLP \u2013 International Music Score Library Project: <a href=\"http:\/\/imslp.org\/\" target=\"_blank\" rel=\"noopener\">http:\/\/imslp.org\/<\/a><\/li>\n<li>Noteflight: <a href=\"https:\/\/www.noteflight.com\/\" target=\"_blank\" rel=\"noopener\">https:\/\/www.noteflight.com\/<\/a><\/li>\n<li>Universidad Polit\u00e9cnica de Madrid: <a href=\"http:\/\/www2.caminos.upm.es\/Departamentos\/matematicas\/grupomaic\/conferencias\/11.Numero%20de%20oro.pdf\" target=\"_blank\" rel=\"noopener\">http:\/\/www2.caminos.upm.es\/Departamentos\/matematicas\/grupomaic\/conferencias\/11.Numero%20de%20oro.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Ins Gaud\u00ed<\/p>\n","protected":false},"author":1,"featured_media":6133,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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