What term describes a recurring countermelody that accompanies entries of the subject and answer in a fugue?

The term that best describes a recurring countermelody accompanying entries of the subject and answer in a fugue is "countersubject." In the context of a fugue, the subject is the main thematic material, while the countersubject serves as a secondary melody that complements the subject when it is stated. This interplay between the subject and countersubject is crucial to the complex texture of the fugue, allowing for elaborate counterpoint.

In contrast, the term "counterpoint" refers more broadly to the technique of combining different melodic lines in a composition, not specifically to a recurring countermelody. The "subject" is the primary theme being developed within the fugue, and "episode" refers to passages that connect the main themes but do not contain either the subject or the countersubject. Thus, "countersubject" is the precise term for the recurring countermelody that enhances the overall structure and intricacy of a fugue.