Interval Inversion

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Chapter 3 · Lesson 03

In short

If you move the lower note of an interval up an octave, you get its inversion. The two sizes always add up to 9 (e.g. the third becomes a sixth), and the quality changes like this: minor becomes major and vice versa, augmented becomes diminished and vice versa, while perfect stays perfect.

Lesson Notes

Every interval has a "partner", its complement within the octave. We find it through inversion, and it is a tool that makes calculating large intervals much easier.

01What inversion is

Inverting an interval means moving its lower note an octave higher, so that it becomes the upper one, or, which is exactly the same, moving the upper note an octave lower. The two notes stay the same; what changes is which one is on the bottom.

The third becomes a sixth

Original · C-E

major third (M3)

Inversion · E-C

minor sixth (m6)

C-E (M3) with the C an octave higher becomes E-C, that is a minor sixth (m6).

02The rule of 9

The two sizes, of the original interval and of its inversion, always add up to 9. So the second becomes a seventh, the third becomes a sixth, the fourth becomes a fifth, and the unison becomes an octave.

The quality changes too, like this: minor becomes major and major becomes minor, augmented becomes diminished and diminished becomes augmented, while perfect stays perfect.

Each interval and its inversion

IntervalInversion

perfect unison P1perfect octave P8

minor 2nd m2major 7th M7

major 2nd M2minor 7th m7

minor 3rd m3major 6th M6

major 3rd M3minor 6th m6

perfect 4th P4perfect 5th P5

augmented 4th A4diminished 5th d5

The intervals of the natural notes with their inversions. The two sizes add up to 9 and the quality flips to its opposite (perfect stays perfect). Every other augmented or diminished interval inverts the same way, augmented to diminished and vice versa.

03Why it is useful

Small intervals you recognize at a glance. Large ones, like the seventh or the sixth, take more counting. With inversion you flip them into something small and easy, work it out there, and then apply the rule of 9 to get back.

For example, if a seventh gives you trouble, invert it and look at its second. If the second is minor, the seventh is major. We will look at this method in detail in the next lesson.

Recap

Inversion: move the lower note up an octave (or the upper note down an octave).
The sizes of an interval and its inversion always add up to 9 (3rd ↔ 6th, 2nd ↔ 7th, 4th ↔ 5th).
The quality flips: minor ↔ major, augmented ↔ diminished, perfect ↔ perfect.
Inversion helps us find the large intervals easily.