https://github.com/alexpof/interactive_mathmusic
Interactive tools for math/music
https://github.com/alexpof/interactive_mathmusic
Last synced: 5 months ago
JSON representation
Interactive tools for math/music
- Host: GitHub
- URL: https://github.com/alexpof/interactive_mathmusic
- Owner: AlexPof
- Created: 2020-02-22T13:55:15.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2022-10-18T13:48:46.000Z (over 3 years ago)
- Last Synced: 2025-09-09T03:51:24.742Z (9 months ago)
- Size: 27.3 KB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# interactive_mathmusic
Interactive tools for math/music
This repository contains web-based interactive tools for math/music.
Developed with [d3.js](https://d3js.org/) and [WebAudioFont](https://surikov.github.io/webaudiofont/).
## Parsimonious graphs on triads for Douthett's and Steinbach's Pm,n relations
Access to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/Pmn_graphs/pmn_graphs.html)
This interactive visualization presents Douthett's and Steinbach's Pm,n relations on various triads.
Two triads are said to be Pm,n-related if *m* pitch classes move by a semitone,
while *n* pitch classes move by a whole tone, the rest of the pitch classes being identical.
The set of triads and the set of Pm,n relations can be selected from the page. The nodes are clickable and will let you play the
corresponding chord.
Shift-clicking on a node saves the chord in a progression which can then be replayed.
For more information :
* 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.
* See this [blog post](https://alpof.wordpress.com/2019/09/22/transformational-music-theory-16/).
## Chord creator with Douthett's and Steinbach's Pm,n relations
Access to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/Pmn_chordcreator/pmn_chordcreator.html)
A 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 Pm,n relations between them.
## Rhythmic canons mod 2
Access to the interactive page is [available here](https://alexpof.github.io/interactive_mathmusic/rhythm_canon_mod2/rhythm_canon_mod2.html)
A *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').
The 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.
It 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
we have A(X)E(X)=1+X+X2+...+XL-1.
The motive and the entries can be swapped, creating a new rhythmic canon mod *p*.
For more information :
* Amiot, E.; 'Structures, Algorithms and algebraic tools for rythmic canons', Perspectives of New Music, 49 (2), 2011, pp. 93-142.
* Caure, H.; 'Modulus p Vuza canons: generalities and resolution of the case {0,1,2k} with p=2', arXiv:1505.06930.