The Art of Fugue

The Art of Fugue or The Art of the Fugue (Die Kunst der Fuge), BWV 1080, is an unfinished work by Johann Sebastian Bach composed in 1748-1749 and published after his death in 1750. The work contains fourteen fugues and four canons: it is considered to contain some of the most complex fugues ever written, and the work as a whole is considered by many to be the greatest contrapuntal composition ever written, if not the greatest-ever piece of absolute music.


The music

The piece is written in parts score without instrument designation, although all of it fits the range of commonly available keyboard instruments in Bach's time, and is indeed technically playable by a solo keyboardist, if very skilled in playing and articulating contrapuntal music. Possibly, Bach intended it to be playable on a variety of instruments or combinations thereof. It has been performed and recorded by harpsichordists, pianists, organists and string quartets among others, and Hermann Scherchen arranged all of the fugues (not the canons) for symphony orchestra as so did Wolfgang Graeser, making this work widely known to the public.

Each of the fugues except the final unfinished one (see however below) use the same, deceptively simple, subject in D minor:


The sources

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.
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: In dotted rhythm, known as "French style" in Bach's day.
7. Contrapunctus VII, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and diminished (halving all note lengths) 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 alla Octava: Canon at the Octave. The two imitating voices are separated by an octave.
15. Canon alla Decima in Contrapunto alla Terza: Canon at the tenth, counterpoint at the third.
16. Canon alla Duodecima in Contrapunto alla Quinta: Canon at the twelfth, counterpoint at the fifth.
17. Canon per Augmentationem in Contrario Motu: Augmented canon in retrograde motion.

An arrangement of Contrapunctus XIII, see below.

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 so-called BACH motif.

The order of the fugues and canons has been debated, especially as there are differences between the manuscript and the printed editions appearing immediately after Bach death. Also musical reasons have been invoked to propose different orders for later publications and/or the execution of the work, e.g. by Wolfgang Graeser in 1927.

The 1751 printed edition contained - apart from a high number of errors and other flaws - a four-part version of Contrapunctus XIII, arranged to be played on two keyboards (rectus BWV 1080/18,1 and inversus BWV 1080/18,2). It is however doubtful whether the printed indication "a 2 Clav.", and the fourth added voice, that is not mirrored according to Bach's usual practice, derive from him, or from his son(s) that supervised this first edition.

The engraving of the copper plates for the printed edition would however have started shortly before the composer's death, according to contemporary sources, but it is unlikely that Bach had any real supervision in that preparation of the printed edition, due to his illness at the time.

The first printed edition also includes an unrelated work as a kind of "encore", the chorale prelude Vor deinem Thron tret Ich hiermit (Herewith I come before Thy Throne), BWV 668a, which Bach is said to have dictated on his deathbed.

A 1742 fair copy manuscript contains Contrapuncti I--III, V--IX, and XI--XIII, plus the octave and retrograde canons and an earlier version of Contrapunctus X.

The unfinished fugue

Contrapunctus XIV breaks off abruptly in the middle of the third section at the 239th measure. The autograph (image at external site ( carries a note in the handwriting of Bach's son Carl Philipp Emanuel Bach saying "ber dieser Fuge, wo der Nahme B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben." ("At the point where the composer introduces the name BACH in the countersubject to this fugue, the composer died.") However, modern scholarship disputes this version, in particular because the musical notes are indisputably in Bach's own hand, written in a time before his deteriorating vision led to erratic handwriting, probably 1748-1749. See e.g. the discussion in Johann Sebastian Bach, the Learned Musician ( by Christoph Wolff, ISBN 039304825X.

Many scholars, including Wolff and Davitt Moroney, have argued that the piece was intended to be a quadruple fugue, with the opening theme of Contrapunctus I to be introduced as the fourth subject. The title Fuga a 3 soggetti, in Italian rather than Latin, was not given by the composer but by CPE Bach, and Bach's Obituary actually makes mention of "a draft for a fugue that was to contain four themes in four voices". The combination of all four themes would bring the entire work to a fitting climax. Wolff also suspected that Bach may have finished the fugue on a lost page, called "fragment X" by him, on which the composer attempted to work out the counterpoint between the four subjects.

A number of musicians and musicologists have conjectured completions of Contrapunctus XIV, notably music theoretician Hugo Riemann, musicologist Donald Tovey, organist Helmut Walcha, and Moroney. Ferruccio Busoni's Fantasia Contrappuntistica is based on Contrapunctus XIV, but is more a work by Busoni than by Bach. Moroney's completion (a midi file can be found here ( is the shortest, and regarded as the most convincing by some. Glenn Gould's recording deliberately stopped at full volume on the first beat of bar 233, the end of the 1751 print edition; the manuscript continues until the first beat of bar 239 and the tenor voice until the end of that bar. Most performers add these bars, and execute a fade out on the last few notes.

See also

Some notable performances of the Art of Fugue

See here ( for a more complete list.



String quartet:

Orchestra :



Template:Mnb The recordings by Walcha (1970) and Moroney include both their completion of Contrapunctus XIV and the unfinished original, while Bergel's includes only his attempt.

Template:Mnb Partial performances on organ (Contrapuncti I--IX) and piano (I, II, IV, IX, XI, XIII inversus, and XIV).

Template:Mnb Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.

External links

eo:La arto de la fugo it:L'Arte della Fuga hu:A fga művszete ja:フーガの技法 pl:Kunst der Fuge


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