Intervals Reference

Complete reference for musical intervals in Relanote.

Interval Notation

Format: <Quality><Number><Modifier>

Quality

Symbol	Name	Description
P	Perfect	Unison, 4th, 5th, octave
M	Major	2nd, 3rd, 6th, 7th
m	Minor	Flattened major intervals
A	Augmented	Raised by half step
d	Diminished	Lowered by half step

Number

The scale degree (1-13+).

Modifier

Symbol	Meaning
+	One octave up
-	One octave down
++	Two octaves up
--	Two octaves down

Complete Interval Table

Interval	Semitones	Name
R / P1	0	Root / Perfect Unison
m2	1	Minor Second
M2	2	Major Second
m3	3	Minor Third
M3	4	Major Third
P4	5	Perfect Fourth
A4 / d5	6	Tritone
P5	7	Perfect Fifth
m6	8	Minor Sixth
M6	9	Major Sixth
m7	10	Minor Seventh
M7	11	Major Seventh
P8	12	Perfect Octave

Extended Intervals

Interval	Semitones	Name
m9	13	Minor Ninth
M9	14	Major Ninth
m10	15	Minor Tenth
M10	16	Major Tenth
P11	17	Perfect Eleventh
A11	18	Augmented Eleventh
P12	19	Perfect Twelfth
m13	20	Minor Thirteenth
M13	21	Major Thirteenth

Interval Arithmetic

Addition

M3 + m3    ; = P5 (4 + 3 = 7 semitones)
P5 + P4    ; = P8 (7 + 5 = 12 semitones)
M2 + M2    ; = M3 (2 + 2 = 4 semitones)

Subtraction

P8 - P5    ; = P4 (12 - 7 = 5 semitones)
M7 - M3    ; = P5 (11 - 4 = 7 semitones)

Inversion

invert(M3)    ; = m6 (12 - 4 = 8 semitones)
invert(P5)    ; = P4 (12 - 7 = 5 semitones)
invert(m2)    ; = M7 (12 - 1 = 11 semitones)

Common Patterns

Major Triad

chord MajorTriad = [ R, M3, P5 ]    ; 0, 4, 7 semitones

Minor Triad

chord MinorTriad = [ R, m3, P5 ]    ; 0, 3, 7 semitones

Dominant 7th

chord Dom7 = [ R, M3, P5, m7 ]    ; 0, 4, 7, 10 semitones

Major 7th

chord Maj7 = [ R, M3, P5, M7 ]    ; 0, 4, 7, 11 semitones

Major Scale

scale Major = { R, M2, M3, P4, P5, M6, M7 }
; 0, 2, 4, 5, 7, 9, 11 semitones

Natural Minor Scale

scale Minor = { R, M2, m3, P4, P5, m6, m7 }
; 0, 2, 3, 5, 7, 8, 10 semitones

Enharmonic Equivalents

These intervals have the same number of semitones:

Semitones	Intervals
6	A4, d5
1	m2, A1
11	M7, d8

In Relanote, enharmonically equivalent intervals are treated as equal:

A4 == d5    ; true (both are 6 semitones)