{"id":1484,"date":"2013-08-06T15:57:06","date_gmt":"2013-08-06T22:57:06","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=1484"},"modified":"2017-08-30T15:11:43","modified_gmt":"2017-08-30T22:11:43","slug":"polarity","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=1484","title":{"rendered":"Polarity"},"content":{"rendered":"<p>The following video compares the perfect fifth with the perfect fourth.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Twin 4 5\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/i-nej_7Ft6I?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>These notes are the next-door neighbors of the tonic. They are equally close to the center. They are both harmonious. Yet there is a great difference in their character.<\/p>\n<p>The difference between these two intervals is <em>polarity<\/em>.<\/p>\n<p>I learned this term from W.A. Mathieu, in his amazing book &#8220;<a title=\"Harmonic Experience\" href=\"http:\/\/www.garygarrett.me\/?p=204\">Harmonic Experience<\/a>.&#8221;<\/p>\n<p>Polarity is the main driver of tension and release in <a title=\"Home\" href=\"http:\/\/www.garygarrett.me\/?p=1262\">tonal music<\/a>. I think it&#8217;s much more important than <a title=\"Harmonic Distance\" href=\"http:\/\/www.garygarrett.me\/?p=1435\">harmonic distance<\/a>, the other component of <a title=\"Consonance and Dissonance\" href=\"http:\/\/www.garygarrett.me\/?p=1380\">consonance<\/a>.<\/p>\n<p>Here&#8217;s how I think polarity works:<\/p>\n<p>Almost all sounds are actually a bundle of waves, of different frequencies. The frequencies in these bundles tend to vibrate at multiples of each other &#8212; 2x, 3x, 4x, 5x some base frequency &#8212; a <a href=\"http:\/\/en.wikipedia.org\/wiki\/Harmonic_series_(music)\">harmonic series<\/a>.<\/p>\n<p>Our ears are highly attuned to such relationships. They help us figure out which frequencies belong together, so we can analyze them and identify the source. If we hear two frequencies in lockstep, three cycles to one, it is <em>very<\/em> likely they come from the same object.<\/p>\n<p>I think this is <a title=\"Why Can We Hear Harmony?\" href=\"http:\/\/www.garygarrett.me\/?p=1446\">why we can hear harmony<\/a>. It&#8217;s a byproduct of our built-in orientation software. The <a href=\"http:\/\/en.wikipedia.org\/wiki\/Overtone\">overtone series<\/a> of a sound\u00a0is a powerful source of information about the object that made it. The harmonic content tells us whether it&#8217;s a barking dog or a friend or rustling leaves. Something in us sorts out and analyzes many harmonic series at once, in real time, identifying sound sources, locating them in space, and even sensing their texture at a distance. It&#8217;s a phenomenal processor.<\/p>\n<p>So the processor recognizes the 3-wiggles-to-1 dance of the perfect fourth. But something is wrong &#8212; the 4 does\u00a0<em>not<\/em>\u00a0belong in the overtone series of the 1. The overtone series is generated by multiplication, not division.<\/p>\n<p>This is a strange input for the mighty processor.<\/p>\n<ul>\n<li>The 4\u00a0<em>has<\/em>\u00a0to belong to the 1, because the two are in step with each other at three beats for one. In nature, that&#8217;s a dead giveaway.<\/li>\n<li>But the 4\u00a0<em>can&#8217;t<\/em>\u00a0belong to the 1, because the ratio is the wrong way around &#8212; natural sounds do not contain 1\/3 in their overtone series.<\/li>\n<li>Maybe the <em>1<\/em> actually belongs to the <em>4<\/em>. The 1 is three times the 4, so if the 4 were the base, all would make sense.<\/li>\n<li>But every other clue, all the harmonics in the\u00a0<a title=\"Mirror Twins\" href=\"http:\/\/www.garygarrett.me\/?p=1459\">drone<\/a>\u00a0(and, importantly,\u00a0the listener&#8217;s memory), are pointing to the 1, hollering &#8220;This is the basic frequency!&#8221;<\/li>\n<\/ul>\n<p>What&#8217;s a supercomputer to do?<\/p>\n<p>I feel this sensation as unrest or instability, a need for something to change. Either the 4 needs to resolve to an <a title=\"The Compass Points\" href=\"http:\/\/www.garygarrett.me\/?p=1273\">overtonal<\/a> note such as the 5 or\u00a0<a title=\"The Major Third\" href=\"http:\/\/www.garygarrett.me\/?p=292\">major 3<\/a>, or the root needs to change.\u00a0Moving the root to the 4 will resolve the\u00a0<a title=\"Consonance and Dissonance\" href=\"http:\/\/www.garygarrett.me\/?p=1380\">dissonance<\/a>, introducing a new reciprocal tension &#8212; now the root &#8220;wants&#8221; to go to the 1, because the ear remembers. There are videos of this <a href=\"http:\/\/www.garygarrett.me\/?p=397\">here<\/a>.<\/p>\n<p>On the lattice, there are two basic polarities, overtonal and reciprocal. Some notes combine both energies.<\/p>\n<p>Overtonal notes are created by <em>multiplying<\/em> the base frequency. They appear in the natural harmonic content of sounds. They sound stable, restful, resolved &#8212; more so the closer they are to the center of the lattice, where <a title=\"Cadences\" href=\"http:\/\/www.garygarrett.me\/?p=1090\">tonal gravity<\/a> is stronger. Pure overtonal notes are in the <a title=\"Leading the Ear\" href=\"http:\/\/www.garygarrett.me\/?p=1271\">Northeast quadrant<\/a> of the lattice.<\/p>\n<p>Reciprocal notes are created by <em>dividing<\/em> the base frequency. The mind recognizes them as being related to the base frequency, but they do not appear in its natural overtone series. They sound unstable, restless, tense &#8212; and, like the overtonal ones, the effect is stronger closer to the center.<\/p>\n<p>Polarity is our sense of the <a title=\"Tonal Gravity\" href=\"http:\/\/www.garygarrett.me\/?p=1076\">tonal gravity field<\/a>. It is how we orient ourselves in <a title=\"Harmonic Space\" href=\"http:\/\/www.garygarrett.me\/?p=306\">harmonic space<\/a>.<\/p>\n<p>Next:\u00a0<a href=\"http:\/\/www.garygarrett.me\/?p=1477\">More Mirror Twins<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The following video compares the perfect fifth with the perfect fourth. These notes are the next-door neighbors of the tonic. They are equally close to the center. They are both harmonious. Yet there is a great difference in their character. The difference between these two intervals is polarity. I learned this term from W.A. Mathieu,&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":[189,112,187],"tags":[298,84,85,36,87,245,27,31,241,66,65],"class_list":["post-1484","post","type-post","status-publish","format-standard","hentry","category-consonance-2","category-thelattice","category-tonal-gravity","tag-book","tag-consonance","tag-dissonance","tag-fifth","tag-fourth","tag-harmonic-series","tag-lattice","tag-mathieu","tag-polarity","tag-resolution","tag-tension"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1484","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=1484"}],"version-history":[{"count":8,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1484\/revisions"}],"predecessor-version":[{"id":2056,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1484\/revisions\/2056"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}