Microtones

Pitches in relanote default to 12-tone equal temperament (12-EDO), which is the same grid every piano in the world uses. But "everything is relative" includes the grid itself — pitches resolve through whatever tuning is in scope. Swap that tuning and the same melody plays at different frequencies.

This page covers three orthogonal mechanisms:

1. Direct cents offsets on individual pitches and intervals — a

per-note escape hatch.

2. Tuning declarations — a named pitch system that scale-degree

references resolve through.

3. Activating a tuning — set tuning = … for a whole piece, or a

piped variant for a single passage.

Cents on a single note

+Xc and -Xc push a pitch by X cents (100 cents = 1 semitone). Modifiers can chain — M3 +12.5c -3c lands the pitch 9.5 cents above the conventional major third.

scale Major = { R, M2, M3, P4, P5, M6, M7 }

; Just-intonation major third — 13.7 cents flat of 12-EDO M3.
| <1> M3 -13.7c <5> |

; A blues 3rd: between m3 and M3, leaning low.
| <1> m3 +30c <5> |

Cents can also be the *whole* pitch, with no interval base — useful when nothing maps cleanly into intervals:

; A pitch 50 cents above C4 (a quarter-tone "C-half-sharp").
| C4 +50c |

; Scale degree with fine-tune offset.
| <3 +5c> |

Tuning declarations

A tuning describes how one octave is divided. The stdlib ships several common ones (see tunings.rela):

; Equal divisions of the octave — 24 quarter-tone steps.
tuning EDO24 = equal { steps: 24 }

; Explicit frequency ratios — 5-limit just intonation.
tuning JustIntonation = ratios [
  1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8
]

; Cents offsets relative to 12-EDO — well-temperament.
tuning WerckmeisterIII = cents [
  0.0, -3.91, -7.82, -5.86, -9.77, -1.96,
  -5.86, -3.91, -5.86, -7.82, -3.91, -7.82
]

; Non-octave equal — Bohlen-Pierce divides 3:1 into 13.
tuning BohlenPierce = ratios_per_period { period: 3/1, steps: 13 }

The four modes (equal, ratios, cents, ratios_per_period) cover the systems most music theory and contemporary microtonalists use.

Activating a tuning

set tuning = X switches the active tuning for the whole program:

set tuning = JustIntonation
scale Major = { R, M2, M3, P4, P5, M6, M7 }

; Now <3> is a just major third, not the tempered 400-cent one.
| <1> <3> <5> |

You can also tag a specific passage:

let just_passage = | <1> <3> <5> | |> in_tuning JustIntonation
let temp_passage = | <1> <3> <5> |

just_passage ++ temp_passage    ; both rooted in the same key, different feel

Why bother

• Period instruments. Werckmeister, Kirnberger, Vallotti — playing

18th-century music in a contemporaneous well-temperament rather than 12-EDO is the difference between a faithful performance and a modernised one.

• Non-Western traditions. Maqam, raga, gamelan and Persian dastgah

use intervals that don't fit on a piano. The cents and ratios_per_period modes are designed for them.

• Contemporary microtonal composition. Composers from Partch to

Glasper drop micro-pitches into otherwise tonal material; the per-note cents offset is the simplest way in.

• Subtle expression. A "blue note" — a third slightly flatter than

m3 — is the difference between a textbook blues phrase and a phrase that sounds played-by-a-human.

Status

The AST supports microtone literals, tuning declarations and the set tuning / |> in_tuning activation forms today (src/ast/sound.mbt). The parser and evaluator still treat them as forward-declarations — they parse and round-trip but don't yet shift MIDI pitch bend or change synthesis frequencies. The audible behaviour lands alongside the parser / evaluator ports.

Listen-through example

The current preview can already expose the neighboring pitch colors that microtonal writing grows from: minor/major thirds and sharpened/flatted neighbors around the fifth.

let tempered = | P1 M3 P5 P8 |:4
let blue     = | P1 m3 P4 P4+ P5 P5- P4 |:4
let answer   = | P1 m3 P5 m7 P8 |:4

tempered ++ blue ++ answer