How does a binary-form piece move away from and return to its home key?

In binary form, a musical structure consisting of two complementary sections, the movement between keys follows a specific harmonic progression.12

The first section begins in the home key (the tonic) and typically modulates to a new tonal center. For compositions in a major key, this involves moving to the dominant (the fifth degree of the scale). For pieces in a minor key, the music modulates to the relative major (the third degree of the scale).12

The second section begins in this new key. After exploring the harmonic possibilities generated by this modulation, the music eventually resolves by returning to the original home key. In some instances, known as "rounded" binary form, the second section may also bring back melodic or rhythmic material from the opening of the first section alongside the return to the tonic.12