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:
- First, we found Middle C
- Then we learned about Basic Intervals
- Next, we studied Scales and the Circle of Fifths
- From there, we learned how to Build Piano Chords
- Then we learned about Chord Inversions
- And Revisited the Circle of Fifths
All of this prepares us for the information you have been waiting for!
How to Invert an Interval
- Find middle C on the piano
- Play a perfect fifth above middle C (i.e., G)
- Move the G down an octave
- 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:
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:
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.
|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)|