temperaments
v0.5.3
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Musical tunings/temperaments for Javascript
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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.