{"id":4750,"date":"2012-04-18T00:13:12","date_gmt":"2012-04-18T00:13:12","guid":{"rendered":"http:\/\/www.warrensenders.com\/journal\/?p=4750"},"modified":"2012-04-18T00:14:18","modified_gmt":"2012-04-18T00:14:18","slug":"pulse-to-pitch-chapter-1","status":"publish","type":"post","link":"https:\/\/www.warrensenders.com\/journal\/pulse-to-pitch-chapter-1\/","title":{"rendered":"Pulse to Pitch, Chapter 1"},"content":{"rendered":"<p>I&#8217;m teaching a class for my daughter&#8217;s homeschool community in which we explore some of the relationships between music and math.  As part of that process, I began making these videos.  This set of five &#8220;movies&#8221; shows the transformation of pulsing single sounds into pitches through the process of repeated acceleration.<\/p>\n<p>Over the next few weeks I&#8217;ll be posting as complete a set of the harmonic intervals as I can manage, all derived from polymetric superimpositions of click tracks in various tempi.<br \/>\n=============================================================<\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/rVKJVoEMAUc\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>This video starts with a 60 mm click track and accelerates it repeatedly by a factor of 4: 1 beat per second \/ 4 bps \/ 16 bps \/ 64 bps \/ 256 bps \/ 1024 bps. The transformation of pulse to pitch is very clear.<\/p>\n<p>=============================================================<\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/tmdlRK7o7Wo\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>Instead of a click track, this video uses a bilabial fricative to provide a more timbrally complex starting sound. It&#8217;s moving at approximately mm60, and I accelerate it repeatedly by a factor of 4: 1 beat per second \/ 4 bps \/ 16 bps \/ 64 bps \/ 256 bps \/ 1024 bps. The transformation of pulse to pitch is clear, but the complexity of the original sound makes for a somewhat &#8220;fuzzier&#8221; pitch identity.<\/p>\n<p>=============================================================<\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/VmBnHF68QVQ\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>Instead of a click track, this video uses handclaps to provide a more &#8220;organic&#8221; starting sound. The claps move at approximately mm60, and I accelerate them repeatedly by a factor of 4, from roughly 1 beat per second to 4 bps, 16 bps, 64 bps, 256 bps, 1024 bps. The transformation of pulse to pitch is clear.<\/p>\n<p>=============================================================<\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/YeYKSD-iGFE\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>Instead of a click track, this video uses a low-register piano tone (C#) to provide a tonally complex starting sound. The impulses move at approximately mm60, and I accelerate them repeatedly by a factor of 4, from roughly 1 beat per second to 4 bps, 16 bps, 64 bps, 256 bps, 1024 bps. The transformation of pulsed pitch to pure pitch is clear (by the time the signal is accelerated 3 or 4 times, the relevant portion of the sound is no longer the original pitch, but the &#8220;attack&#8221; of the piano note).<\/p>\n<p>=============================================================<\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/y2baTHufmoo\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>Instead of a click track, this video uses a low-register piano tone (C#) to provide a tonally complex starting sound. The impulses come more slowly than the previous default tempo of mm 60. As I accelerate them repeatedly by a factor of 4, the transformation of pulsed pitch to pure pitch is clear. By the time the signal is accelerated 3 or 4 times, the relevant portion of the sound is no longer the original pitch, but the &#8220;attack&#8221; of the piano note \u2014 note that the final pitch at the end of the movie is quite different from that at the end of the previous video!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m teaching a class for my daughter&#8217;s homeschool community in which we explore some of the relationships between music and math. As part of that process, I began making these videos. This set of five &#8220;movies&#8221; shows the transformation of pulsing single sounds into pitches through the process of repeated acceleration. Over the next few [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[87,9],"tags":[1116,1117,1120,1119,1115,1121,1118],"class_list":["post-4750","post","type-post","status-publish","format-standard","hentry","category-education","category-music","tag-acoustics","tag-physics","tag-physics-of-sound","tag-pulse","tag-sound","tag-tone","tag-vibration"],"_links":{"self":[{"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/posts\/4750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/comments?post=4750"}],"version-history":[{"count":2,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/posts\/4750\/revisions"}],"predecessor-version":[{"id":4752,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/posts\/4750\/revisions\/4752"}],"wp:attachment":[{"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/media?parent=4750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/categories?post=4750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.warrensenders.com\/journal\/wp-json\/wp\/v2\/tags?post=4750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}