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The Art of Fugue

(Redirected from Die Kunst der Fuge)

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.

Table of contents

The music

The piece is written in parts score without instrument designation(s), 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 and made this work widely known to the public.

The fugues are simply labeled "Contrapunctus" and a Latin numeral, sometimes with additional qualifiers for the contrapuntal devices used. Different canonical techniques are illustrated by four canons (labeled by interval and technique).

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:

  • Contrapunctus I and II (BWV 1080/1 and 1080/2): Simple monothematic 4-voice fugues on main theme
  • Contrapunctus III and IV (BWV 1080/3 and 1080/4): Simple monothematic 4-voice fugues on inversion of main theme, i.e. the theme is "turned upside down"
  • Contrapunctus V (BWV 1080/5): 4-voice counterfugue, uses main theme in both regular and inverted form. Has many stretto entries, as does Contrapunctus VI and VII.
  • Contrapunctus VI "in stylo Francese" (BWV 1080/6): Ditto but in dotted rhythm (known as "French style" in Bach's day)
  • Contrapunctus VII "a 4 per augmentationem et diminutionem" (BWV 1080/7): Uses "augmented" (doubling all note lengths, i.e. half as fast) and "diminished" (halving all note lengths) versions of the main subject and its inversion
  • Contrapunctus VIII (BWV 1080/8): 3-voice triple fugue (i.e. with three subjects)
  • Contrapunctus IX "alla duodecima" (BWV 1080/9), X "alla decima" (BWV 1080/10): 4-voice double fugues (two subjects)
  • Contrapunctus XI (BWV 1080/11): 4-voice triple fugue
  • Contrapunctus XII (BWV 1080/12): 4-voice mirror fugues (i.e. the complete score can be inverted without loss of musicality). The "rectus" (normal) and "inversus" (upside-down) versions are generally played back to back.
  • Contrapunctus XIII (BWV 1080/13): Also a mirror fugue, but 3-voice, and is also a counterfugue.
  • Canon alla octava (BWV 1080/14): canon in the octave
  • Canon alla decima in contrapunto alla terza (BWV 1080/15): canon in the tenth, counterpoint at the third
  • Canon alla duodecima in contrapunto alla quinta (BWV 1080/16): canon in the twelfth, counterpoint at the fifth
  • Canon per augmentationem in contrario motu (BWV 1080/17): augmented canon in retrograde motion
  • Contrapunctus XIV "Fuga a 3 soggetti"(BWV 1080/19): Unfinished 4-voice triple, possibly quadruple, fugue (i.e. with three, possibly four, subjects), the third of which is based on the so-called BACH motif (the notes B-A-C-H as in German nomenclature, in which B is B flat and H is B natural).

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

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 first 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 1751 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.

The unfinished fugue

Contrapunctus XIV breaks off abruptly in the middle of the third section (measure 239). The autograph (image at external site) carries a note in the handwriting of Bach's son Carl Philipp Emanuel Bach saying "Über dieser Fuge, wo der Nahme BACH 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 (see e.g. the discussion in "Johann Sebastian Bach, the Learned Musician" by Christoph Wolff) disputes this version, in particular because the musical notes are indisputably in Bach's own hand, and from a time (probably 1748–1749) before his deteriorating vision led to erratic handwriting.

Many scholars (including Davitt Moroney and Christoph Wolff) 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" 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. Some musicians argued that Bach may have finished the fugue on a lost page (fragment x), which he wrote first in order 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 (as part of an edition for string quartet of the Art of Fugue), organist Helmut Walcha, and musicologist/harpsichordist Davitt Moroney. Ferruccio Busoni's Fantasia Contrappuntistica is based on Contrapunctus XIV, but is more a work by Busoni than by Bach. Moroney's completion is the shortest, and regarded as the most convincing by some. Glenn Gould's recording deliberately breaks off 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 diminuendo ("fade out") on the last few notes.

See also

Some notable performances of the Art of Fugue

External links








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