{"id":1423,"date":"2013-07-29T13:04:11","date_gmt":"2013-07-29T20:04:11","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=1423"},"modified":"2017-08-30T15:09:02","modified_gmt":"2017-08-30T22:09:02","slug":"polarity-experiment","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=1423","title":{"rendered":"Polarity Experiment"},"content":{"rendered":"<p>In the <a title=\"Consonance Experiment\" href=\"http:\/\/www.garygarrett.me\/?p=1409\">last post<\/a> I did a <a title=\"Consonance and Dissonance\" href=\"http:\/\/www.garygarrett.me\/?p=1380\">consonance<\/a> experiment, listening to\u00a0<a title=\"Intervals\" href=\"http:\/\/www.garygarrett.me\/?p=1227\">intervals<\/a> with wider and wider spacing.<\/p>\n<p>In that experiment, I kept the <a title=\"The Lattice\" href=\"http:\/\/www.garygarrett.me\/?p=342\">axis (3)<\/a> and <a title=\"The Compass Points\" href=\"http:\/\/www.garygarrett.me\/?p=1273\">direction<\/a> (multiplication, overtonal) the same, and increased the distance.<\/p>\n<p>This time I&#8217;ll keep the axis and the distance the same, and switch direction. Each illustration will compare a note with its mirror twin, its <a title=\"The Compass Points\" href=\"http:\/\/www.garygarrett.me\/?p=1273\">reciprocal<\/a>.<\/p>\n<p>First up is the strongest polarity flip there is, the perfect fourth and fifth. One divides the tonic by 3, the other multiplies it by 3.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity flip 4 5\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/KgH1Bt03f4E?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>The 4 is clearly unstable, it wants to move. The 5 is clearly stable. If a song ends with this interval, I will feel completely satisfied.<\/p>\n<p>The next matchup is the b7- and the 2. The b7- is the crucial note that provides the tension\u00a0in\u00a0<a href=\"http:\/\/www.garygarrett.me\/?p=1294\">dominant-type seventh chords<\/a>\u00a0and makes their resolution so satisfying. Here it is in undiluted form.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Flip b7  2\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/_5307rcbwqM?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>The 2 is fairly stable. Quite a few songs end on <a title=\"Compound Notes\" href=\"http:\/\/www.garygarrett.me\/?p=383\">this note<\/a>, and there is a pretty good sense of resolution, maybe with some wistfulness mixed in.<\/p>\n<p>The two notes are about equally harmonious, and of opposite polarity. This is the same pattern as the 4 and 5, only weaker.<\/p>\n<p>Moving outward, we get the b3- and 6+ pair:<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Flip b3 6+\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/4Yj0zxVz1x8?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>The pattern continues &#8212; now both notes are rather dissonant, with the b3- weakly unstable and the 6+ weakly stable. It would be rather unsettling to end a song on the 6+, but maybe you could get away with it.<\/p>\n<p>Here are the next two:<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Flip b6  3+\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/pnp1QnVi9oE?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 are interesting. They are dissonant, all right, and the b6- is unstable and the 3+ is stable. But I actually hear the polarity a little more strongly than the last pair.<\/p>\n<p>I think my ear is trying to interpret these notes as out-of-tune versions of the b6 (a strongly unstable note) and the 3 (strongly stable).<\/p>\n<p>How is my ear to interpret this 3+ note, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Ditone\">Pythagorean major third<\/a>? Can I even <em>hear<\/em> a ratio of 81\/64? Maybe not well enough to really recognize it.<\/p>\n<p>Perhaps the ear &#8220;decides&#8221; that it&#8217;s simpler to read this strange note as a badly tuned version of a <a title=\"The Major Third\" href=\"http:\/\/www.garygarrett.me\/?p=292\">simpler interval<\/a>, one I am familiar with. So I hear it as an out-of-tune 5\/4 instead of an in-tune 81\/64.<\/p>\n<p>This is why equal temperament works, as Mathieu demonstrates so well in <a title=\"Harmonic Experience\" href=\"http:\/\/www.garygarrett.me\/?p=204\">Harmonic Experience<\/a>. A painting doesn&#8217;t have to be\u00a0<em>exactly<\/em>\u00a0straight on the wall for the eye to interpret it as straight. Thank goodness! In the same way, a note doesn&#8217;t have to be\u00a0<em>exactly<\/em>\u00a0in tune to be heard as that note. The ear is willing to accept &#8220;close enough&#8221; and hear it as the real thing, though the consonance will not be as good.<\/p>\n<p>Maybe the part of the mind that processes this stuff is like a <a href=\"http:\/\/www.popsci.com\/technology\/article\/2013-07\/quantum-computer-gets-double-check\">quantum computer<\/a>, taking in the sound, trying out all possibilities at once, and spitting out the &#8220;most likely&#8221; interpretation, which would be the solution with the lowest &#8220;<a href=\"http:\/\/www.physicsclassroom.com\/class\/energy\/u5l1b.cfm\">potential energy<\/a>,&#8221; the one that is closest to the center, just like real gravity.<\/p>\n<p>We&#8217;re probably too far out now to really recognize these intervals as what they are, but for the heck of it:<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Flip b2  7+\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/XSdikEh3WII?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>Suitably nasty, and now the sense of polarity is pretty much gone, I can&#8217;t hear it.<\/p>\n<p>Finally:<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Flip b5  #4++\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/7iXm-Vrl7aY?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>The Pythagorean spine, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Circle_of_fifths\">sequence of fifths<\/a>, has come full circle &#8212; almost. The two notes are 24 cents apart, a <a href=\"http:\/\/en.wikipedia.org\/wiki\/Pythagorean_comma\">Pythagorean Comma<\/a>. All that remains of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Tonality\">tonal harmony<\/a> at this distance is a generic sort of dissonance. I hear no polarity at all. The <a title=\"Tonal Gravity\" href=\"http:\/\/www.garygarrett.me\/?p=1076\">tonal gravity field<\/a> is too weak to detect.<\/p>\n<p>Here&#8217;s one more video to bring it all back <a title=\"Home\" href=\"http:\/\/www.garygarrett.me\/?p=1262\">home<\/a>. I start to <a href=\"http:\/\/en.wiktionary.org\/wiki\/smell_the_barn\">smell the stables<\/a> at about the b3-\/6+, and the sense of direction gets rapidly stronger from there.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Polarity Sequence\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/FYM8-ODeN30?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>Next:\u00a0<a href=\"http:\/\/www.garygarrett.me\/?p=1435\">Harmonic Distance<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the last post I did a consonance experiment, listening to\u00a0intervals with wider and wider spacing. In that experiment, I kept the axis (3) and direction (multiplication, overtonal) the same, and increased the distance. This time I&#8217;ll keep the axis and the distance the same, and switch direction. Each illustration will compare a note with&#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":[189,120,112,126,187],"tags":[298,84,85,39,90,241,124,88,188],"class_list":["post-1423","post","type-post","status-publish","format-standard","hentry","category-consonance-2","category-justintonation","category-thelattice","category-the-notes","category-tonal-gravity","tag-book","tag-consonance","tag-dissonance","tag-interval","tag-overtonal","tag-polarity","tag-pythagorean","tag-reciprocal","tag-tonal-gravity-2"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1423","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=1423"}],"version-history":[{"count":10,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1423\/revisions"}],"predecessor-version":[{"id":2053,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1423\/revisions\/2053"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}