{"id":71,"date":"2012-06-11T23:39:00","date_gmt":"2012-06-12T06:39:00","guid":{"rendered":"https:\/\/schoenblog.com\/?p=71"},"modified":"2012-06-11T23:58:24","modified_gmt":"2012-06-12T06:58:24","slug":"hilary-hahn-wants-your-tone-rows","status":"publish","type":"post","link":"https:\/\/schoenblog.com\/?p=71","title":{"rendered":"Hilary Hahn wants your &#8220;tone rows&#8221;"},"content":{"rendered":"<div class=\"fcbkbttn_buttons_block\" id=\"fcbkbttn_left\"><div class=\"fcbkbttn_button\">\n\t\t\t\t\t<a href=\"https:\/\/www.facebook.com\/randols\" target=\"_blank\">\n\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/schoenblog.com\/wp-content\/plugins\/facebook-button-plugin\/images\/standard-facebook-ico.png\" alt=\"Fb-Button\" \/>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div><div class=\"fcbkbttn_like \"><fb:like href=\"https:\/\/schoenblog.com\/?p=71\" action=\"like\" colorscheme=\"light\" layout=\"button_count\"  size=\"small\"><\/fb:like><\/div><div class=\"fb-share-button  \" data-href=\"https:\/\/schoenblog.com\/?p=71\" data-type=\"button_count\" data-size=\"small\"><\/div><\/div><p>The violinist Hilary Hahn posted a video asking people to submit &#8220;tone rows&#8221; for some as yet unrevealed purpose related to her <a href=\"http:\/\/hilaryhahncontest.com\/\">Encores Contest<\/a>, ending June 15. \u00a0I am using her announcement to experiment with embedding a video on this blog.<\/p>\n<p><iframe loading=\"lazy\" src=\"http:\/\/www.youtube.com\/embed\/4GgnKiy4Jc8\" frameborder=\"0\" width=\"560\" height=\"315\"><\/iframe><\/p>\n<p>I wonder if she will want an<a href=\"http:\/\/en.wikipedia.org\/wiki\/All-interval_twelve-tone_row\" target=\"_blank\"> all-interval twelve-tone row<\/a>. \u00a0I wrote my Princeton thesis in 1988 on some attempts to classify those. \u00a0Wikipedia says &#8220;There are 3,856 distinct all-interval twelve-tone rows.&#8221; \u00a0(A row is not distinct if it is just a transposition up or down of another row, so for each of these there are actually 11 others.) \u00a0In fact, if you remove the inversions, you get 1,928, a finding of Stefan Bauer-Mengelberg and Malvin Ferentz from 1965. \u00a0In my thesis I described several further operations that allowed me to reduce the number of distinct all-interval twelve-tone row generators to just 286. \u00a0The total number of all-interval 12-tone rows is 46,272 and the total number of twelve-tone rows of any type is 12! or 479,001,600.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The violinist Hilary Hahn posted a video asking people to submit &#8220;tone rows&#8221; for some as yet unrevealed purpose related to her Encores Contest, ending June 15. \u00a0I am using her announcement to experiment with embedding a video on this &hellip; <a href=\"https:\/\/schoenblog.com\/?p=71\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-71","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/posts\/71","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/schoenblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=71"}],"version-history":[{"count":5,"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/posts\/71\/revisions"}],"predecessor-version":[{"id":74,"href":"https:\/\/schoenblog.com\/index.php?rest_route=\/wp\/v2\/posts\/71\/revisions\/74"}],"wp:attachment":[{"href":"https:\/\/schoenblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=71"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schoenblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=71"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schoenblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=71"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}