A fugue is a strict form of counterpoint. It doesn't refer to any particular instrumental combination, length or style. Strictly speaking it is a composition technique as well as a compositon or section of a compostion that uses such a technique. In a fugue, a particular theme, known as a subject is elaborated and developed through imitation. Developments of the theme, known as expositions, are interrupted by episodes or more freely composed, still contrapuntal, variations of either parts of the theme, or freely derived material. Composers have developed numerous ways to deal with a fugue subject and various methods of arcane compositional techniques for fugal counterpoint.
The acknowledged master of the fugue is Johann Sebastian Bach. He demonstrated his mastery in both his improvisations as well as in his two major collections of fugues: the fugues of the two books of The Well Tempered Clavier and his unfinished masterwork: The Art of the Fugue. Two stories can show the flair and personality of Bach. Berlin's Spenersche Zeitung of 11 May 1747 presents this report of a visit between Bach and Frederick the Great:
"His August Self immediately gave orders that Bach be admitted, and went, at his entrance, to the so-called Forte and Piano, condescending also to play, in His Most August Person and without any preparation, a theme - for the Capellmeister Bach, which he should execute in a fugue. This was done so happily by the aformentioned Capellmeister that not only was His Majesty pleased to show his satisfaction thereat, but also all those present were seized with astonishment....In the evening, His Majesty charged him again with the execution of a fugue, in six parts, which he accomplished just as skillfully as on the previous occasion, to the pleasure of His majesty and to the general admiration."
A more apocryphal story relates that Bach was listening to another organist improvise a fugue and loudly began singing alternate options for continuing the fugue.
The Fugue Subject
Things to Listen for
The fugue subject is heard monophonically in the very beginning of the work. As the piece progresses see if you can distinguish between sections of the work that feature the fugue subject (expositions) and sections that do not (episodes). Listen for the return of the subject throughout the piece.