Inverting Intervals

Interval inversion pairs two intervals that together fill an octave. For example, C up to E becomes E up to C in the next octave. To invert this third, move the lower C up an octave, or move the higher E down an octave. The pitch classes stay the same while their order changes.

If interval names are new to you, start with generic intervals and specific intervals.

The numbers add to nine

For example, 3 + 6 = 9. The two complementary intervals fill an octave; the shared middle note is counted in both interval numbers.

A perfect unison expands to a perfect octave, and a perfect octave collapses to a perfect unison. These boundary cases do not reverse two distinct pitches.

The quality changes too

Use both tables. A perfect fourth becomes a perfect fifth; a major third becomes a minor sixth.

For the diminished-fourth example, take C up to F flat. The letters give a fourth and the pitch distance is four semitones. Move C up an octave: F flat up to C is an augmented fifth, spanning eight semitones. Keep the spelling F flat throughout the calculation.

These rules describe simple intervals and their octave complements. For an interval wider than an octave, first reduce it to the corresponding simple interval by removing complete octaves.

Play a pair and its inversion

In standard tuning, use string 2. Play C at fret 1, then E at fret 5: a major third. Now play E at fret 5, then the higher C at fret 13: a minor sixth. Move your hand between notes if needed; this is a listening exercise, not a stretch to hold.

Try naming the inversion of a minor seventh before checking the tables. It is a major second.

Reference: Robert Hutchinson’s Inversion of intervals explained and Open Music Theory: intervals and dyads.