Interval Inversion

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)

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

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.