Inversion is an important compositional and analytical technique in music, involving both variable and constant features. You can practice the concept of inversion with intervals by flipping the position of the two notes by either moving the lower note up an octave or the upper note down an octave.
Study the examples of inversion below, and notice how the interval sizes change between the same two notes in each pair.
The example above also illustrates how 2nds and 7ths invert each other, 3rds and 6ths invert each other, and 4ths and 5ths invert each other. Note also how the sum of an interval and its inversion always equals 9, which is the number of steps spanned by the operation including the stationary note.
Changes in Number Size Under Inversion
- 2nds — 7ths (2+7 = 9)
- 3rds — 6ths (3+6 = 9)
- 4ths — 5ths (4+5 = 9)
The changes in interval qualities under inversion are another constant feature of the technique: major and minor intervals invert each other, augmented and diminished intervals invert each other, and perfect intervals invert each other.
Changes in Interval Quality Under Inversion
- Major — Minor
- Augmented — Diminished
- Perfect — Perfect
Study these examples that illustrate the change of both number size and quality under inversion.
Once you understand the results of interval inversion, you can apply the technique to help write and identify intervals. It can be especially helpful for larger intervals involving accidentals. For example, if you want to write a M6 above E-flat, you could simply first write a m3 below it (since 3rds and 6ths invert each other and minor and major invert each other), then invert, as in the second example above.
In-class practice: Writing and playing intervals in inversion