Interval Inversions
To invert an interval is move the root note to the top. Effectively viewing the previous top note from its lower octave, e.g C → E is now E → C. In the example below, the type of interval changes from Major 3rd to Minor 6th (Interval Size: 9 - 3 = 6, Quality: Major → Minor).
Tips:
- The Rule of 9 (Interval Size): Subtract the original interval number from 9 to determine its inversion.
- Unison ↔ Octave
- Second ↔ Seventh
- Third ↔ Sixth
- Fourth ↔ Fifth
- Quality Changes: The quality of an interval changes to its opposite when inverted.
- Major intervals become minor (and vice versa)
- Augmented intervals become diminished (and vice versa)
- Perfect intervals remain perfect
| Interval | Inversion | Diagram |
|---|---|---|
| Minor 2nd | Major 7th |  |
| Major 2nd | Minor 7th |  |
| Minor 3rd | Major 6th |  |
| Major 3rd | Minor 6th | |
| Perfect 4th | Perfect 5th |  |
| Perfect 5th | Perfect 4th |  |
| Minor 6th | Major 3rd |  |
| Major 6th | Minor 3rd |  |
| Minor 7th | Major 2nd |  |
| Major 7th | Minor 2nd |  |
Note: Because a tritone divides the octave into exactly two equal halves (six semitones), it is perfectly symmetrical and is the only interval that inverts to itself.
Exercises
- Ascend a scale from root to octave using intervals, e.g. in C Ionian
C → D,C → E, etc. Then descend from the root’s octave in the same way. Recognize the inversion.
Triad Inversions
https://appliedguitartheory.com/lessons/learning-guitar-chord-inversions/ has diagrams we can use for inspo