{"id":530,"date":"2007-06-12T12:07:38","date_gmt":"2007-06-12T08:07:38","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=530"},"modified":"2025-06-27T18:16:15","modified_gmt":"2025-06-27T14:16:15","slug":"la-geometrie-de-la-guitare","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=530","title":{"rendered":"La g\u00e9om\u00e9trie de la guitare"},"content":{"rendered":"\n<p>La recherche d&rsquo;une gamme temp\u00e9r\u00e9e am\u00e8ne \u00e0 placer les frettes sur une guitare, de mani\u00e8re que les positions de ces frettes suivent une progression g\u00e9om\u00e9trique, et que la douzi\u00e8me frette soit au milieu de la corde. Cette construction n&rsquo;est pas r\u00e9alisable \u00e0 la r\u00e8gle et au compas, mais la g\u00e9om\u00e9trie projective permet de graduer homographiquement un segment, et en 1843, Daniel Str\u00e4hle (organiste su\u00e9dois), publie <a href=\"https:\/\/www.euler-math-toolbox.de\/Programs\/Examples\/Equal%20Tempered%20Scale%20by%20Strahle.html\">cette construction<\/a> qu&rsquo;il est int\u00e9ressant d&rsquo;analyser en terme de minimisation de l&rsquo;erreur globale.<\/p>\n\n\n\n<p>Voici un retour historique sur cette question :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2025\/06\/frettes2-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 frettes2.\"><\/object><a id=\"wp-block-file--media-a3803af1-6b65-4d18-a22c-e796e973911b\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2025\/06\/frettes2-1.pdf\">frettes2<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2025\/06\/frettes2-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a3803af1-6b65-4d18-a22c-e796e973911b\">T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>La recherche d&rsquo;une gamme temp\u00e9r\u00e9e am\u00e8ne \u00e0 placer les frettes sur une guitare, de mani\u00e8re que les positions de ces frettes suivent une progression g\u00e9om\u00e9trique, et que la douzi\u00e8me frette soit au milieu de la corde. Cette construction n&rsquo;est pas r\u00e9alisable \u00e0 la r\u00e8gle et au compas, mais la g\u00e9om\u00e9trie projective permet de graduer homographiquement [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":1060,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,4],"tags":[43,32],"coauthors":[54],"class_list":["post-530","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-contextualiser-les-apprentissages","category-geometrie","tag-histoire-des-mathematiques","tag-lycee"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/530","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=530"}],"version-history":[{"count":1,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/530\/revisions"}],"predecessor-version":[{"id":532,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/530\/revisions\/532"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/media\/1060"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=530"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=530"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}