Final answer:
A fugue is not a character piece because, unlike a ballade, impromptu, fantasie, and étude, it does not express a specific mood or emotion but instead is a contrapuntal composition with a strict structure.
Step-by-step explanation:
A fugue is NOT a character piece. While a ballade, impromptu, fantasie, and étude are all character pieces that express certain moods or emotions and are typically written for solo piano, a fugue is a contrapuntal composition in which a short melody or phrase (the subject) is introduced by one part and successively taken up by others and developed by interweaving the parts. It follows a strict structure and is not meant to portray a specific character or mood in the way that character pieces do.