What is the structure of music called that includes repeated sections and can provide contrast?

The appropriate term for a structure of music that includes repeated sections and offers contrast is indeed binary. Binary form is characterized by its two distinct sections, generally labeled A and B. Each section is typically repeated, allowing for the exploration of different musical ideas while maintaining clarity and coherence through the use of contrast. This form can manifest in various ways, often providing a framework that allows for development and variation of themes within each of the sections.

Theme and Variations involves taking a theme and altering it through various treatments, which is different from the straightforward repeated sections characteristic of binary form. Through-composed refers to a structure where the music continuously evolves without repetition, representing different sections and ideas throughout the piece. Strophic form features repeated verses or stanzas but maintains the same music for each, which doesn't emphasize contrast between sections as directly as binary does.