How did binary form help shape the development of sonata form?

Sonata form evolved directly from the binary form prominent in the 17th and early 18th centuries. While binary form consists of two complementary sections, sonata form expanded this into a more complex three-part structure: the exposition, development, and recapitulation.12

The influence of binary form on sonata form is primarily harmonic and structural:

• Tonal Motion: In binary form, the first section typically moves from the home key to a new key, while the second section returns to the home key. Sonata form echoes this motion, with the exposition moving to a new key and the recapitulation returning to the original key.13
• Structural Kinship: The exposition corresponds to the first part of binary form, while the development and recapitulation together correspond to the second. Specifically, the "rounded" binary form—where the second section returns to the melodic material and key of the first—provided a clear structural template for the sonata-allegro design.132

While sonata form is sometimes called "compound binary form" to acknowledge these origins, it is distinguished by its dialectical treatment of themes and greater complexity.1