What type of writing saw an increase in four-part, polyphonic imitation?

The increase in four-part, polyphonic imitation is most closely associated with motet writing. Motets, which originated in the medieval period and flourished during the Renaissance, typically feature multiple independent melodies that interweave to create a rich, textured sound. This type of composition often showcased the composers' skills in imitation, where a musical idea is introduced by one voice and then echoed or developed by others.

Motets allowed for intricate counterpoint, a hallmark of polyphonic music, where multiple melodic lines are layered together. This emphasis on polyphony and imitation became particularly pronounced as composers sought to explore more complex musical ideas and highlight the expressive capabilities of the text being set.

In contrast to the other choices listed, fugue writing also emphasizes imitation, but it typically has a more structured and specific form, with a clear subject and answer following a precise format. Opera writing focuses more on drama and vocal expression rather than strict polyphonic imitation, while sonata writing is generally more homophonic in texture, emphasizing a single melody supported by harmonies. Therefore, the correct association with four-part, polyphonic imitation is found in motet writing.