{"id":413,"date":"2012-11-21T10:15:04","date_gmt":"2012-11-21T18:15:04","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=413"},"modified":"2017-08-18T09:05:44","modified_gmt":"2017-08-18T16:05:44","slug":"mixed-messages","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=413","title":{"rendered":"Mixed Messages"},"content":{"rendered":"<p>The harmonic <a title=\"The Lattice\" href=\"https:\/\/www.garygarrett.me\/?p=342\">lattice<\/a> can be divided into four <a href=\"http:\/\/www.mathsisfun.com\/definitions\/quadrant-graph-.html\">quadrants<\/a>.<\/p>\n<p>Northeast is pure <a title=\"The Chord of Nature\" href=\"https:\/\/www.garygarrett.me\/?p=250\">overtonal<\/a> energy. All these notes are reached by multiplication alone. <a href=\"http:\/\/www.mathsisfun.com\/definitions\/power.html\">Powers<\/a> of 3 and 5 are in the <a href=\"http:\/\/www.mathsisfun.com\/definitions\/numerator.html\">numerators<\/a>, and the <a href=\"http:\/\/www.mathsisfun.com\/definitions\/denominator.html\">denominators<\/a> are all powers of 2.<\/p>\n<p>Southwest is pure <a title=\"A Reciprocal Note: The Fourth\" href=\"https:\/\/www.garygarrett.me\/?p=397\">reciprocal<\/a> energy. You get there by dividing. All the 3&#8217;s and 5&#8217;s are on the bottom of the <a href=\"http:\/\/www.mathsisfun.com\/definitions\/ratio.html\">ratio<\/a>\u00a0(or fraction), and the powers of 2 are on the top.<\/p>\n<p>Northwest is mixed reciprocal and overtonal energy. You multiply by fives and divide by threes.<\/p>\n<p>Southeast is also mixed. Multiply by threes and divide by fives.<\/p>\n<p>The <a href=\"http:\/\/en.wikipedia.org\/wiki\/Major_sixth\">major sixth<\/a> is in the northwest quadrant. First divide the tonic by 3, which gives you a perfect fourth. Then multiply that by 5, and you get the major sixth. Its ratio is 5\/3. You can do this in any order, of course &#8212; multiplying by 5 gets you to the major third, and dividing by 3 brings you to the sixth again.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Sixth\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/91yqf2yjWDY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<p>A different flavor yet! What do you hear? How does it make you feel?<\/p>\n<p>Musical sensation can be related to other senses and emotions, but really these feelings have their own quality. It&#8217;s like a new sense. I had a friend once who had never tasted a peach. She didn&#8217;t like the feel of the skin, and she hadn&#8217;t dared bite into one. I was saddened, of course, but how to describe the taste of a ripe peach to someone who&#8217;s never tasted one? You can draw comparisons forever, but nothing will prepare them for the reality.<\/p>\n<p>That was a long time ago. I hope that some time later, she found herself in the <a href=\"http:\/\/online.wsj.com\/article\/SB10001424052970203946904574300192082040918.html\">perfect place<\/a> and went for it. There should be a First Peach ceremony. Yum!<\/p>\n<p>The individual qualities of these notes are easier for me to hear in just intonation than in equal temperament. They are purer flavors, a more direct experience. Later, I&#8217;ll present some notes that are very close together in pitch, yet feel different. In just intonation, there are different notes for peach, nectarine and apricot. In equal temperament, a single note, close in pitch, will represent all three. Once you&#8217;ve tasted the actual fruits, equal temperament works <em>better<\/em> than it did before. You know what it is you&#8217;re supposed to be tasting.<\/p>\n<p>OK, I&#8217;m out on a quivering limb of analogy now, and way ahead of my story. We have enough notes now to start playing with them.<\/p>\n<p>Next:\u00a0<a href=\"https:\/\/www.garygarrett.me\/?p=441\">Names<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The harmonic lattice can be divided into four quadrants. Northeast is pure overtonal energy. All these notes are reached by multiplication alone. Powers of 3 and 5 are in the numerators, and the denominators are all powers of 2. Southwest is pure reciprocal energy. You get there by dividing. All the 3&#8217;s and 5&#8217;s are&#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,"_kad_post_classname":"","footnotes":""},"categories":[112,126],"tags":[298,12,10,27,90,92,89,88,91],"class_list":["post-413","post","type-post","status-publish","format-standard","hentry","category-thelattice","category-the-notes","tag-book","tag-equal-temperament","tag-just-intonation","tag-lattice","tag-overtonal","tag-peach","tag-quadrant","tag-reciprocal","tag-sixth"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/413","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=413"}],"version-history":[{"count":9,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/413\/revisions"}],"predecessor-version":[{"id":1998,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/413\/revisions\/1998"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}