{"id":1380,"date":"2013-07-22T11:18:58","date_gmt":"2013-07-22T18:18:58","guid":{"rendered":"http:\/\/www.garygarrett.me\/?p=1380"},"modified":"2017-08-25T07:41:30","modified_gmt":"2017-08-25T14:41:30","slug":"consonance-and-dissonance","status":"publish","type":"post","link":"https:\/\/www.garygarrett.me\/?p=1380","title":{"rendered":"Consonance and Dissonance"},"content":{"rendered":"<p>I just passed the 10,000 photo mark on the stop motion animations, good thing I&#8217;m not hand-drawing them like Winsor McCay!<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Gertie the Dinosaur 1914\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/ww6zqGHlgsc?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 one I&#8217;m working on, <a title=\"Real Girl for Real\" href=\"http:\/\/www.garygarrett.me\/?p=1214\">Real Girl<\/a>, has a lot of dissonant notes in it. The melody ranges far from the roots and makes some slightly dizzying harmonic jumps. I want to use it as a framework for discussing consonance and dissonance. While it&#8217;s in progress, I want to lay down some groundwork.<\/p>\n<p>The Wikipedia article\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/Consonance_and_dissonance\">Consonance and Dissonance<\/a> is really thorough. Here&#8217;s a quote from the introduction:<\/p>\n<p><em>In\u00a0<a title=\"Music\" href=\"http:\/\/en.wikipedia.org\/wiki\/Music\">music<\/a>, a\u00a0<b>consonance<\/b>\u00a0(Latin\u00a0con-, &#8220;with&#8221; +\u00a0sonare, &#8220;to sound&#8221;) is a\u00a0<a title=\"Harmony\" href=\"http:\/\/en.wikipedia.org\/wiki\/Harmony\">harmony<\/a>,\u00a0<a title=\"Chord (music)\" href=\"http:\/\/en.wikipedia.org\/wiki\/Chord_(music)\">chord<\/a>, or\u00a0<a title=\"Interval (music)\" href=\"http:\/\/en.wikipedia.org\/wiki\/Interval_(music)\">interval<\/a>\u00a0considered stable (at rest), as opposed to a\u00a0<b>dissonance<\/b>\u00a0(Latin\u00a0dis-, &#8220;apart&#8221; +\u00a0sonare, &#8220;to sound&#8221;), which is considered unstable (or temporary, transitional). In more general usage, a\u00a0consonance\u00a0is a combination of notes that sound pleasant to most people when played at the same time;\u00a0dissonance\u00a0is a combination of notes that sound harsh or unpleasant to most people.<\/em><\/p>\n<p>This definition has two distinct concepts in it &#8212; the &#8220;stability&#8221; of a harmony, and whether the notes sound pleasant or unpleasant together. I used to think of consonance\/dissonance as a linear spectrum, with consonant notes at one end and dissonant ones at the other.<\/p>\n<p>After working with the lattice, and reading <a title=\"Harmonic Experience\" href=\"http:\/\/www.garygarrett.me\/?p=204\">Mathieu<\/a>, I now see consonance as having two distinct components, that do not necessarily track together:<\/p>\n<ol>\n<li>How the notes sound together, away from any musical context. The range would be from smooth and harmonious to rough and grating.<\/li>\n<li>The stability of the interval. Does it create a sensation of rest, or does it feel restless, ready to move?<\/li>\n<\/ol>\n<p>I propose that these two qualities can be directly seen on the lattice as follows:<\/p>\n<ol>\n<li>The way the notes will sound when simply played together is a function of the <em>distance<\/em> between the notes in <a title=\"Harmonic Space\" href=\"http:\/\/www.garygarrett.me\/?p=306\">harmonic space<\/a> (how far apart they are\u00a0on the <a title=\"The Lattice\" href=\"http:\/\/www.garygarrett.me\/?p=342\">lattice<\/a>). The farther apart the two notes are, the less harmonious they will sound when played together.<\/li>\n<li>The stability of the interval is a function of the <em>direction<\/em> of the interval on the lattice (whether it&#8217;s generated by <a title=\"The Chord of Nature\" href=\"http:\/\/www.garygarrett.me\/?p=250\">multiplying<\/a>, <a title=\"A Reciprocal Note: The Fourth\" href=\"http:\/\/www.garygarrett.me\/?p=397\">dividing<\/a>, or a <a title=\"Mixed Messages\" href=\"http:\/\/www.garygarrett.me\/?p=413\">combination of the two<\/a>). Intervals generated by multiplying (moving to the East and North on the lattice) are restful, those generated by dividing (moving West and South) are unstable and restless.<\/li>\n<\/ol>\n<p>The interval quality is also powerfully affected by which primes (3, 5, 7) are used to generate the interval, but I hear this as a sort of flavor or color, rather than as consonance per se.<\/p>\n<p>The first component, the sound of the notes simply played together, is a property of the interaction of those frequencies in the ear. It isn&#8217;t dependent on the musical context in which it appears.<\/p>\n<p>The sense of stability or instability, on the other hand, depends entirely on context.\u00a0This sensation comes from the <em>direction<\/em> of the interval, which implies that the interval must start somewhere (the <a title=\"The Tonic\" href=\"http:\/\/www.garygarrett.me\/?p=187\">tonic<\/a>\u00a0or <a href=\"http:\/\/en.wikipedia.org\/wiki\/Root_(chord)\">root<\/a>) and end somewhere (the harmony note), so as to have a direction. One note is\u00a0<a title=\"Home\" href=\"http:\/\/www.garygarrett.me\/?p=1262\">home<\/a>\u00a0base, the other is an excursion from that base.<\/p>\n<p>Here a couple of examples to show the difference.<\/p>\n<p>The perfect fifth is the most consonant interval on the lattice that actually involves a distance. (Octaves and unisons are more consonant, but on the lattice, they cover no distance at all &#8212; multiplying the\u00a0<a href=\"http:\/\/en.wikipedia.org\/wiki\/Frequency\">frequency<\/a>\u00a0of a note by 1 gives a unison, which is of course the same note, and multiplying or dividing by two gives an\u00a0<a title=\"Octave Reduction\" href=\"http:\/\/www.garygarrett.me\/?p=276\">octave<\/a>, which, by a miraculous\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Octave\">quirk of human perception<\/a>, also sounds like the same note, harmonically.)<\/p>\n<p>To make a fifth, you multiply by 3. You can then then multiply or divide by 2 at will, (which doesn&#8217;t add any distance) to put it in the octave you desire. The frequencies of the two notes in this video are related by a ratio of 3:2. There is no context, just the two notes sounding together.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Fifth\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/m7Md7oQYVNc?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>This is clearly a consonant interval. There is a smoothness, a harmoniousness to the sound that I imagine would be perceived as such by anyone in the world. Two notes in a ratio of 3:2 will sound like <em>that<\/em> no matter what the context.<\/p>\n<p>So how do stability and instability enter in? It happens when there is a reference note, which can be the\u00a0<a title=\"Home\" href=\"http:\/\/www.garygarrett.me\/?p=1262\">tonic<\/a> (the main key center around which everything is arranged), a <a title=\"Tonal Gravity\" href=\"http:\/\/www.garygarrett.me\/?p=1076\">root<\/a>\u00a0(a local tonal center that changes from chord to chord), or even a bass note, which, if it is not the root of the chord, shifts the harmonic feel of the chord.<\/p>\n<p>The music in this next video establishes that the tonal center is the 1, and then introduces the 1-5 interval.<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Overtonal Fifth\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/jIed9YhAu_A?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 interval sounds stable; the ear does not crave a change. There is resolution.<\/p>\n<p>In the next video, the music establishes a new tonal center in the ear. Now it sounds like the 5 is home. Listen to what happens when I introduce the very same 1-5 interval:<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Reciprocal Fifth\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/qZLgnIdJ2_4?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 interval is <em>exactly<\/em> the same, and the effect is quite different. There is tension. Something&#8217;s gotta move!<\/p>\n<p>I can make this point more clearly by resolving the tension. Hear the unfinished quality, and how it resolves?<\/p>\n<div class=\"entry-content-asset videofit\"><iframe loading=\"lazy\" title=\"Reciprocal Fifth Resolved\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/FQAGcK3ON1U?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>Aaaaah.<\/p>\n<p>In the first video, home base is the 1, and the 5 is an overtonal note &#8212; that is, it is generated by <em>multiplying<\/em> the home note by 3. It sounds restful and stable.<\/p>\n<p>In the second video, the tonal center is the 5, and the 1 is reciprocal, that is, it is generated by <em>dividing<\/em> by 3.<\/p>\n<p>So the <em>same exact <\/em>interval can be stable or unstable according to harmonic context, even though the &#8220;degree of roughness&#8221; is the same. That&#8217;s why I think Wikipedia&#8217;s two-part definition is referring to two different things, which should be thought of separately.<\/p>\n<p>Next:\u00a0<a href=\"http:\/\/www.garygarrett.me\/?p=1409\">Consonance Experiment<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I just passed the 10,000 photo mark on the stop motion animations, good thing I&#8217;m not hand-drawing them like Winsor McCay! The one I&#8217;m working on, Real Girl, has a lot of dissonant notes in it. The melody ranges far from the roots and makes some slightly dizzying harmonic jumps. I want to use it&#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,"footnotes":""},"categories":[189,120,112,126,187],"tags":[298,36,62,19,39,27,31,49,90,88,185,34,60],"class_list":["post-1380","post","type-post","status-publish","format-standard","hentry","category-consonance-2","category-justintonation","category-thelattice","category-the-notes","category-tonal-gravity","tag-book","tag-fifth","tag-harmonic-space","tag-harmony","tag-interval","tag-lattice","tag-mathieu","tag-octave","tag-overtonal","tag-reciprocal","tag-root","tag-tonic","tag-unison"],"_links":{"self":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1380","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=1380"}],"version-history":[{"count":10,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1380\/revisions"}],"predecessor-version":[{"id":2051,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=\/wp\/v2\/posts\/1380\/revisions\/2051"}],"wp:attachment":[{"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1380"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1380"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.garygarrett.me\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}