What happens to augmented and diminished intervals when they are inverted?

In the study of harmony, when an interval is inverted—meaning the lower pitch is moved up an octave to become the higher pitch—its quality changes in a predictable manner.1

Specifically, when you invert an augmented interval, it becomes a diminished interval, and conversely, when you invert a diminished interval, it becomes an augmented interval.1

This relationship is part of a broader system of interval inversion where:
* Major intervals become minor and vice versa.1
* Perfect intervals remain perfect.1

These inversions are considered complements, as the original interval and its inversion together encompass the span of an octave.21