The Art of Fugue

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A portrait which may show Bach in 1750
A portrait which may show Bach in 1750

The Art of Fugue or The Art of the Fugue (original German: Die Kunst der Fuge), BWV 1080, is an incomplete masterpiece[1] by Johann Sebastian Bach (1685-1750). The work was probably started in 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."[2]

Each of the 14 fugues except the final unfinished one (however, see below) use the same deceptively simple subject in D minor:


Image:Kunst der Fuge.png

Contents

[edit] Sources of the work

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. The 14 iterations of the subject may stand for the composers 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: 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 Ottava: 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 inverted 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 BACH motif, B♭–A–C–B♮ ('H' in German letter notation).

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's 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 deinen 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 augmented canons and an earlier version of Contrapunctus X.

[edit] Instrumentation

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[3] that the Art of Fugue was an intellectual exercise, meant to be studied and not heard. However, musicologists today, such as Gustav Leonhardt,[4] agree that the Art of Fugue was probably intended to be played on a keyboard instrument.[5] 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.[6]

[edit] The unfinished fugue

The final page of Contrapunctus XIV
The final page of Contrapunctus XIV

Contrapunctus XIV breaks off abruptly in the middle of the third section at the 239th measure. The autograph carries a note in the handwriting of Bach's son Carl Philipp Emanuel Bach saying “Über 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.[7]

In Glenn Gould's recording, the music 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.

Many scholars, including Gustav Nottebohm (1881), 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, organists Helmut Walcha and Lionel Rogg, 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[8]

In 2006, Slovenian industrial rock group Laibach (part of the NSK collective) performed their interpretation of Kunst der Fuge in Leipzig, Germany as part of the Bach week celebrations, following this in 2008 with a series of live performances across Europe and an album.

In 2007, New Zealand organist and conductor Indra Hughes completed a doctoral thesis about the unfinished ending of Contrapunctus 14, proposing that the work was left unfinished not because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.[9][10]

Douglas Hofstadter's book Gödel, Escher, Bach discussed the unfinished fugue and Bach's supposed death during composition as an illustration of the Church-Turing Thesis, specifically the notion that logical systems can be made to "destroy themselves" by proving contradictions in their own rules.

[edit] The permutation matrix

In 1991 a theory was published by Zoltán Göncz answering the question of how Bach planned the appearance of the fourth subject, the main subject of the cycle:

In the course of the exposition of the first three subjects (first subject: mm. 1–21, second subject: mm. 114–141, third subject: mm. 193–207), Bach applied a serial sequence of voice entries decided in advance, by which he determined the space and time parameters of the subject entries. The superimposition of the three exposition matrices foreshadows, and develops as a negative, the sequence of the voice entries of the fourth subject. The copying of the four subjects onto each other displays a characteristic construction of Bach’s oeuvre occurring mainly in the vocal fugues: that of the permutation fugue.

Commons

However paradoxical, it follows from the logic of composing a quadruple fugue that the combinations joining all four subjects (i.e. those combinations which appear last when performing the work) were already completed in the very first stage of composition, because the possibility of overlapping the four subjects (1+2+3+4) is the sine qua non of writing a quadruple fugue. The process of composition does not proceed in a linear way from the beginning, but with all four parts in view. [11]

One of the striking features of Contrapunctus XIV is that in this movement Bach applied the stretto of whole expositions, layering the first two expositions atop each other prior to introducing the third subject. In the exposition of the first three subjects he “programmed” the later permutation stretti, then applied the expositions as “programs”, “algorithms”. The permutation matrix, apart from originating authentically with Bach, can be proved to have been ready at the time of the genesis of the work (that is, earlier than the surviving section).

The discovery of the permutation matrix was one of the most essential requirements for achieving a reconstruction of Contrapunctus XIV which might approach the original form planned by Bach. (Göncz, Z.: Reconstruction of the Final Contrapunctus of The Art of Fugue, in: International Journal of Musicology Vol. 5, pp. 25–93. 1997 ISBN 3-631-49809-8; Vol. 6, pp. 103–119. 1998 ISBN 3-631-33413-3)[12]

[edit] Some notable recordings of the Art of Fugue

See http://www.jsbach.org/1080.html for a more complete list.

Harpsichord:

Organ:

Piano:

String quartet:

Orchestra :

Other:

[edit] Notes and references

  1. ^ Some consider it a work which was completed, but is incompletely preserved today, either because its publication by engraving was not completed, or because the last pages of the manuscript were misplaced by Bach's son. See notes below.
  2. ^ Johann Sebastian Bach, the Learned Musician by Christoph Wolff, page 433, ISBN 0-393-04825-X.
  3. ^ The Art of the Fugue
  4. ^ http://links.jstor.org/sici?sici=0027-4631(195307)39%3A3%3C463%3ATAOFBL%3E2.0.CO%3B2-0
  5. ^ D. Schulenberg. "Expression and Authenticity in the Harpsichord Music of J.S. Bach". The Journal of Musicology, Vol. 8, No. 4 (Autumn, 1990), pp. 449–476
  6. ^ The Art of the Fugue
  7. ^ See e.g. the discussion in Johann Sebastian Bach, the Learned Musician by Christoph Wolff, ISBN 0-393-04825-X.
  8. ^ a midi file can be found online here
  9. ^ University of Auckland News, Volume 37, Issue 9 (May 25, 2007)
  10. ^ The thesis is available online: http://hdl.handle.net/2292/392
  11. ^ Hence Schweitzer remarks, 'It is an error to say he did not complete The Art of the Fugue. He died before the engraving was completed; hence the work has come down to us in a seemingly incomplete form.' (A. Schweitzer, J.S. Bach, trans. E. Newman, 1911 (1938 reissue, A & C Black, London, I, 423.)
  12. ^ Score published by Carus-Verlag [CV 18.018]. http://www.carus-verlag.com/index.php3?selSprache=1&BLink=KKArtikel&ArtNummer=1801800
  13. ^ a b c 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.
  14. ^ a b Partial performances on organ (Contrapuncti I–IX) and piano (I, II, IV, IX, XI, XIII inversus, and XIV).
  15. ^ The recording, which includes both the unfinished original and Rogg's completion, in the year of its release won the Grand Prix du Disque from the Charles Cros Academy.
  16. ^ Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.

[edit] Media

Contrapunctus I

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[edit] See also

[edit] External links