Explorations in musical theory and manipulation using Racket, and the associated
rsound package. Support from my functional library rakeda.
This contains a bunch of utilities focused on lists of integers modulo 12 (notes in an octave) and note names. We also create named chords, and define some Neo-Riemannian transforms.
This is very much a work in progress.
The basic functions for manipulating and converting between note numbers (integers) and note names ('C to 'B), and providing basic functions for transposing, inverting, and modulo 12.
transpose transpose* invert invert*inversionsnote->num num->note num->note* collapsemap-note
Transpositions and inversions expect note numbers. map-note is a wrapper for note names, for example (map-note (transpose 4) '(C D E)).
Functions that take more than one argument are already curried so that you can easily use them in higher-order functions without explicitly doing partial evaluation.
Chords are implemented as a simple type with two fields: root note and chord name, e.g. (chord 'E 'minor). A hash table of common chords are defined in chords so that we can switch between note numbers, note names, and chord names using the provided conversion functions. This includes a reverse lookup (num->chord...) that tries to match a list of note numbers to a defined chord name.
chord->num num->chord note->chord chord->notes chord->notes* canonicalmap-chord map-chord<contains-note? chord-contains?random-chord random-related-chord random-related-chords random-chords-with-note random-chord-generator
A mapping function is also provided for chords, e.g. (map-chord inversions (chord 'D 'major)). There are also functions for finding notes in one or more chords, and for generating chords within some constraints.
Scales are based on a root note and a scale name, e.g. major, minor, myxolydian
scale->num scale->notes scale->notes*
Define the PLR group of functions on triads from [Neo-Riemannian Theory] (https://en.wikipedia.org/wiki/Neo-Riemannian_theory).
- P is an involution (i.e. a permutation with cycle length 2) between the major and minor triad of the same root: P(Cmaj) = Cmin
- R is an involution between relative major and minor triads: R(Cmaj) = Amin
- L doesn't have a recognised musical mapping: L(Cmaj) = Emin
It also defines the related transforms N, S, and H, and a function nrt/compose to chain them over a starting chord.
The function view-chord plots a chord as a series of points on a modulo 12 circle with lines joining them, as a way of visualising a chord shape. I scratched the itch but not sure how useful it is.
By leveraging the rsound Racket package, we can hear notes and chords. This is still in development but the most important function so far is play-chord, for obvious reasons. This module could really go anywhere; it's tempting to go all in and build out higher layers of composition and performance, but we already have Overtone and others for that.
This is a space for defining audio things like instruments. There's a basic dual saw-wave generator, and a simple sine wave. Maybe others to come.