Interval

Two notes played sequentially or simultaneously form an interval. An interval measures the distance between notes in semitones (one twelfth of an octave.) All chords and scales are formed by two or more intervals (three or more notes), so intervals are as fundamental to harmony as pitch or notes. Some intervals have multiple names (for historical tuning reasons, and for theoretical reasons).

For a simple primer on intervals, read Pitch & Intervals.

Semitones	Name of Interval	Formula	Mnemonic
0	Unison	R	—
1	Semitone	♭2	Jaws
1	Half-step	♭2	Jaws
1	Minor Second	♭2	Jaws
2	Whole Tone	2	Happy Birthday
2	Whole-step	2	Happy Birthday
2	Major Second	2	Happy Birthday
3	Minor Third	♭3	Brahams’ Lullaby
3	Augmented Second	♯2	Brahams’ Lullaby
4	Major Third	3	Davy Crockett
4	Diminished Fourth	♭4	Davy Crockett
5	Perfect Fourth	4	Eine Kleine Nachtmusik
5	Augmented Third	♯3	Eine Kleine Nachtmusik
6	Tritone	♯4 or ♭5	The Simpsons Theme
6	Augmented Fourth	♯4	The Simpsons Theme
6	Diminished Fifth	♭5	The Simpsons Theme
7	Perfect Fifth	5	Star Wars: Luke’s Theme
8	Minor Sixth	♭6	In My Life
8	Augmented Fifth	♯5	In My Life
9	Diminished Seventh	♭♭7	My Bonnie Lies Over the Ocean
9	Major Sixth	6	My Bonnie Lies Over the Ocean
10	Minor Seventh	♭7	Star Trek
10	Augmented Sixth	♯6	Star Trek
11	Major Seventh	7	Take on Me
12	Octave	8va	Somewhere Over the Rainbow
13	Minor Ninth	♭9	—
14	Major Ninth	9	—
15	Augmented Ninth	♯9	—
16	Diminished Eleventh	♭11	—
17	Perfect Eleventh	11	—
17	Octave + Fourth	8va + 4	—
18	Augmented Eleventh	♯11	—
18	Octave + Tritone	8va + ♯4	—
19	Perfect Twelfth	12 (bogus)	—
19	Octave + Fifth	8va + 5	—
20	Minor Thirteenth	♭13	—
21	Major Thirteenth	13	—
22	Augmented Thirteenth	♯13	—

Interval Classes

In musical set theory, the octave and unison are not treated as intervals (see octave equivalence) and all possible intervals are grouped by inversion into six interval classes, denoted by colors in the intervals table.

1. Minor second / Major seventh
   1 semitone + 11 semitones = 12 semitones (1 octave)
    

2. Major second / Minor seventh
   2 semitones + 10 semitones = 12 semitones (1 octave)
    

3. Minor third / Major sixth
   3 semitones + 9 semitones = 12 semitones (1 octave)
    

4. Major third / Minor sixth
   4 semitones + 8 semitones = 12 semitones (1 octave)
    

5. Perfect fourth / Perfect fifth
   5 semitones + 7 semitones = 12 semitones (1 octave)
    

6. Tritone (its own inversion)
   6 semitones + 6 semitones = 12 semitones (1 octave)

Equal-tempered intervals that share an interval class (six classes above) have mathematically related tuning ratios (a × b = 2, e.g. P4 × P5 = 2, or 4/3 × 3/2 = 2), with the same amount of purity or impurity (tuning error compared to their just-intoned interval peers).

For more on interval classes, see Intervals as Prime Forms.