{"id":276,"date":"2012-11-12T11:47:46","date_gmt":"2012-11-12T19:47:46","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=276"},"modified":"2017-08-18T08:58:10","modified_gmt":"2017-08-18T15:58:10","slug":"octave-division","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=276","title":{"rendered":"Octave Reduction"},"content":{"rendered":"<p>Doubling the frequency of a note certainly changes it. The ear hears a higher-pitched note.\u00a0But there is something in the essence of the note that does not change, a character that stays consistent through the octaves.<\/p>\n<p>This allows a process called <a href=\"http:\/\/en.wikipedia.org\/wiki\/Octave\">octave<\/a> reduction. When you&#8217;re working with notes as ratios, it&#8217;s convenient to multiply or divide the raw ratio by 2, as many times as is necessary to bring it into the same octave as the <a title=\"The tonic\" href=\"http:\/\/www.garygarrett.me\/?p=187\">tonic<\/a>.<\/p>\n<p>3\/1 generates a <a href=\"http:\/\/en.wikipedia.org\/wiki\/Perfect_fifth\">perfect fifth<\/a>. <a href=\"http:\/\/www.garygarrett.me\/wp-content\/uploads\/2012\/11\/3-1.mp3\">3-1<\/a><\/p>\n<p>This note is actually an octave plus a fifth above the tonic. Now divide by 2 and you have 3\/2, one and a half times the original frequency, and just a fifth above.\u00a0<a href=\"http:\/\/www.garygarrett.me\/wp-content\/uploads\/2012\/11\/3-2.mp3\">3-2<\/a><\/p>\n<p>The reference frequency is 1, the octave is 2, so what you want to achieve with octave reduction is a ratio, or fraction, between 1 and 2.<\/p>\n<p>These are the beginnings of a scale, a collection of notes within a single octave. Such a scale can be repeated up and down the octaves to cover the whole range of hearing.<\/p>\n<p>Next:\u00a0<a href=\"http:\/\/www.garygarrett.me\/?p=292\">The Major Third<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Doubling the frequency of a note certainly changes it. The ear hears a higher-pitched note.\u00a0But there is something in the essence of the note that does not change, a character that stays consistent through the octaves. This allows a process called octave reduction. When you&#8217;re working with notes as ratios, it&#8217;s convenient to multiply or&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"footnotes":""},"categories":[120,126],"tags":[298,36,49,59,34,60],"class_list":["post-276","post","type-post","status-publish","format-standard","hentry","category-justintonation","category-the-notes","tag-book","tag-fifth","tag-octave","tag-ratio","tag-tonic","tag-unison"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/276","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=276"}],"version-history":[{"count":10,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/276\/revisions"}],"predecessor-version":[{"id":1990,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/276\/revisions\/1990"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=276"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=276"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}