Background
The term "fuga" was used from the late Middle Ages to the early Baroque for strict imitation or canon, but fugal writing in the modern sense first appears in 16th-century vocal polyphony and in instrumental forms, including the ricercare, fantasia and canzone, derived from it. Fuga, in its present sense, appears alongside 'fantasia' in the "Tabulature nova" (1624) of Scheidt. Another kind of fugue emerged from the keyboard toccatas of Froberger and Buxtehude, and the idea of including fugal passages in the toccata led to the 'prelude and fugue' combination. J.C.F. Fischer's "Ariadne musica" (1702) is a collection of preludes and fugues in various keys which served as an example for Bach's "Well-tempered Clavier".Construction and Processes
A typical Bach fugue would be constructed as follows. In the opening section, the exposition, the main theme or subject is announced in the tonic. After which the second voice enters with the answer, i.e. the same theme, usually at the dominant pitch, while the first may proceed to a countersubject. The answer may be either a "real" answer which is "in" the dominant key (having all the pitches of the subject transposed to the new key), or a "tonal" answer, which is "on" the dominant pitch level but where some pitches are slightly altered to correspond more to the original, tonic key. This procedure is repeated at different octaves until all the voices have entered and the exposition is complete. An extra statement of the subject or answer following the exposition is called a 'redundant entry'; a set of such entries is a 'counter-exposition'.
The exposition is the only essential for the definition of a piece as a fugue, but most fugues proceed to further entries of the subject, which may be separated by 'episodes', often based on material from the exposition, often tonally unstable and modulatory, frequently employing the use of sequences. The 'middle entries', normally in keys other than the tonic or dominant, may treat the theme in stretto (with overlapping entries) or vary it in some way. In 'augmentation' the note values are lengthened, in 'diminution' they are shortened; in 'inversion' the subject is upside down, in retrograde the subject appears in reverse note order. A 'false entry' begins the subject but does not complete it. The final entry of the subject is usually in the tonic key. Often a closing section appears, utilizing a pedal point on the dominant pitch and/or emphasizing the subdominant key.
Examples
Bach's "Well-tempered Clavier," in two volumes, contains some of his greatest fugues but did not exhaust his command of fugal technique. His suites, concertos and cantatas frequently combine fugue and ritornello form, and he introduced the combination of the subject and a number of counter-subjects in various vertical permutations. In the "Art of Fugue" he explored the potentialities of a single main theme in a cycle of 14 fugues, including pairs of invertible or mirror fugues, a species unique to this work.
The Toccata in D minor is an example of the form established by Buxtehude, in which the fugue is interspersed with sections of free fantasia. The Passacaglia in C minor serves as a prelude to a double fugue, one of whose subjects is identical with the first half of the passacaglia theme. From the later years of Bach's life comes the gigantic Prelude in E-flat major, and the Fugue ("St. Anne's") in the same key.