A brief episodic passage between two subject entries during the exposition.
The exposition of a fugue features the orderly, sequential entry of the subject in each and every voice. Often, this happens without missing a beat: when one subject entry ends, the next one begins. The very first of Bach's fugues in the Well-Tempered Clavier, is a perfect example:
Here is a diagram of the first section from Bach's Well-Tempered Clavier, Book 2, No. 12 in F minor. It is a fugue for three voices. The diagram shows the exposition and the first extended episode.
The diagram shows an episodic region in yellow between entries two and three, that is, within the exposition. This is a codetta. A much larger episode appears after the third entry, after the exposition. As such, it is an episode, not a codetta.
Why the codetta at all? At least two possibilities, one technical, the other psychological. When you consider that the second subject entry is technically an answer, at a different pitch or even key (if the subject modulates), and that the third entry is usually a return to the tonality of the first entry, you can see that one might need a bridge passage to smoothly connect the two, much like joining two segments of railroad tracks that don't quite match up. This is the technical reason for the codetta. An alternate term is a bridge. The psychological reason is simple and powerful: when you delay an expectation, it creates added tension and a heightened resolution when the expectation is finally met.
Codetta is the diminutive for coda; it means "little tail". Both words share a common meaning of an ending that is, in a way, auxiliary to the primary material, though, artistically desirable to tie up the loose ends with the finesse of a compelling conclusion.
Credit goes to Siglind Bruhn for her excellent diagrams.
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