{"id":1477,"date":"2013-08-07T13:50:48","date_gmt":"2013-08-07T20:50:48","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=1477"},"modified":"2017-08-30T15:12:29","modified_gmt":"2017-08-30T22:12:29","slug":"more-mirror-twins","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=1477","title":{"rendered":"More Mirror Twins"},"content":{"rendered":"<p><a title=\"Mirror Twins\" href=\"https:\/\/www.garygarrett.me\/?p=1459\">Mirror twins<\/a> are pairs of <a title=\"Intervals\" href=\"https:\/\/www.garygarrett.me\/?p=1227\">intervals<\/a>, exactly opposite each other on the <a title=\"The Infinite Lattice\" href=\"https:\/\/www.garygarrett.me\/?p=995\">lattice<\/a>.<\/p>\n<p>The two intervals are <a href=\"http:\/\/www.mathsisfun.com\/reciprocal.html\">reciprocals<\/a>\u00a0of each other, which means their <a title=\"Notes As Ratios\" href=\"https:\/\/www.garygarrett.me\/?p=267\">ratios<\/a> are flipped &#8212; if one is 5\/3, the other is 3\/5.<\/p>\n<p><a href=\"https:\/\/www.garygarrett.me\/?p=1435\">Harmonic distance<\/a> is the same for each interval &#8212; the only difference is <a title=\"The Compass Points\" href=\"https:\/\/www.garygarrett.me\/?p=1273\">polarity<\/a>. Listening to mirror twin pairs gives a good idea of what polarity sounds like.<\/p>\n<p>The clearest example is the\u00a0<a title=\"Polarity\" href=\"https:\/\/www.garygarrett.me\/?p=1484\">fifth\/fourth pair<\/a>, multiplying and dividing the tonic by 3.<\/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>Beautiful, consonant notes, one with <a title=\"The Compass Points\" href=\"https:\/\/www.garygarrett.me\/?p=1273\">overtonal energy, and the other with reciprocal energy<\/a>.<\/p>\n<p>The next closest pair is the <a title=\"The Major Third\" href=\"https:\/\/www.garygarrett.me\/?p=292\">major third<\/a> \/ <a title=\"Reciprocal Thirds\" href=\"https:\/\/www.garygarrett.me\/?p=469\">minor sixth<\/a>. This has a different flavor. Now the tonic is multiplied and divided by 5.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Twin 3 b6\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/t_XsKosJEPc?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 overtonal third feels stable and restful, though not <em>quite<\/em> as much so as the fifth. These notes are a bit farther from the center than the 5 and 4. The reciprocal sixth sounds more dissonant\u00a0than the 4.<\/p>\n<p>The next closest note to the center is the septimal flatted seventh, or <a href=\"https:\/\/en.wikipedia.org\/wiki\/Harmonic_seventh\">harmonic seventh<\/a>. The ratio of <a title=\"Seven\" href=\"https:\/\/www.garygarrett.me\/?p=581\">this note<\/a> is 7\/1, and its mirror twin is 1\/7. I have not yet consciously used the mirror-seventh, and it&#8217;s not on my drawing of the lattice. The note is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Septimal_major_second\">septimal major second<\/a>, at 231 <a title=\"Cents\" href=\"https:\/\/www.garygarrett.me\/?p=770\">cents<\/a>, a dissonant interval indeed. The yellow lens shows where I would put it on the lattice.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Twin 7b7 72\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/mP_NZIt5ZWg?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>Oy! That should put to rest the idea that <a title=\"Untempered Vs. Tempered\" href=\"https:\/\/www.garygarrett.me\/?p=499\">just intonation<\/a> is all about <a title=\"Consonance Experiment\" href=\"https:\/\/www.garygarrett.me\/?p=1409\">consonance<\/a>! The septimal major second is nastier than anything <a title=\"Why Equal Temperament?\" href=\"https:\/\/www.garygarrett.me\/?p=1020\">equal temperament<\/a> has to offer. I like the word &#8220;<a title=\"\u201cUntempered\u201d vs. \u201cJust Intonation\u201d\" href=\"https:\/\/www.garygarrett.me\/?p=789\">untempered<\/a>&#8221; for this music because it better captures the wild and wooly nature of JI. &#8220;Just Intonation&#8221; sounds a bit stuffy to me, and the natural intervals of whole number ratios are anything but academic, they are burned in at a <a title=\"Why Can We Hear Harmony?\" href=\"https:\/\/www.garygarrett.me\/?p=1446\">very basic level<\/a>. Equal temperament is brilliant, but it&#8217;s actually the headier and less visceral of the two. IMO.<\/p>\n<p>The next pair is a little further out &#8212; each note requires\u00a0two moves on the lattice.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Twin 2 b7\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/2xmS4CujVN8?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 ratios are 9\/1 and 1\/9. I still hear the 2 as stable, though it is less consonant than the previous notes. The b7- is suitably dissonant. It\u00a0<a title=\"The Power of the Seventh Chord\" href=\"https:\/\/www.garygarrett.me\/?p=1294\">cranks up the tension<\/a> in <a href=\"http:\/\/en.wikipedia.org\/wiki\/Dominant_seventh_chord\">dominant-seventh-type chords<\/a>, the workhorse tension-resolution chords of classical music.<\/p>\n<p>I hear the effect of <em>both<\/em> tension and resolution diminishing somewhat, as <a title=\"Tonal Gravity\" href=\"https:\/\/www.garygarrett.me\/?p=1076\">tonal gravity<\/a> gets weaker farther from the <a title=\"Home\" href=\"https:\/\/www.garygarrett.me\/?p=1262\">tonic<\/a>.<\/p>\n<p>These last two videos each contain a minor seventh. One is overtonal, the other reciprocal. The septimal flatted seventh, or <a title=\"Seven\" href=\"https:\/\/www.garygarrett.me\/?p=581\">harmonic seventh<\/a>, is a stable, resolved note, the signature of barbershop harmony.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Tenacious Q - Barbershop Harmony Time\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/6SSZqzZKT1g?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>Septimal sevenths abound in this music, and they are sweet and consonant and stable.<\/p>\n<p>The b7-, on the other hand, is dissonant and tense. It makes the ear want to change.<\/p>\n<p>In equal temperament, these two notes are played exactly the same. ET weakens and obscures the difference, but it still can come through because of\u00a0<a title=\"Why Equal Temperament?\" href=\"https:\/\/www.garygarrett.me\/?p=1020\">context<\/a>.<\/p>\n<p>The common &#8220;&#8230; and many more&#8221; tag, sung at the end of Happy Birthday, is a great example. That last note, &#8220;more,&#8221; is a harmonic seventh, 7\/1, the stable, beautiful barbershop note at 969 <a title=\"Cents\" href=\"https:\/\/www.garygarrett.me\/?p=770\">cents<\/a>. If you play &#8220;and many more&#8221; on a piano, the ear will hear the last note as a septimal seventh, only with less impact, because it is very\u00a0sharp, at 1000 cents.<\/p>\n<p>Next:\u00a0<a href=\"https:\/\/www.garygarrett.me\/?p=1446\">Why Can We Hear Harmony?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mirror twins are pairs of intervals, exactly opposite each other on the lattice. The two intervals are reciprocals\u00a0of each other, which means their ratios are flipped &#8212; if one is 5\/3, the other is 3\/5. Harmonic distance is the same for each interval &#8212; the only difference is polarity. Listening to mirror twin pairs gives&#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":[189,179,120,297,112,126],"tags":[30,246,298,84,85,19,39,27,244,241,83,18],"class_list":["post-1477","post","type-post","status-publish","format-standard","hentry","category-consonance-2","category-equal-temperament-2","category-justintonation","category-septimalharmony","category-thelattice","category-the-notes","tag-animation","tag-barbershop","tag-book","tag-consonance","tag-dissonance","tag-harmony","tag-interval","tag-lattice","tag-mirror-twins","tag-polarity","tag-seventh","tag-stop-motion"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1477","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=1477"}],"version-history":[{"count":10,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1477\/revisions"}],"predecessor-version":[{"id":2057,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1477\/revisions\/2057"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}