How does the exposition establish contrasting key areas in sonata form?

In sonata form, the exposition establishes contrasting key areas through a dynamic tonal shift rather than a simple reliance on thematic differentiation.1

The process typically unfolds as follows:

• Tonic Foundation: The exposition begins firmly rooted in the tonic, or home key, of the composition.1
• Modulation: To create tonal contrast, the music moves decisively away from the home key toward a closely related, distinct key. For works in a major key, this is almost invariably the dominant key; for works in a minor key, it is typically the relative major.12
• Technique: This modulation is often achieved by emphasizing chords common to both keys, known as "pivots," or by using secondary dominants and chromatic chords to prepare for the arrival of the new key area.32
• Structural Goal: This opposition of tonalities creates a sense of tension that the subsequent development and recapitulation sections aim to reconcile.14

While composers often use two distinct themes to help the listener perceive this tonal design, the contrast of keys remains the defining structural characteristic of the exposition.1