Intervals

An interval is the distance between two notes, written without committing to either of them. Intervals are the smallest "relative" unit in the language; scales are sets of intervals, chords are sets of intervals, melodies are sequences of scale-degree references that resolve through intervals.

Notation

Every interval is <quality><degree> with optional semitone modifiers:

text

P1   m2   M2   m3   M3   P4   A4   d5   P5   m6   M6   m7   M7   P8

Quality	Letter
Root / unison	`R` (equivalent to `P1`)
Perfect	`P` (1, 4, 5, 8…)
Major	`M` (2, 3, 6, 7…)
Minor	`m`
Augmented	`A`
Diminished	`d`

The number is the scale degree.

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P1   ; perfect unison (0 semitones)
m2   ; minor second   (1)
M2   ; major second   (2)
m3   ; minor third    (3)
M3   ; major third    (4)
P4   ; perfect fourth (5)
A4   ; augmented 4th, a.k.a. tritone (6)
d5   ; diminished 5th, also 6 — enharmonic to A4
P5   ; perfect fifth  (7)
m6   ; minor sixth    (8)
M6   ; major sixth    (9)
m7   ; minor seventh  (10)
M7   ; major seventh  (11)
P8   ; perfect octave (12)

Semitone modifiers

Append + to raise by a semitone, - to lower. Stack them for larger shifts:

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P5+   ; perfect fifth + 1 = 8 semitones (enharmonic to m6)
M3-   ; major third - 1 = 3 (enharmonic to m3)
P1++  ; +2 semitones = M2
P4--  ; -2 semitones = 3

Cents and microtones

Internally relanote works in cents (100 cents per semitone), so microtones and alternative tunings are first-class. MIDI output emits pitch-bend messages for any fractional semitone.

Chromatic passages

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

let up   = | P1 P1+ M2 M2+ M3 P4 |
let down = | P5 P5- P4 P4- M3 M3- M2 |

A full chromatic scale

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let chromatic = |
  P1 P1+ M2 M2+ M3 P4
  P4+ P5 P5+ M6 M6+ M7
  P8
|

Blue notes

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let blues = | P1 m3 P4 P4+ P5 m7 P1 - |

Neighbour tones

A common ornament — step away by a semitone, return:

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let upper = | P5 P5+ P5 - |
let lower = | P5 P5- P5 - |
let both  = | P5 P5+ P5 - P5 P5- P5 - |

Whole-tone

Only major seconds:

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let whole_tone = | P1 M2 M3 A4 m6+ M7 |

Arithmetic

Intervals add and subtract:

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M3 + m3    ; = P5     (4 + 3)
P8 - P5    ; = P4     (12 - 7)
M2 + M2    ; = M3     (2 + 2)

Common shapes built from intervals

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[P1, M3, P5]            ; major triad
[P1, m3, P5]            ; minor triad
[P1, M3, P5, m7]        ; dominant 7th
[P1, M2, M3, P4, P5, M6, M7]    ; major scale
[P1, M2, m3, P4, P5, m6, m7]    ; natural minor

Intervals as functions

Because intervals are values, you can build transformations out of them:

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let up_a_fifth = \i -> i + P5

P1 |> up_a_fifth    ; P5
M3 |> up_a_fifth    ; M7

Enharmonic equality

Two intervals with the same semitone distance compare equal:

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A4 == d5    ; both six semitones (tritone)

Listen-through example

Hear the page as interval color: a major outline, a minor outline and a chromatic neighbor-tone turn.

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let major_outline = | P1 M3 P5 P8 |:4
let minor_outline = | P1 m3 P5 P8 |:4
let color_turn    = | P4 P4+ P5 P5- P4 |:4

major_outline ++ minor_outline ++ color_turn