Inverting Intervals
After this lesson, you'll know how to invert an interval and predict right away the name and quality of its inversion.
To invert an interval means swapping the positions of its two notes, so that the lower note becomes the upper one.
Two ways to do it
- You can move the lower note up an octave.
- Or you can move the upper note down an octave.
Only simple intervals can be inverted. In a compound interval, the lower note moved up an octave is still the lower note, and the upper note moved down an octave is still the upper note: nothing has been swapped.
What each interval becomes
| Interval | Inversion |
|---|---|
| Unison | Octave |
| Second | Seventh |
| Third | Sixth |
| Fourth | Fifth |
| Fifth | Fourth |
| Sixth | Third |
| Seventh | Second |
| Octave | Unison |
The unison can be inverted even though it is not really an interval: raise or lower one of its two notes by an octave and you get an octave.
What happens to the quality
| Interval | Inversion |
|---|---|
| diminished | augmented |
| minor | major |
| major | minor |
| augmented | diminished |
| perfect | perfect |
Table of inverted intervals
| Interval to invert | Example | Inversion |
|---|---|---|
| Minor second | E-F | Major seventh (F-E) |
| Major second | C-D | Minor seventh (D-C) |
| Augmented second | C-D# | Diminished seventh (D#-C) |
| Diminished third | C#-Eb | Augmented sixth (Eb-C#) |
| Minor third | D-F | Major sixth (F-D) |
| Major third | C-E | Minor sixth (E-C) |
| Augmented third | C-E# | Diminished sixth (E#-C) |
| Perfect fourth | C-F | Perfect fifth (F-C) |
| Augmented fourth | F-B | Diminished fifth (B-F) |
| Diminished fifth | B-F | Augmented fourth (F-B) |
| Perfect fifth | C-G | Perfect fourth (G-C) |
| Augmented fifth | C-G# | Diminished fourth (G#-C) |
| Minor sixth | E-C | Major third (C-E) |
| Major sixth | C-A | Minor third (A-C) |
| Augmented sixth | C-A# | Diminished third (A#-C) |
| Diminished seventh | C#-Bb | Augmented second (Bb-C#) |
| Minor seventh | D-C | Major second (C-D) |
| Major seventh | C-B | Minor second (B-C) |
| Perfect octave | C-C | Unison |
Memory aid: the rule of 9
The number of an interval and the number of its inversion always add up to 9. That's 2 plus 7, 3 plus 6, 4 plus 5, and for the unison, 1 plus 8.
1. Rewrite the table of inverted intervals starting from D instead of C. Include the minor and major seconds, the minor and major thirds, the perfect and augmented fourths, the perfect fifth, the sixths and the sevenths.
2. Give the inversion, with its quality, of each of these intervals: G-B, A-F, E-Bb, D-G, B-A, F#-E.
Next, we'll listen to intervals as harmony and sort them into consonances and dissonances.