Inverting intervals
Music theory · Intervals · Level 4 · 8 min
To invert an interval, move the lower note up an octave (or the upper note down an octave). C-E (a third) becomes E-C (a sixth). The two intervals complement each other to make an octave.
M:4/4 L:1/4 Q:1/4=72 K:C [CE]2 [Ec]2 | [CG]2 [Gc]2 | [CA]2 [Ac]2 | [CB]2 [Bc]2 |]
Three foolproof rules
- The numbers add up to 9: 3 ↔ 6, 4 ↔ 5, 2 ↔ 7, 1 ↔ 8.
- The qualities swap: major ↔ minor, augmented ↔ diminished; perfect stays perfect.
- The half steps add up to 12.
| Interval | Inversion |
|---|---|
| m2 (1 half step) | M7 (11) |
| M3 (4) | m6 (8) |
| m3 (3) | M6 (9) |
| P4 (5) | P5 (7) |
| A4 (6) | d5 (6) — the tritone inverts into a tritone! |
Calculation trick: large intervals are hard to count. To name E up to D, think D up to E instead: a major second → so E-D is a minor seventh. For a sixth, work out the inverted third. It is much quicker.
Why does it matter? In harmony a chord can be voiced in any order: interval inversion explains why an inverted major chord contains fourths and sixths instead of thirds and fifths. And by ear, fourths and fifths, thirds and sixths are "cousins": learning one helps recognise the other.
Careful: "9", not "8"! Although an octave spans 8 letters, the middle note is counted twice (C-E-C: E belongs to both intervals).
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