Interval inversion
Move the lower note up an octave and the interval inverts; the numbers add up to nine and the qualities swap.
Applied
Content under musical review. It may contain inaccuracies.
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Move the lower note up an octave and the interval inverts; the numbers add up to nine and the qualities swap.
Applied
To invert an interval, move its lower note up an octave (or its upper note down an octave). The two notes stay the same, but the one that was below is now on top. The new interval is the complement of the original: together they fill an octave.
A major third and its inversion, a minor sixth. Same two notes, different order:
A perfect fifth and its inversion, a perfect fourth:
On the fretboard, the perfect fifth and the perfect fourth share notes. Notice how every A has a D just above it (a fourth) and another below it (a fifth):
String 6, Fret 5: A2 · 5 · Fifth
String 6, Fret 1: F2 · ♭7 · Scale tone
| Interval | Abbreviation | Semitones |
|---|---|---|
| unison | P1 (1) | 0 |
| minor second | m2 (♭2) | 1 |
| major second | M2 (2) | 2 |
| minor third | m3 (♭3) | 3 |
| major third | M3 (3) | 4 |
| perfect fourth | P4 (4) | 5 |
| augmented fourth (tritone) | A4 (♯4) | 6 |
| perfect fifth | P5 (5) | 7 |
| minor sixth | m6 (♭6) | 8 |
| major sixth | M6 (6) | 9 |
| minor seventh | m7 (♭7) | 10 |
| major seventh | M7 (7) | 11 |
| octave | P8 (8) | 12 |
Measure an interval, then swap the notes. Check that the half steps of the two add up to twelve:
From C to E From E to CTwo rules are all you need to invert any simple interval:
| Interval | Half steps | Inversion | Half steps |
|---|---|---|---|
| minor second | 1 | major seventh | 11 |
| major second | 2 | minor seventh | 10 |
| minor third | 3 | major sixth | 9 |
| major third | 4 | minor sixth | 8 |
| perfect fourth | 5 | perfect fifth | 7 |
| augmented fourth | 6 | diminished fifth | 6 |
The tritone is the only one that inverts into itself in half steps: six and six.
On the guitar this saves work. If you want a major sixth above a note and the shape feels awkward, look for a minor third below the target note: it's the same pair of notes in another octave.
A C chord has C, E and G. Put E in the bass (C/E) and the distance from E up to C is a minor sixth: the original third, inverted. That's why chord inversions have a different colour even with the same notes.
Inversion keeps the type of consonance: thirds and sixths are imperfect consonances; seconds and sevenths, dissonances. The exception is the fourth-fifth pair: the perfect fifth is a perfect consonance, but in tonal counterpoint a perfect fourth above the bass is treated as a dissonance.
Compound intervals are inverted by first reducing them to simple ones: a major tenth reduces to a major third, and its inversion is a minor sixth.