What an interval is
An interval is the distance between two notes and is described by two pieces of information: the number (how many note names you count, endpoints included) and the quality (perfect, major, minor, augmented, diminished). From C to E you count three names (C D E): it is a third; it contains 4 semitones, so it is a major third.
Simple intervals, counted from C
- 0 semitones: unison (C–C)
- 1: minor second (C–Db)
- 2: major second (C–D)
- 3: minor third (C–Eb)
- 4: major third (C–E)
- 5: perfect fourth (C–F)
- 6: tritone, that is, augmented fourth (C–F#) or diminished fifth (C–Gb)
- 7: perfect fifth (C–G)
- 8: minor sixth (C–Ab)
- 9: major sixth (C–A)
- 10: minor seventh (C–Bb)
- 11: major seventh (C–B)
- 12: octave (C–C)
Beyond the octave come the compound intervals: ninth = octave + second (C–D an octave higher), eleventh = octave + fourth, thirteenth = octave + sixth. These are the names you find in chord symbols (Cmaj9, G13).
Inversion
Inverting an interval means moving the lower note up an octave. There are two rules:
- the numbers always add up to 9 (third ↔ sixth, second ↔ seventh, fourth ↔ fifth);
- the quality is swapped (major ↔ minor, augmented ↔ diminished; perfect stays perfect).
The semitones of the two intervals always add up to 12. Examples: C–E (major third, 4) becomes E–C (minor sixth, 8); B–F (diminished fifth) becomes F–B (augmented fourth): the tritone inverts into another tritone.
Consonance and dissonance
In the tonal tradition: perfect consonances (unison, fifth, octave), imperfect consonances (thirds and sixths), dissonances (seconds, sevenths, tritone). The perfect fourth is consonant between the upper voices but is treated as a dissonance when it forms with the bass. This classification underlies all of counterpoint and voice leading.
In production
- Parallel thirds and sixths are the basis of pop vocal harmonies.
- The empty fifth (power chord C5 = C G) gives energy without saying whether the chord is major or minor: useful in rock and in rage pads.
- The tritone is the engine of the dominant: in G7 the notes B and F want to resolve to C and E.
Real example
In “Maria” from West Side Story (Bernstein, 1957) the melody of the name rises by a tritone and immediately settles, rising by a semitone, on the perfect fifth: tension and resolution in three notes. “Over the Rainbow” instead opens with an ascending octave leap, a classic example for recognizing the interval by ear.