For those of you in a hurry, we’ll give away the ending first: take any interval (x), subtract it from 9, and you are left with the inversion of that interval.  Now let’s review:

All of this prepares us for the information you have been waiting for!

How to Invert an Interval

  1. Find middle C on the piano
  2. Play a perfect fifth above middle C (i.e., G)
  3. Move the G down an octave
  4. You have inverted a perfect fifth, which results in a perfect fourth

By moving the top note of an interval down an ocatave, you invert that interval.  It also works in reverse: if you start over with C and G, and move the bottom note up an octave, you again end up with a perfect fourth.  Try it!

Now take 9, subtract the original interval, and you end up with the inversion: 9 – 5 = 4.  Our original formula gives us the following results:

Original Interval Inversion
1 8
2 7
3 6
4 5
5 4
6 3
7 2
8 1

//

For example, a second (C to D) becomes a seventh (D to C) when inverted. A third (C to E) becomes a sixth (E to C), a fourth (C to F) becomes a fifth (F to C), and so on.

How to Determine the Type of Inversion

It’s all well and good to know that a second becomes a seventh, but what type of seventh (e.g., major, minor, augmented, dimished)?  You could count the half-steps, but do enough of this stuff and you will know just by looking at (or thinking of) the notes. Until then there are a few simple rules to follow:

  • Inversions of perfect intervals are perfect.
  • Inversions of major intervals are minor, and inversions of minor intervals are major.
  • Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.

Applying these rules gives us the following table:

Original Interval Inversion
Perfect Perfect
Major Minor
Minor Major
Diminished Augmented
Augmented Diminished

//

So just as the numbers in the inversion table are turned upside down, the type of interval flips as well (unless, of course, it is perfect). Elaborating our previous examples, C to D is a major second, and D to C is a minor seventh. C to E is a major third, and E to C is a minor sixth, C to F is a perfect fourth, and F to C is a perfect fifth, and so on. Who knew this could be so much fun?

We will wrap up by summarizing some rules and presenting a table that shows the common name and alternate name for each interval, along with examples and inversions.  Don’t get hung up on the alternate names — most of them are rarely used.  They are more, er…theoretical.  The table and rules are adapted from “Interval,” an excellent Connexions learning module developed by Catherine Schmidt-Jones.

Summary Notes: Perfect Intervals

* A perfect prime is often called a unison. It is two notes of the same pitch.
* A perfect octave is often simply called an octave. It is the next “note with the same name”.
* Perfect intervals – unison, fourth, fifth, and octave – are never called major or minor.

Summary Notes: Augmented and Diminished Intervals

* An augmented interval is one half step larger than the perfect or major interval.
* A diminished interval is one half step smaller than the perfect or minor interval.

The examples given name the note reached if you start on C and go up the named interval.

No.of half steps
Common Name Example Alternate Name Example Inversion
0 Perfect Unison (P1) C Diminished Second D double flat Octave (P8)
1 Minor Second (m2) D flat Augmented Unison C sharp Major Seventh (M7)
2 Major Second (M2) D Diminished Third E double flat Minor Seventh (m7)
3 Minor Third (m3) E flat Augmented Second D sharp Major Sixth (M6)
4 Major Third (M3) E Diminished Fourth F flat Minor Sixth (m6)
5 Perfect Fourth (P4) F Augmented Third E sharp Perfect Fifth (P5)
6 Tritone (TT) F sharp or G flat Augmented Fourth or Diminished Fifth F sharp or G flat Tritone (TT)
7 Perfect Fifth (P5) G Diminished Sixth A double flat Perfect Fourth (P4)
8 Minor Sixth (m6) A flat Augmented Fifth G sharp Major Third (M3)
9 Major Sixth (M6) A Diminished Seventh B double flat Minor Third (m3)
10 Minor Seventh (m7) B flat Augmented Sixth A sharp Major Second (M2)
11 Major Seventh (M7) B Diminished Octave C’ flat Minor Second (m2)
12 Perfect Octave (P8) C’ Augmented Seventh B sharp Perfect Unison (P1)

//