{"id":1710,"date":"2021-02-27T08:06:39","date_gmt":"2021-02-27T15:06:39","guid":{"rendered":"http:\/\/www.timsummers.org\/?p=1710"},"modified":"2021-02-27T10:08:47","modified_gmt":"2021-02-27T17:08:47","slug":"chord-progressions","status":"publish","type":"post","link":"http:\/\/www.timsummers.org\/?p=1710","title":{"rendered":"chord progressions"},"content":{"rendered":"\n<p>A few simple patterns within the ternary harmony system can yield a surprising wealth of familiar <a href=\"https:\/\/en.wikipedia.org\/wiki\/Diatonic_and_chromatic\">diatonic<\/a> chord progressions with close to zero computational effort.<\/p>\n\n\n\n<p>To keep things simple, I&#8217;m going to do just one sequence, reachable with only a bit shift operation. All the major\/minor folds of thirds fall naturally into the right place.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/cycle_CM.png\"><img loading=\"lazy\" width=\"791\" height=\"436\" src=\"http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/cycle_CM.png\" alt=\"\" class=\"wp-image-1718\" srcset=\"http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/cycle_CM.png 791w, http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/cycle_CM-300x165.png 300w, http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/cycle_CM-768x423.png 768w\" sizes=\"(max-width: 791px) 100vw, 791px\" \/><\/a><\/figure>\n\n\n\n<p>And it sounds familiar (in pure ratios of 3:2 relative to C Major):<\/p>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/ii_V_I_CM_just.mp3\"><\/audio><figcaption>diatonic cycle in C Major. (just intonation)<\/figcaption><\/figure>\n\n\n\n<p>Just for the sake of argument, here&#8217;s the same thing in equal temperament. It&#8217;s largely the same, perhaps a bit duller:<\/p>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"http:\/\/www.timsummers.org\/wp-content\/uploads\/2021\/02\/ii_V_I_CM_equal.mp3\"><\/audio><figcaption>diatonic cycle in C Major (equal temperament)<\/figcaption><\/figure>\n\n\n\n<p>What stands out is that the chord progressions taken together form the entire scale. <\/p>\n\n\n\n<p>The memory of all seven becomes a prediction space with a prime number of options. (This is further reinforced by the fact that many musical instruments give a strong overtone at the fifth.)<\/p>\n\n\n\n<p>It turns out that a regular &#8216;stride&#8217; over the prediction space forms important musical categories &#8212; key, scale, arpeggio &#8212; in an absolutely algorithmic way.  The efficiency of this description in machine language will allow us eventually to seamlessly join the world of music notation to the world of audio.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A few simple patterns within the ternary harmony system can yield a surprising wealth of familiar diatonic chord progressions with close to zero computational effort. To keep things simple, I&#8217;m going to do just one sequence, reachable with only a bit shift operation. All the major\/minor folds of thirds fall naturally into the right place. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[60],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/posts\/1710"}],"collection":[{"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1710"}],"version-history":[{"count":6,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/posts\/1710\/revisions"}],"predecessor-version":[{"id":1724,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=\/wp\/v2\/posts\/1710\/revisions\/1724"}],"wp:attachment":[{"href":"http:\/\/www.timsummers.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1710"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.timsummers.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}