{"id":40107761,"url":"https://github.com/alexpof/interactive_mathmusic","last_synced_at":"2026-01-19T11:35:01.965Z","repository":{"id":190945308,"uuid":"242350271","full_name":"AlexPof/interactive_mathmusic","owner":"AlexPof","description":"Interactive tools for math/music","archived":false,"fork":false,"pushed_at":"2022-10-18T13:48:46.000Z","size":28,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-09-09T03:51:24.742Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":null,"has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/AlexPof.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null}},"created_at":"2020-02-22T13:55:15.000Z","updated_at":"2022-10-18T13:48:51.000Z","dependencies_parsed_at":"2023-08-27T09:40:03.211Z","dependency_job_id":null,"html_url":"https://github.com/AlexPof/interactive_mathmusic","commit_stats":null,"previous_names":["alexpof/interactive_mathmusic"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/AlexPof/interactive_mathmusic","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexPof%2Finteractive_mathmusic","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexPof%2Finteractive_mathmusic/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexPof%2Finteractive_mathmusic/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexPof%2Finteractive_mathmusic/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/AlexPof","download_url":"https://codeload.github.com/AlexPof/interactive_mathmusic/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexPof%2Finteractive_mathmusic/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28566590,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-19T08:53:44.001Z","status":"ssl_error","status_checked_at":"2026-01-19T08:52:40.245Z","response_time":67,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.6:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2026-01-19T11:35:01.899Z","updated_at":"2026-01-19T11:35:01.958Z","avatar_url":"https://github.com/AlexPof.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"# interactive_mathmusic\nInteractive tools for math/music\n\nThis repository contains web-based interactive tools for math/music.\nDeveloped with [d3.js](https://d3js.org/) and [WebAudioFont](https://surikov.github.io/webaudiofont/).\n\n## Parsimonious graphs on triads for Douthett's and Steinbach's P\u003csub\u003em,n\u003c/sub\u003e relations\n\nAccess to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/Pmn_graphs/pmn_graphs.html)\n\nThis interactive visualization presents Douthett's and Steinbach's P\u003csub\u003em,n\u003c/sub\u003e relations on various triads.\nTwo triads are said to be P\u003csub\u003em,n\u003c/sub\u003e-related if *m* pitch classes move by a semitone,\nwhile *n* pitch classes move by a whole tone, the rest of the pitch classes being identical.\nThe set of triads and the set of P\u003csub\u003em,n\u003c/sub\u003e relations can be selected from the page. The nodes are clickable and will let you play the\ncorresponding chord.\nShift-clicking on a node saves the chord in a progression which can then be replayed.\n\n\nFor more information :\n\n  * The original paper : Douthett, Jack, and Peter Steinbach. 1998. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42 (2): 241–263.\n\n  * See this [blog post](https://alpof.wordpress.com/2019/09/22/transformational-music-theory-16/).\n\n## Chord creator with Douthett's and Steinbach's P\u003csub\u003em,n\u003c/sub\u003e relations\n\nAccess to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/Pmn_chordcreator/pmn_chordcreator.html)\n\nA variant of the above interactive page, which allows the user to create the chords of his choice and to visualize Douthett's and Steinbach's P\u003csub\u003em,n\u003c/sub\u003e relations between them.\n\n## Rhythmic canons mod 2\n\nAccess to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/rhythm_canon_mod2/rhythm_canon_mod2.html)\n\nA *rhythmic canon 'modulo 2'* is a periodic tiling of the integers by a pattern of beats, such that only an odd number of players play on each beat ('modulo 2').\n\nThe study of rhythmic canons mod *p* (with *p* prime) is closely related to the study of polynomials and their factorization in a finite field Fp.\nIt was proved by Amiot that any polynomial in Fp (the *motive*) tiles the integers modulo p, i.e. for any polynomial A(X) in Fp, there exists E(X) in Fp (the *entries*), and *L* such that\nwe have A(X)E(X)=1+X+X\u003csup\u003e2\u003c/sup\u003e+...+X\u003csup\u003eL-1\u003c/sup\u003e.\nThe motive and the entries can be swapped, creating a new rhythmic canon mod *p*.\n\nFor more information :\n\n  * Amiot, E.; 'Structures, Algorithms and algebraic tools for rythmic canons', Perspectives of New Music, 49 (2), 2011, pp. 93-142.\n\n  * Caure, H.; 'Modulus p Vuza canons: generalities and resolution of the case {0,1,2k} with p=2', arXiv:1505.06930.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falexpof%2Finteractive_mathmusic","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Falexpof%2Finteractive_mathmusic","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falexpof%2Finteractive_mathmusic/lists"}