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)