Chords (31EDO)

`chords31(beats, scale, progression)`

Returns a ChordPattern that steps through a chord progression in 31-tone equal temperament. All intervals are calculated in 31EDO steps; chord tones are not constrained to 12EDO semitones.

chords31(beats: number, scale: ScalePattern | string, progression: string): ChordPattern

The scale argument should come from scales31().

Progression format

Space- or comma-separated chord tokens:

'Ineu IVneu V^maj Ineu'

Each token has the form:

<Roman><microShift?><quality?><slash?>

Roman numerals

Uppercase only. I through VII.

Microtonal accidentals (microShift)

Written after the Roman numeral, before the quality. Multiple symbols accumulate.

Symbol	Step change	Cents	Example
`^`	+1	+39	`V^maj` → V raised 39 cents
`^^`	+2	+77	`IV^^neu`
`v`	−1	−39	`Iv` → I lowered 39 cents
`vv`	−2	−77	`IIIvvmaj`
`#`	+5	+194	`IVb#maj` (chromatic sharp)
`b`	−5	−194	`IIIbneu` (chromatic flat)

Symbols can be combined: Iv^ = −1 + 1 = net 0; IVb^ = −5 + 1 = −4 steps.

Chord qualities

Triads

Quality	Steps	Sound
`maj`	0, 10, 18	Major (387 cent third)
`min`	0, 8, 18	Minor (310 cent third)
`neu`	0, 9, 18	Neutral (348 cent third) — exclusive to 31EDO
`dim`	0, 8, 16	Diminished
`aug`	0, 10, 21	Augmented

Seventh chords

Quality	Steps	Sound
`maj7`	0, 10, 18, 28	Major 7th
`min7`	0, 8, 18, 27	Minor 7th
`neu7`	0, 9, 18, 27	Neutral triad + neutral 7th
`7`	0, 10, 18, 27	Dominant 7th (major triad + neutral 7th)

Omitting a quality gives a diatonic triad built from the current scale’s intervals.

Ties

~ or _ after a chord extends it by one step (same as chords()):

chords31(4, key, 'Ineu~~ Vmaj')   // Ineu for 3 beats, Vmaj for 1

Octave shift

Append < (down) or > (up) to shift all chord tones by one octave (31 steps). Repeat for multiple octaves, or use <N> with a signed integer.

Syntax	Octaves
`IVmaj<`	−1
`IVmaj>`	+1
`IVmaj<<`	−2
`IVmaj<-2>`	−2 (explicit)

Compatible with microShift prefixes — ^^IVmaj< raises the root 2 steps and voices the chord one octave lower.

// Neutral chord voiced an octave lower for bass texture
const prog = chords31(4, key, 'Ineu IVneu< Vmaj Ineu')

Inversions & slash chords

Identical syntax to chords():

Imaj/1 — first inversion (bottom tone raised one octave)
Vmaj/I — V major over I bass

Examples

Basic neutral progression

const key  = scales31(4, 'D4:neutral')
const prog = chords31(4, key, 'Ineu IVneu Vmaj Ineu')
yield cast(pad, prog, seq(4, '{0,2,4},~,~,~'), ctx)

Microtonal root inflection

// V^maj: dominant root raised 39 cents — adds upward pull before resolution
// IV^neu: subdominant root raised 39 cents with neutral quality — dreamlike colour
const progA = chords31(8, key, 'Ineu IVneu V^maj Ineu')
const progB = chords31(8, key, 'Imaj IV^neu Vvmaj Imaj')

Exposing the neutral third via arpeggio

When cast() uses a ChordPattern, sequence degree 1 is the chord’s third. With neu quality that third is the 31EDO-exclusive 348-cent interval:

// degree 0 = root, degree 1 = 3rd (neu/maj/min), degree 2 = 5th
yield cast(harp, prog, seq(8, '0,_,_,1,_,_,2,_'), ctx)

Alternating between Ineu and Imaj progressions makes the tuning difference clearly audible through this arpeggio.

Chromatic flat to reach a distant root

// IIIbneu: degree III (step 9 in neutral) shifted −5 steps → step 4
// Neutral triad built on that lowered root
chords31(8, key, 'Imaj IVmaj IIIbneu Vmaj')

Combining with `scales31()`

function* song(ctx) {
  const c    = ctx.cycle
  const mode = Math.floor(c / 8) % 2 === 0 ? 'neutral' : 'major'
  const key  = scales31(8, `E4:${mode}`)
  const prog = mode === 'neutral'
    ? chords31(8, key, 'Ineu IVneu V^maj Ineu')
    : chords31(8, key, 'Imaj IV^neu Vvmaj Imaj')

  yield cast(strings({ attack: 1.4, gain: 0.20 }), prog,
    seq(8, '{0,2,4},~,~,~,~,~,~,~'), ctx)
}

See the Dusk Gate preset for a complete working example.