Intervals

An interval is the distance between two notes. Intervals are the basic vocabulary of music theory — chords are stacks of intervals, scales are a sequence of intervals, and understanding them makes everything else fall into place. More practically: if you can hear intervals, you can figure out melodies by ear.

Interval Names and Sizes

Semitones   Name                   Example (from C)
0           Unison (P1)            C - C
1           Minor 2nd (m2)         C - D♭
2           Major 2nd (M2)         C - D
3           Minor 3rd (m3)         C - E♭
4           Major 3rd (M3)         C - E
5           Perfect 4th (P4)       C - F
6           Tritone (A4/d5)        C - F#/G♭
7           Perfect 5th (P5)       C - G
8           Minor 6th (m6)         C - A♭
9           Major 6th (M6)         C - A
10          Minor 7th (m7)         C - B♭
11          Major 7th (M7)         C - B
12          Octave (P8)            C - C

Interval Quality

The quality (perfect, major, minor, augmented, diminished) describes exactly how many semitones separate the notes:

Perfect — unison, 4th, 5th, octave. Called "perfect" because they don't have a major/minor version. A perfect 5th is always 7 semitones.
Major/Minor — 2nds, 3rds, 6ths, 7ths. A major interval is one semitone larger than minor.
Augmented — one semitone larger than perfect or major. An augmented 4th (tritone) = 6 semitones.
Diminished — one semitone smaller than perfect or minor. A diminished 5th (tritone) = 6 semitones.

The tritone (augmented 4th / diminished 5th) is exactly halfway through the octave — it's the same interval whether you call it an A4 or d5, which is part of why it sounds so unstable and why it drives harmonic motion in tonal music.

Consonance and Dissonance

Some intervals sound stable (consonant), others sound tense (dissonant):

Consonant:  Unison, octave, perfect 5th, perfect 4th, major/minor 3rd, major/minor 6th
Dissonant:  Minor 2nd, major 7th, tritone (most dissonant)
Mild:       Major 2nd, minor 7th (context-dependent)

Dissonance isn't bad — it's tension, and tension resolves to consonance. The minor 7th of a dominant chord (G7's F) wants to resolve down to the major 3rd of the tonic (E in C major). The tritone in the same chord wants to resolve inward or outward. This is why the V7-I resolution is so satisfying.

Compound Intervals

Intervals larger than an octave: a 9th is an octave + a 2nd, an 11th is an octave + a 4th, a 13th is an octave + a 6th. Jazz chords (maj9, 7#11, 13) are named by these compound intervals. A G13 chord stacks thirds from G up to E — the 13th above G.

Ear Training

The best way to learn intervals is to associate them with songs. Classic reference tones:

m2 — "Jaws" theme, "Joy to the World" (descending)
M2 — "Happy Birthday" (first two notes)
m3 — "Smoke on the Water" (opening riff), "Greensleeves"
M3 — "When the Saints Go Marching In", "Oh What a Beautiful Mornin'"
P4 — "Here Comes the Bride", "Amazing Grace"
Tritone — "The Simpsons" theme, "Maria" (West Side Story)
P5 — "Star Wars" theme, "Twinkle Twinkle Little Star"
m6 — "The Entertainer", "When Doves Cry"
M6 — "My Bonnie Lies Over the Ocean", "NBC" jingle
m7 — "Star Trek" theme, "Somewhere" (West Side Story)
M7 — "Don't Know Why" (Norah Jones), "Take On Me" (A-ha)