{"id":172082,"date":"2025-10-12T11:51:44","date_gmt":"2025-10-12T11:51:44","guid":{"rendered":"https:\/\/raed.academy\/?p=172082"},"modified":"2025-10-12T11:51:44","modified_gmt":"2025-10-12T11:51:44","slug":"la-base-matematica-de-la-musica","status":"publish","type":"post","link":"https:\/\/raed.academy\/ca\/la-base-matematica-de-la-musica\/","title":{"rendered":"La base matem\u00e0tica de la m\u00fasica"},"content":{"rendered":"<div id=\"attachment_120239\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-120239\" class=\"wp-image-120239 size-full\" src=\"https:\/\/raed.academy\/wp-content\/uploads\/2022\/06\/Pilar-Bayer-dst.webp\" sizes=\"(max-width: 600px) 100vw, 600px\" srcset=\"https:\/\/raed.academy\/wp-content\/uploads\/2022\/06\/Pilar-Bayer-dst.webp 600w, https:\/\/raed.academy\/wp-content\/uploads\/2022\/06\/Pilar-Bayer-dst-440x264.webp 440w\" alt=\"Pilar Bayer\" width=\"600\" height=\"360\" aria-describedby=\"caption-attachment-120239\" \/><p id=\"caption-attachment-120239\" class=\"wp-caption-text\">Dra. Pilar Bayer<\/p><\/div>\n<p><a href=\"https:\/\/raed.academy\/ca\/academics\/dra-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener\"><em><strong>Pilar Bayer<\/strong><\/em><\/a>, catedr\u00e0tica em\u00e8rita de la <strong>Universitat de Barcelona<\/strong>, fundadora del <strong>Seminari de Teoria de Nombres de Barcelona<\/strong>, membre de la<strong> Junta de Govern<\/strong> de la <strong>Societat Catalana de Matem\u00e0tiques<\/strong> i acad\u00e8mica numer\u00e0ria i vicepresidenta de la Secci\u00f3 de Ci\u00e8ncies Experimentals de la <strong>Reial Acad\u00e8mia Europea de Doctors<\/strong> (RAED), explica a l&#8217;article <strong>&#8220;La base matem\u00e0tica del so digital&#8221;<\/strong>, publicat al n\u00famero 790 de la revista <strong>&#8220;Serra d&#8217;Or&#8221;<\/strong>, corresponent al present mes d&#8217;octubre, la connexi\u00f3 que existeix entre matem\u00e0tica i m\u00fasica al llarg de segles de pensament cient\u00edfic i art\u00edstic, analitzant les lleis num\u00e8riques que permeten entendre i reproduir el so.<\/p>\n<p>Bayer parteix al seu article d&#8217;una c\u00e8lebre frase del fil\u00f2sof i matem\u00e0tic alemany del segle XVII <strong>Gottfried Leibniz<\/strong>: &#8220;La m\u00fasica \u00e9s un exercici ocult d&#8217;aritm\u00e8tica, realitzat per l&#8217;esperit, que ignora sap comptar&#8221;. Aix\u00ed introdueix la paradoxa que tot i que no cal saber matem\u00e0tiques per gaudir o compondre m\u00fasica, l&#8217;o\u00efda humana s\u00ed que fa c\u00e0lculs de forma inconscient cada cop que escolta una melodia. La capacitat de distingir timbres, recon\u00e8ixer veus o identificar instruments prov\u00e9 en realitat de la forma en qu\u00e8 el cervell interpreta les vibracions de l&#8217;aire, explica. En aquest sentit, l&#8217;experta assenyala que el timbre, all\u00f2 que diferencia una trompeta d&#8217;un viol\u00ed o una veu d&#8217;una altra, es pot descriure matem\u00e0ticament gr\u00e0cies a la denominada an\u00e0lisi de Fourier, una eina que descompon qualsevol so en els seus components harm\u00f2nics. <strong>Joseph Fourier<\/strong>, cient\u00edfic franc\u00e8s del segle XIX, va desenvolupar aquesta teoria per estudiar la transmissi\u00f3 de la calor, per\u00f2 les seves equacions van acabar revolucionant la forma en qu\u00e8 avui es compr\u00e8n i tracta el so.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-164602 alignleft\" src=\"https:\/\/raed.academy\/wp-content\/uploads\/2025\/05\/musica-y-matematicas-no-atrib-pixabay.com-dst.webp\" sizes=\"(max-width: 600px) 100vw, 600px\" srcset=\"https:\/\/raed.academy\/wp-content\/uploads\/2025\/05\/musica-y-matematicas-no-atrib-pixabay.com-dst.webp 600w, https:\/\/raed.academy\/wp-content\/uploads\/2025\/05\/musica-y-matematicas-no-atrib-pixabay.com-dst-440x264.webp 440w\" alt=\"\" width=\"600\" height=\"360\" \/>L&#8217;acad\u00e8mica descriu tamb\u00e9 com la c\u00f2clea, l&#8217;\u00f2rgan de l\u2019orella interna, actua com un teclat biol\u00f2gic que descompon les freq\u00fc\u00e8ncies sonores, de manera similar al que fa l&#8217;an\u00e0lisi matem\u00e0tica. La freq\u00fc\u00e8ncia, mesurada en hertzs, determina el to; la combinaci\u00f3 de freq\u00fc\u00e8ncies, els acords; i la superposici\u00f3 d&#8217;ones, el timbre caracter\u00edstic de cada instrument. L&#8217;autora porta aquests principis al m\u00f3n digital, de manera que una vegada el so es converteix en dades num\u00e8riques, les eines matem\u00e0tiques permeten el seu emmagatzemament, reproducci\u00f3 i manipulaci\u00f3. Gr\u00e0cies a la conversi\u00f3 de la informaci\u00f3 sonora en seq\u00fc\u00e8ncies bin\u00e0ries, una pe\u00e7a musical pot comprimir-se en formats com MP3 o WAV i reproduir-se a qualsevol dispositiu.<\/p>\n<p>Bayer subratlla que la m\u00fasica digital \u00e9s el resultat de segles de pensament matem\u00e0tic. Des de les ones sinusoidals que representen cada nota fins als algoritmes que transformen el so en bits, la matem\u00e0tica \u00e9s al cor de cada can\u00e7\u00f3. L&#8217;acad\u00e8mica conclou amb una reflexi\u00f3 que uneix art i ci\u00e8ncia: &#8220;No sabem si Fourier era un apassionat de la m\u00fasica, per\u00f2 \u00e9s probable que hagu\u00e9s quedat sorpr\u00e8s en descobrir com les seves investigacions han trobat aplicaci\u00f3 en la m\u00fasica digital&#8221;.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pilar Bayer exposa la connexi\u00f3 entre matem\u00e0tica i m\u00fasica al llarg de segles de pensament cient\u00edfic i art\u00edstic, analitzant les lleis num\u00e8riques que permeten entendre i reproduir el so, a l&#8217;article &#8220;La base matem\u00e0tica del so digital&#8221;<\/p>\n","protected":false},"author":12,"featured_media":164603,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[229,332,436,298,301,410],"tags":[],"class_list":["post-172082","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-art","category-biologia-ca","category-computacio","category-fisica-ca","category-matematiques","category-musica-ca","et-has-post-format-content","et_post_format-et-post-format-standard"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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