The Art of Fugue - Structure

Structure

In the 1751 printed edition, the various movements are roughly arranged by increasing order of sophistication of the contrapuntal devices used. The Arabic number in the title indicates the number of voices in the fugue, with the exception of the last one, where a 3 Soggetti means "with 3 subjects":

Simple fugues:

1. Contrapunctus I, and
2. Contrapunctus II: Simple monothematic 4-voice fugues on main theme, accompanied by a 'French' style dotted rhythm motif.
3. Contrapunctus III, and
4. Contrapunctus IV: Simple monothematic 4-voice fugues on inversion of main theme, i.e. the theme is "turned upside down":

Counter-fugues, in which a variation of the main subject is used in both regular and inverted form:

5. Contrapunctus V: Has many stretto entries, as do Contrapuncti VI and VII.
6. Contrapunctus VI, a 4 in Stylo Francese: This adds both forms of the theme in diminution (halving note lengths), with little rising and descending clusters of semiquavers in one voice answered or punctuated by similar groups in demisemiquavers in another, against sustained notes in the accompanying voices. The dotted rhythm, enhanced by these little rising and descending groups, suggests what is called "French style" in Bach's day, hence the name Stylo Francese.
7. Contrapunctus VII, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and diminished versions of the main subject and its inversion.

Double and triple fugues, with two and three subjects respectively:

8. Contrapunctus VIII, a 3: Triple fugue.
9. Contrapunctus IX, a 4 alla Duodecima: Double fugue
10. Contrapunctus X, a 4 alla Decima: Double fugue.
11. Contrapunctus XI, a 4: Triple fugue.

Mirror fugues, in which the complete score can be inverted without loss of musicality:

12. Contrapunctus XII, a 4: The rectus (normal) and inversus (upside-down) versions are generally played back to back.
13. Contrapunctus XIII, a 3: The second mirror fugue in 3 voices, also a counter-fugue.

Canons, labeled by interval and technique:

14. Canon per Augmentationem in Contrario Motu: Augmented canon in inverted motion.
15. Canon alla Ottava: Canon at the Octave. The two imitating voices are separated by an octave.
16. Canon alla Decima in Contrapunto alla Terza: Canon at the tenth, counterpoint at the third.
17. Canon alla Duodecima in Contrapunto alla Quinta: Canon at the twelfth, counterpoint at the fifth.

An arrangement of Contrapunctus XIII, see below.

18. Fuga a 2 (rectus), and Alio modo Fuga a 2 (inversus)
19. Fuga a 4 Soggetti (Contrapunctus XIV): 4-voice triple, possibly quadruple, fugue, the third subject of which is based on the BACH motif, B♭ - A – C – B♮ ('H' in German letter notation). It has been noted that -- contrary to popular belief -- the fourteenth fugue was finished, but Johann Sebastian Bach's works' inheritors lost the last page in their haste to publish it.

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