Inversion

Counterpoint technique in which the interval direction is changed. Each ascending interval becomes a descending interval and vice versa. An example from Bach's BWV Invention. This motive:

Is transformed by inversion:

intervals in original motive	2nd ascending	2nd ascending	2nd ascending	3rd descending	2nd ascending	3rd descending
intervals in inverted motive	2nd descending	2nd descending	2nd descending	3rd ascending	2nd descending	3rd ascending

They look like reflection on a mirror. For that reason it is sometimes called mirror inversion:

In the previous case each interval retains its quality, but it does not have to be like this. A major 2nd could become a minor 2nd as we can see in the following example from the same Invention:

See a complete analysis of this invention.

The Quarendo invenietis canon from Bach's Musical Offering is an example of a canon by inversion: