The Art of Fugue or The Art of the Fugue (original German: Die Kunst der Fuge), BWV 1080, is an incomplete masterpiece by Johann Sebastian Bach (1685–1750). The work was most likely started at the beginning of the 1740s, if not earlier. The first known surviving version, which contained 12 fugues and 2 canons, was copied by the composer in 1745. This manuscript has a slightly different title, added afterwards by his son-in-law Johann Christoph Altnickol: Die Kunst der Fuga. Bach's second version was published in 1751 after his death. It contains 14 fugues and 4 canons. "The governing idea of the work", as the eminent Bach specialist Christoph Wolff put it, is "an exploration in depth of the contrapuntal possibilities inherent in a single musical subject."
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":
1. Contrapunctus I, and
2. Contrapunctus II: Simple monothematic 4-voice fugues on main theme, accompanied by a 'French' style dotted rhythm motif. The 14 iterations of the subject may stand for the composer's surname (B + A + C + H = 14)
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.
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.
18. Fuga a 2 (rectus), and Alio modo Fuga a 2 (inversus)
Unfinished quadruple fugue:
19. Fuga a 3 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).
Manuscript copies of the Art of Fugue, as well as the first printed edition, use open scoring, where each voice is written on its own staff. This has led to the assumption that the Art of Fugue was an intellectual exercise, meant to be studied and not heard. However, musicologists today, such as Gustav Leonhardt, agree that the Art of Fugue was probably intended to be played on a keyboard instrument. Leonhardt's arguments included the following:
1. It was common practice in the 17th and early 18th centuries to publish keyboard pieces in open score, especially those that are contrapuntally complex. Examples include Frescobaldi's Fiori musicali (1635), Samuel Scheidt's Tabulatura Nova (1624), works by Johann Jakob Froberger (1616–1667), Franz Anton Maichelbeck (1702–1750), and others.
2. The range of none of the ensemble or orchestral instruments of the period corresponds to any of the ranges of the voices in The Art of Fugue. Furthermore, none of the melodic shapes that characterize Bach's ensemble writing are found in the work, and there is no basso continuo.
3. The fugue types used are reminiscent of the types in The Well-Tempered Clavier, rather than Bach's ensemble fugues; Leonhardt also shows an "optical" resemblance between the fugues of the two collections, and points out other stylistic similarities between them.
4. Finally, since the bass voice in The Art of Fugue occasionally rises above the tenor, and the tenor becomes the "real" bass, Leonhardt deduces that the bass part was not meant to be doubled at 16-foot pitch, thus eliminating the pipe organ as the intended instrument, leaving the harpsichord as the most logical choice.
The fact that it is playable on a keyboard at all is evidence for some that this was Bach's intended instrument, as it is not possible to play most of his ensemble pieces on a keyboard instrument.
This recordings uses a licensed sample library published from the McGill University, Canada.