Here is an example of Mozart’s theme and variations K265 based on “Ah, Vous Dirai-je, Maman.” The eighth variation is written in the key of C minor, the parallel minor of C major, the original key of the piece.
Because parallel keys share a tonic but have different modes (that is, they start on the same note but have different interval patterns in their scales), they provide interesting comparisons and contrasts. The mode is changed (major to minor), but Mozart could keep the same departure, the tonic. Because of this charming effect, composers often like to use parallel relationships when they want to change the key, creating both coherence and diversity. The relative relationships are the same. The tonics are different but they share diatonic pitches, so the listener will notice the same sonority between the two modes.