{"id":212,"date":"2010-09-19T12:18:52","date_gmt":"2010-09-19T12:18:52","guid":{"rendered":"http:\/\/www.icmm.csic.es\/within-experimental-error\/?p=212"},"modified":"2020-03-21T11:04:08","modified_gmt":"2020-03-21T11:04:08","slug":"vincenzo-galilei","status":"publish","type":"post","link":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/2010\/09\/19\/vincenzo-galilei\/","title":{"rendered":"Vincenzo Galilei"},"content":{"rendered":"

\"\"<\/a>
\nA professional musician, lutenist, composer and music theorist, Vincenzo Galilei deserves an outstanding place in the history of science as a co-discoverer, through experimentation, of one of the first non-linear relations known in physics. <\/p>\n

Pythagorean tradition holded that two strings vibrating consonantly have lengths (at equal tension applied) or tensions (at equal length) in a ratio of simple whole numbers and that the pitch depends linearly on length and tension. Vincenzo Galilei’s experiments led him to conclude that this is true with regard to the lengths but is not with regard to the tension applied. For the same tension applied, two strings will vibrate in an octave interval if their lengths are in a 1:2 ratio (and the interval will be a perfect fifth if the ratio were 2:3). However, two strings of equal length will produce an octave when the tensions applied, for instance through weighing scales, are in a 1:4 ratio (4:9 for a perfect fifth). That is to say that the pitch of sound (or, better, its frequency) is inversely poportional to the length of the string and linearly proportional to the square root of the tension (if the linear density of the string is held constant).<\/p>\n

The most renowned sons of Vincenzo Galilei inherited his musical ability (Michelagnolo, a composer) and analytical and empirical capacity (Galileo). By the end of the first day of his Dialogue<\/em> Galileo reflects on musical consonance and dissonance in terms of frequencies and its effect on the eardrum, also describing his father’s findings. <\/p>\n

\"\"<\/a>
\nM\u00fasico de profesi\u00f3n, laudista, compositor y te\u00f3rico de la m\u00fasica, a Vincenzo Galilei (ca.<\/em> 1520-1591)\u00a0 habr\u00eda que concederle un puesto destacado en la historia de la ciencia, como descubridor, mediante la experimentaci\u00f3n, de una de las primeras relaciones no lineales de la f\u00edsica.<\/p>\n

La tradici\u00f3n pitag\u00f3rica establec\u00eda que dos cuerdas vibrando en intervalos consonantes tienen longitudes (a igual tensi\u00f3n) o tensiones (a igual longitud) en una relaci\u00f3n de n\u00fameros enteros sencillos y que la altura de sonido depende directamente de longitud y tensi\u00f3n. Los experimentos de Vincenzo Galilei le llevaron a concluir que, si bien eso es cierto para la longitud, no lo es para la tensi\u00f3n. Dos cuerdas sometidas a igual tensi\u00f3n dar\u00e1n, por ejemplo, un intervalo de octava si sus longitudes est\u00e1n en una relaci\u00f3n 1:2 (y el intervalo ser\u00e1 de quinta si la relaci\u00f3n es 3:2). Sin embargo, dos cuerdas de igual longitud dar\u00e1n una octava justa cuando se las somete, por ejemplo mediante pesos, a tensiones en una relaci\u00f3n 1:4 (que ser\u00e1 9:4 para una quinta). Es decir, la altura de sonido (o, mejor dicho, la frecuencia) es inversamente proporcional a la longitud de la cuerda y directamente proporcional a la ra\u00edz cuadrada de la tensi\u00f3n (si se mantiene constante la masa por unidad de longitud).<\/p>\n

Los dos hijos m\u00e1s famosos de Vincenzo heredaron su capacidad musical (Michelagnolo, compositor) y anal\u00edtica y experimental (Galileo). Al final de la primera jornada de sus Di\u00e1logos<\/em>, Galileo reflexiona sobre la consonancia y disonancia en m\u00fasica en t\u00e9rminos de frecuencias y de su efecto sobre el t\u00edmpano, y recoge tambi\u00e9n el hallazgo de su padre.<\/p>\n","protected":false},"excerpt":{"rendered":"

A professional musician, lutenist, composer and music theorist, Vincenzo Galilei deserves an outstanding place in the history of science as a co-discoverer, through experimentation, of one of the first non-linear relations known in physics. Pythagorean tradition holded that two strings …<\/span> Sigue leyendo →<\/span><\/a><\/p>\n","protected":false},"author":73,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-212","post","type-post","status-publish","format-standard","hentry","category-science-and-music"],"_links":{"self":[{"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/posts\/212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/users\/73"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/comments?post=212"}],"version-history":[{"count":1,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/posts\/212\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/posts\/212\/revisions\/858"}],"wp:attachment":[{"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/media?parent=212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/categories?post=212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.icmm.csic.es\/within-experimental-error\/wp-json\/wp\/v2\/tags?post=212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}