{"id":111766,"date":"2020-12-06T14:55:18","date_gmt":"2020-12-06T13:55:18","guid":{"rendered":"https:\/\/orellana.org\/blog\/?p=111766"},"modified":"2020-12-09T13:36:32","modified_gmt":"2020-12-09T12:36:32","slug":"veltempererede-12-hvorfor","status":"publish","type":"post","link":"https:\/\/orellana.org\/blog\/2020\/12\/veltempererede-12-hvorfor\/","title":{"rendered":"Veltempererede 12 toner &#8211; hvorfor?"},"content":{"rendered":"<p><a href=\"https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered.png\" data-gallery><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-111797\" src=\"https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered-1024x634.png\" alt=\"\" width=\"640\" height=\"396\" srcset=\"https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered-1024x634.png 1024w, https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered-300x186.png 300w, https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered-768x475.png 768w, https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered.png 1318w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<p><span data-expression=\"RowBox[{&quot;I&quot;, &quot; &quot;, &quot;dag&quot;, &quot; &quot;, &quot;er&quot;, &quot; &quot;, &quot;den&quot;, &quot; &quot;, &quot;ligesv\\.e6vende&quot;, &quot; &quot;, &quot;stemning&quot;, &quot; &quot;, &quot;den&quot;, &quot; &quot;, &quot;absolut&quot;, &quot; &quot;, &quot;mest&quot;, &quot; &quot;, &quot;udbredte&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;Ligesv\\.e6vende&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;eller&quot;, &quot; &quot;, &quot;veltempereret&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;stemning&quot;, StyleBox[RowBox[{&quot; &quot;, &quot; &quot;}]], &quot;inddeler&quot;, &quot; &quot;, &quot;en&quot;, &quot; &quot;, &quot;oktav&quot;, &quot; &quot;, &quot;i&quot;, &quot; &quot;, &quot;12&quot;, &quot; &quot;, &quot;logaritmisk&quot;, &quot; &quot;, &quot;fordelte&quot;, &quot; &quot;, &quot;skridt&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;og&quot;, &quot; &quot;, &quot;g\\.f8r&quot;, &quot; &quot;, &quot;p\\.e5&quot;, &quot; &quot;, &quot;den&quot;, &quot; &quot;, &quot;m\\.e5de&quot;, &quot; &quot;, &quot;alle&quot;, &quot; &quot;, &quot;toner&quot;, &quot; &quot;, &quot;ligestillede&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;Dette&quot;, &quot; &quot;, &quot;giver&quot;, &quot; &quot;, &quot;god&quot;, &quot; &quot;, &quot;mening&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;}]], &quot;da&quot;, &quot; &quot;, &quot;det&quot;, &quot; &quot;, &quot;s\\.e5&quot;, &quot; &quot;, &quot;er&quot;, &quot; &quot;, &quot;muligt&quot;, &quot; &quot;, &quot;at&quot;, &quot; &quot;, &quot;spille&quot;, &quot; &quot;, &quot;musik&quot;, &quot; &quot;, &quot;i&quot;, &quot; &quot;, &quot;alle&quot;, &quot; &quot;, &quot;tonearter&quot;, StyleBox[RowBox[{&quot;,&quot;, &quot; &quot;, &quot; &quot;}]], &quot;uden&quot;, &quot; &quot;, &quot;problemer&quot;, StyleBox[RowBox[{&quot;.&quot;, &quot; &quot;}]], &quot;Men&quot;, &quot; &quot;, &quot;hvorfor&quot;, &quot; &quot;, &quot;lige&quot;, &quot; &quot;, &quot;12&quot;, &quot; &quot;, &quot;toner&quot;, &quot;? Den mest optimale ligesv\\.e6vende inddeling af oktaven i et antal halvtoner, antager vi at v\\.e6re den inddeling, der kommer s\\.e5 t\\.e6t som muligt p\\.e5 de \\&quot;naturlige\\&quot; intervaller, og som har  et \\&quot;rimeligt\\&quot; antal toner, alts\\.e5 et antal, der g\\.f8r det praktisk muligt at konstruere og spille p\\.e5 f.eks. et klaviatur. I det nedenst\\.e5ende fors\\.f8ger vi at unders\\.f8ge om 12 er det optimale antal.&quot;}]\">I dag er den ligesv\u00e6vende stemning den absolut mest udbredte. Ligesv\u00e6vende, eller veltempereret, stemning\u00a0\u00a0inddeler en oktav i 12 logaritmisk fordelte skridt, og g\u00f8r p\u00e5 den m\u00e5de alle toner ligestillede. Dette giver god mening, da det s\u00e5 er muligt at spille musik i alle tonearter uden problemer. Men hvorfor lige 12 toner? Den mest optimale ligesv\u00e6vende inddeling af oktaven i et antal halvtoner, antager vi at v\u00e6re den inddeling, der kommer s\u00e5 t\u00e6t som muligt p\u00e5 de &#8220;naturlige&#8221; intervaller, og som har\u00a0\u00a0et &#8220;rimeligt&#8221; antal toner, alts\u00e5 et antal, der g\u00f8r det praktisk muligt at konstruere og spille p\u00e5 f.eks. et klaviatur. I det nedenst\u00e5ende har jeg sammen med Noah (i forbindelse med en gymnasieopgave han er i gang med) unders\u00f8gt om 12 er det optimale antal.<\/span><\/p>\n<p>Hent <a href=\"\/blog\/wp-content\/uploads\/2020\/12\/12-Toner.nb.pdf\">PDF<\/a> eller <a href=\"https:\/\/www.wolframcloud.com\/obj\/orellana\/Published\/12-Toner.nb\">l\u00e6s online<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I dag er den ligesv\u00e6vende stemning den absolut mest udbredte. Ligesv\u00e6vende, eller veltempereret, stemning\u00a0\u00a0inddeler en oktav i 12 logaritmisk fordelte skridt, og g\u00f8r p\u00e5 den m\u00e5de alle toner ligestillede. Dette giver god mening, da det s\u00e5 er muligt at spille musik i alle tonearter uden problemer. Men hvorfor lige 12 toner? Den mest optimale ligesv\u00e6vende [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":111797,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[14,76,11,64],"tags":[],"class_list":["post-111766","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-diary","category-familie","category-music","category-sci"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/orellana.org\/blog\/wp-content\/uploads\/2020\/12\/Well-tempered.png","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/pa2eXm-t4G","_links":{"self":[{"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/posts\/111766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/comments?post=111766"}],"version-history":[{"count":25,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/posts\/111766\/revisions"}],"predecessor-version":[{"id":111806,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/posts\/111766\/revisions\/111806"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/media\/111797"}],"wp:attachment":[{"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/media?parent=111766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/categories?post=111766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/orellana.org\/blog\/wp-json\/wp\/v2\/tags?post=111766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}