Interval inversion

Take an interval and move its lower note up an octave, so the notes swap places. That is inversion, and the result is entirely predictable.

Two rules

The numbers add up to nine.

The quality flips.

So C up to E is a major third; E up to C is a minor sixth. C up to G is a perfect fifth; G up to C is a perfect fourth.

Why nine and not eight

Because interval numbers count inclusively — a third spans three letter names, counting both ends. Both intervals count the shared notes, so the total is one more than the seven steps of the octave.

Why it is worth knowing

It halves what you need to learn. Get thirds solid and you get sixths free. Get seconds and you get sevenths. Most people find the smaller intervals easier to recognise, so learning those and inverting is faster than learning all thirteen separately.

It explains chord inversions. When a C major triad appears as E–G–C, the outer interval is now a minor sixth rather than a perfect fifth. The chord has not changed; the intervals inside it have rearranged. See chord inversions.

It explains counterpoint conventions. Two voices moving in parallel thirds invert to parallel sixths, which is why both are used freely — and why parallel fifths, which invert to parallel fourths, were treated as a single problem.