Scales (31EDO)

`scales31(beats, dsl)`

Returns a ScalePattern tuned to 31-tone equal temperament (31EDO). The API mirrors scales() but uses 31EDO interval arithmetic throughout.

scales31(beats: number, dsl: string): ScalePattern

DSL format

Identical to scales():

'C4:major'               — single scale, repeated every cycle
'D4:neutral,E4:minor'    — two scales, cycling every beats

Available modes

All modes share the same 7-note diatonic skeleton; only the interval sizes differ.

Mode	Steps (degree 1–7)	Notes
`major`	0, 5, 10, 13, 18, 23, 28	Meantone major
`minor`	0, 5, 8, 13, 18, 21, 26	Meantone natural minor
`neutral`	0, 5, 9, 13, 18, 22, 27	Neutral 3rd & 6th (≈ maqam Rast)
`dorian`	0, 5, 8, 13, 18, 23, 26
`phrygian`	0, 3, 8, 13, 18, 21, 26
`lydian`	0, 5, 10, 15, 18, 23, 28
`mixolydian`	0, 5, 10, 13, 18, 23, 26
`locrian`	0, 3, 8, 13, 16, 21, 26

1 octave = 31 steps. Each step ≈ 38.7 cents.

Characteristic intervals

Interval	12EDO (cents)	31EDO (cents)	Steps
Minor 3rd	300	310	8
Neutral 3rd	—	348	9
Major 3rd	400	387	10
Perfect 5th	700	697	18

The neutral mode’s third (step 9) sits exactly between minor and major — a sound unavailable in 12EDO.

Examples

const key  = scales31(4, 'E4:neutral')      // E neutral, 4 beats per cycle
const low  = scales31(8, 'E3:minor')        // octave lower, minor
const prog = scales31(8, 'D4:neutral,D4:major')  // cycling neutral → major

Pass a ScalePattern to cast() just like a regular scales() result:

yield cast(synth, key, seq(4, '0,_,2,_,4,_,3,_'), ctx)

Degree → frequency mapping

cast() converts sequence degrees to frequencies using 31EDO math:

freq = rootHz × 2 ^ ((step + octaveShift × 31) / 31)

Degrees wrap across octaves automatically:

degree 0 = root
degree 7 = root + 1 octave
degree -1 = root − 1 scale step (wraps downward)