{"id":2524,"date":"2022-10-04T12:20:00","date_gmt":"2022-10-04T10:20:00","guid":{"rendered":"https:\/\/reach.ircam.fr\/?p=2524"},"modified":"2024-12-10T12:22:17","modified_gmt":"2024-12-10T11:22:17","slug":"mathematical-morphology-operators-for-harmonic-analysis","status":"publish","type":"post","link":"https:\/\/reach.ircam.fr\/index.php\/2022\/10\/04\/mathematical-morphology-operators-for-harmonic-analysis\/","title":{"rendered":"Mathematical Morphology Operators for Harmonic Analysis"},"content":{"rendered":"\n<p>Gonzalo Romero-Garc\u00eda, Isabelle Bloch, Carlos Agon<\/p>\n\n\n\n<p><em>MCM 2022 &#8211; 8th International Conference Mathematics and Computation in Music<\/em>, Jun 2022, Atlanta, United States. pp.255-266<\/p>\n\n\n\n<p><a href=\"https:\/\/hal.science\/hal-03638362v2\/file\/MCM_2022_v1%20%281%29.pdf\">Read full publication.<\/a><\/p>\n\n\n\n<p><strong>Abstract<\/strong>: Mathematical Morphology provides powerful tools for image processing, analysis and understanding. In this paper, we will work on how to apply these tools to analyze scores, that are image-like representations of Music. To do that, we will consider chroma rolls, a representation of scores similar to piano rolls that use chromas instead of pitches. Endowing this representation with a lattice structure, one can define Mathematical Morphology operators, and setting a group structure to the Time-Frequency plane allows us to use the notion of structuring element. We will show throughout some examples how this relates with the notion of pitch-class set and chord progressions, and we will analyze two Chopin&rsquo;s Nocturnes with this technique.<\/p>\n\n\n\n<p><a href=\"https:\/\/hal.science\/hal-03638362v2\/file\/MCM_2022_v1%20%281%29.pdf\">Read full publication.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gonzalo Romero-Garc\u00eda, Isabelle Bloch, Carlos Agon MCM 2022 &#8211; 8th International Conference Mathematics and Computation in Music, Jun 2022, Atlanta, United States. pp.255-266 Read full publication. Abstract: Mathematical Morphology provides powerful tools for image processing, analysis and understanding. In this paper, we will work on how to apply these tools to analyze scores, that are [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":2525,"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":[46],"tags":[],"class_list":["post-2524","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-research"],"aioseo_notices":[],"blog_post_layout_featured_media_urls":{"thumbnail":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-150x150.png",150,150,true],"full":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130.png",882,431,false]},"categories_names":{"46":{"name":"Publications","link":"https:\/\/reach.ircam.fr\/index.php\/category\/research\/publications-research\/"}},"tags_names":[],"comments_number":"0","wpmagazine_modules_lite_featured_media_urls":{"thumbnail":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-150x150.png",150,150,true],"cvmm-medium":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-300x300.png",300,300,true],"cvmm-medium-plus":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-305x207.png",305,207,true],"cvmm-portrait":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-400x431.png",400,431,true],"cvmm-medium-square":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-600x431.png",600,431,true],"cvmm-large":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130.png",882,431,false],"cvmm-small":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130-130x95.png",130,95,true],"full":["https:\/\/reach.ircam.fr\/wp-content\/uploads\/2024\/12\/Screenshot-2024-12-10-122130.png",882,431,false]},"_links":{"self":[{"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/posts\/2524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/comments?post=2524"}],"version-history":[{"count":1,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/posts\/2524\/revisions"}],"predecessor-version":[{"id":2526,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/posts\/2524\/revisions\/2526"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/media\/2525"}],"wp:attachment":[{"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/media?parent=2524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/categories?post=2524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/reach.ircam.fr\/index.php\/wp-json\/wp\/v2\/tags?post=2524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}