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AP® Music Theory · Unit 2 · Topic 2.6

Interval Inversion

Interval inversion flips which note is on bottom by moving one note an octave, so the numeric size and its inversion always add to nine, and their half-step counts always add to twelve.

Watch it drawn3 questionsPractice

Take any interval and move the lower note up an octave above the upper note, or move the upper note down an octave below the lower note. Either way you flip which note sits on the bottom. The two notes are the same two pitch classes, just rearranged, and that rearrangement is called inversion. Because an octave always contains eight numbered scale steps counted inclusively, the original size and its inversion always add up to nine: a third (3) inverts to a sixth (6), a second (2) inverts to a seventh (7), a unison (1) inverts to an octave (8).

Quality flips in a predictable way too. Major becomes minor and minor becomes major, augmented becomes diminished and diminished becomes augmented, while perfect stays perfect. That is why a major third does not invert to a major sixth, it inverts to a minor sixth. You can check any inversion by counting half steps instead of letter names: the half-step counts of an interval and its inversion always add up to twelve, matching the twelve half steps in an octave.

This matters because inversion is how you simplify awkward intervals and recognize the same two notes in different arrangements, which comes up constantly once you start analyzing chords and voice leading. Knowing the 9-minus-n and 12-minus-n shortcuts lets you find an inversion instantly without redrawing the staff, and lets you double check your interval identification by working backward from the inversion.

Key terms

Inversion
Rearranging the two notes of an interval, usually by moving one note an octave, so their order flips.
Numeric size
The counted distance between two notes by letter name, such as a third or a sixth, counted inclusively.
Half step
The smallest distance between two pitches on a keyboard, such as from E to F.
Perfect interval
An interval quality, such as a fourth, fifth, or octave, that stays perfect when inverted.

Watch it explained

  1. How it worksHow does moving the lower note up an octave turn a third into a sixth?
  2. Worked exampleFind the inversion of a minor third, an augmented fourth, and a perfect fifth.
  3. Worked exampleFind the inversion of a major third and confirm it becomes a minor sixth, not a major sixth.

Check yourself

Your turn1 of 2
Inverting an interval always makes its numeric size and the inverted size add up to nine. An interval has numeric size 5. What numeric size does its inversion have?

End of topic.

Next: Compound Intervals →