Intervals - Inversions

Inverting an interval means to turn it upside down - the bottom note becomes the top note and vice versa.

Does it matter which note we choose to move?

No.  You can invert interval two different ways: moving the bottom note to the top, or moving the top note to the bottom.  The result is the same either way, just written in different octaves.  In an exam, unless it says otherwise, do whatever is easiest.

There is a simple formula for working out the inversion of ANY interval.

NUMBER:  Remember the number 9.

9 - [Interval number] = [Inversion number]

So, a sixth inverted becomes a third - obviously, the reverse is also true (a third becomes a sixth).

QUALITY:  This is a bit more complicated, but not a lot ...

• PERFECT remains PERFECT
• MAJOR becomes MINOR [and vice versa]
• AUGMENTED becomes DIMINISHED [and vice versa]

Invert these intervals:

Interval	Inversion
Minor 3rd
Diminished 5th
Major 7th
Perfect octave
Major 6th
Augmented 2nd
Augmented unison

The only interval this DOESN’T work for is the Augmented Octave.  WHY NOT?

If you follow the proceedure given here, an Augmented Octave would becomes a Diminished Unison.  But think about it - to diminish an interval is to make it a semitone smaller.  Yet a perfect unison is the interval between any note and itself.  So, you cannot diminish a unison, only augment it (make it larger).

Notice, this works for intervals up to an octave.

Here's the link to our worksheet.

https://docs.google.com/file/d/0B9JdpU-tw7FuRm9lb2g1ZTNySDA/edit?usp=sharing