temperaments

Musical tunings/temperaments for Javascript

Installation

npm i temperaments

Documentation

Below are some examples. The main API documentation is hosted on the project Github pages.

To generate documentation locally run:

npm run doc

Equal temperaments

import Temperament from 'temperaments';

// Twelve-tone equal temperament for 5-limit = 2.3.5
const edo12 = Temperament.fromVals([12], '2.3.5');

// How many steps represents a major seventh
edo12.steps('15/8'); // 11

// How many cents is a major seventh in 12edo
edo12.tune('15/8'); // 1100.0

Rank-2 temperaments

import Temperament from 'temperaments';

// Meantone as the val-join of 12edo and 19edo
const meantone = Temperament.fromVals([12, 19], '2.3.5');

// How many cents is the fifth in POTE meantone
meantone.tune('3/2'); // 696.239

// How about with tempered octaves
meantone.tune('3/2', {temperEquaves: true}); // 697.049

// How big is that octave
meantone.tune('2/1', {temperEquaves: true}); // 1201.397

POTE Mapping vector

import {toMonzo, dot} from 'xen-dev-utils';
import {Temperament} from 'temperaments';

// Porcupine temperament from the porcupine comma
// The subgroup 2.3.5 is automatically inferred
const porcupine = Temperament.fromCommas(['250/243']);

const POTE = porcupine.getMapping();

const minorThird = toMonzo('6/5');
const perfectFourth = toMonzo('4/3');

const m3Cents = dot(minorThird, POTE); // 327.901
const P4Cents = dot(perfectFourth, POTE); // 491.851

// These are the same because we're in porcupine
2 * P4Cents; // 983.702
3 * m3Cents; // 983.702

Fractional just intonation subgroups

import {Temperament} from 'temperaments';

const pinkan = Temperament.fromCommas(
  ['676/675', '1216/1215'],
  '2.3.13/5.19/5'
);

// CTE optimized
pinkan.tune('15/13', {constraints: ['2/1']}); // 248.846

Named temperaments

const passion = Temperament.fromName('passion');

Color temperaments

import {colorTemperament} from 'temperaments';
const mavila = colorTemperament('Layobi');

const superkleismic = colorTemperament('Tritriyo & Zotriyo');

Color commas

import {colorComma} from 'temperaments';

const comma = colorComma('Loru');

Large subgroups

Temperament instances get computationally expensive beyond subgroups larger than ~8. If you just need the TE mapping you can get it through optimized numeric methods.

import {tenneyVals, Subgroup, vanishCommas} from 'temperaments';

const magicMapping = tenneyVals([19, 22], new Subgroup(5));

// Not an exact TE mapping, but pretty close.
const miracleMapping = vanishCommas(["225/224", "1029/1024"]);

Gotchas

Subgroup needs to be explicit if the commas do not involve all of the primes in the limit.

// Specifying 5-limit is required if you do not want 2.5
const augmented = Temperament.fromCommas(['128/125'], 5);

If you want a mapping vector that covers a full prime limit, must pass {primeMapping: true} to Temperament.getMapping for subgroups that aren't full prime limits.

const slendric = Temperament.fromCommas(['1029/1024']);
const POTE = slendric.getMapping({primeMapping: true});

Additional resources

To work with named temperaments like Meantone or Marvel see named-temperaments.