Interval inversion
When an interval is inverted, the lower note moves up an octave, or the upper note down an octave. C–E becomes E–C, the third becomes the sixth. The inverted interval completes the original to an octave and is therefore also called the complementary interval.
- Rule 1
- The numbers of interval and inversion add up to 9
- Rule 2
- major ↔ minor, augmented ↔ diminished, perfect stays perfect
- Also called
- complementary interval (completion to the octave)
- Not to be confused with
- chord inversion
Putting the lower note on top
Take two notes, say C and E, and put the lower one an octave higher. C–E (major third) becomes E–C (minor sixth). The same works if you put the upper note an octave lower. Two rules hold without exception:
- The numbers of interval and inversion add up to 9. A third (3) becomes a sixth (6), a fourth (4) a fifth (5), the second (2) a seventh (7).
- The quality turns around. Major becomes minor, minor becomes major, augmented becomes diminished, diminished becomes augmented, perfect stays perfect.
A major third becomes a minor sixth
On the left the major third C–E (four semitones), on the right its inversion E–C, a minor sixth (eight semitones). 4 + 8 = 12, so an octave.
A perfect fifth becomes a perfect fourth
The perfect fifth C–G (seven semitones) inverts to the perfect fourth G–C (five semitones). Perfect stays perfect.
An augmented fourth becomes a diminished fifth
The augmented fourth F–B (six semitones) becomes the diminished fifth B–F. The tritone is the only interval that inverts into an interval of the same size (6 + 6 = 12, in equal temperament).
In the glossary: Octave · Third · Perfect intervals
Overview
| Interval | becomes | Semitones |
|---|---|---|
| Unison | octave | 0 + 12 |
| Second (minor/major) | seventh (major/minor) | 1 + 11, 2 + 10 |
| Third (minor/major) | sixth (major/minor) | 3 + 9, 4 + 8 |
| Fourth (perfect) | fifth (perfect) | 5 + 7 |
| Fourth (augmented) | fifth (diminished) | 6 + 6 |
The semitone counts of an interval and its inversion always add up to 12, so an octave. That is why an interval and its inversion are also called complementary intervals: they complete each other to the octave.
What it is useful for
If you hear the smaller intervals reliably, you can work out the larger ones by inversion: a sixth that is hard to hit can be thought of as an inverted third. In singing a wide leap can be derived through its complement: a sixth upwards corresponds to a third downwards. When identifying intervals in notation it is often enough to count out the smaller counterpart.
In harmony teaching inversion explains why certain intervals are judged together. Third and sixth are both imperfect consonances and may be moved in parallel. Fifth and fourth belong together, though the fourth above the bass is treated as a dissonance even though its inversion, the fifth, is consonant. Second and seventh are both dissonant, in different registers: the wide seventh sounds more open than the narrow second. In counterpoint, double (invertible) counterpoint rests on the same principle: if you swap the voices, every interval turns into its complement, and fifths become fourths.
Distinctions
Interval inversion is something different from chord inversion. There a different chord note moves to the bass and the chord keeps its name. Here a two-note interval is turned over and gets a new name.
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Related terms
Chord inversionOctaveThirdAugmented fourthTritonePerfect intervalsSix-four chord
Editor: Maik Krohm · reviewed on 3 October 2026
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