THE ART OF FUGUE

'''The Art of Fugue''' or '''The Art of the Fugue''' (original German: '''Die Kunst der Fuge'''), BWV 1080, is an unfinished work by the German composer Johann Sebastian Bach. The work was probably started in 1742. Bach's first version, which contained 12 fugues and 2 canons, was copied in 1745. This manuscript has a slightly different title, added afterwards by his son-in-law Altnickol: ''Die Kunst der Fuga''. His second version was published after his death in 1750. It contains fourteen fugues and four canons. ''The Art of Fugue'' is one of the most complex works ever penned by Bach and is considered a crowning achievement of western art.
Each of the fugues except the final unfinished one (see however below) use the same, deceptively simple, subject in D minor:

Contents

Sources of the work

Instrumentation

The unfinished fugue

The permutation matrix

Some notable recordings of the Art of Fugue

Notes and references

Media

See also

External links

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.
: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♮.
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''.

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^[1] that the ''Art of Fugue'' was an intellectual exercise, meant to be studied and not heard. However, musicologists today, such as Gustav Leonhardt,^[2] agree that the ''Art of Fugue'' was probably intended to be played on a keyboard instrument.^[3] 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.^[4]

The unfinished fugue

''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.^[5]
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^[6] is the shortest, and regarded as the most convincing by some.
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.^[7][8]

The permutation matrix

In 1991 an astonishing discovery was published by Zoltán Göncz answering the question with fairly great certainty 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.

However paradoxical, it follows from the logic of composing a quadruple fugue that the combinations joining all four subjects and rendered the ''latest'' 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.
One of the striking features of Contrapunctus XIV is that in this movement Bach applied the stretto of ''whole expositions''. 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 conditions to achieve that the reconstruction of Contrapunctus XIV could come near to ''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)^[9]

Some notable recordings of the Art of Fugue

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

★ Gustav Leonhardt (1969)

★ Davitt Moroney (1985) ¹⁰

★ Menno Van Delft (1999)

★ Sébastian Guillot (2006)
''Piano'':

★ Charles Rosen (1967)

★ Tatiana Nikolayeva (1992)

★ Walter Riemer (2006), using a fortepiano of Mozart type
''Organ'':

★ Helmut Walcha (1956, 1970) ^[10]

★ Glenn Gould (1962) incomplete ^[11]

★ Lionel Rogg (1970) ^[12]

★ André Isoir (1983[?])

★ Marie-Claire Alain (1993)
''String quartet'':

★ Roth Quartet (1934-5) includes conjectural end played by Donald Tovey on keyboard.

★ Italian Quartet (1985)

★ Juilliard String Quartet (1989)

★ Keller Quartet (1997)

★ The Stuggart Chamber Orchester (2002)

★ Emerson Quartet (2003)
''Orchestra '':

★ Milan Munclinger with Ars Rediviva (1959, 1966, 1979)

★ Hermann Scherchen with Orchestre de la RTSI (1965) ^[13]

★ Karl Ristenpart with Chamber Orchestra of the Saar (1965)

★ Jordi Savall with Hesperion XX (1986)

★ Erich Bergel with Cluj Philharmonic Orchestra (1991) ¹⁰

★ Karl Münchinger & Stuttgarter Kammerorchester (1965)
''Other'':

★ Musica Antiqua Köln (director Reinhard Goebel) for string quartet/harpsichord and various such instrumental combinations (1984)

★ Berliner Saxophon Quartett for saxophone (1990)

★ József Eötvös for two eight-string guitars (2002)

★ Amsterdam Loeki Stardust Quartet for recorder quartet (1998)

★ Fretwork for Consort of Viols (2002)

Notes and references

1. http://pipedreams.publicradio.org/articles/artoffugue/performed.shtml
2. http://links.jstor.org/sici?sici=0027-4631(195307)39%3A3%3C463%3ATAOFBL%3E2.0.CO%3B2-0
3. 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
4. http://pipedreams.publicradio.org/articles/artoffugue/keyboard.shtml
5. See e.g. the discussion in
''Johann Sebastian Bach, the Learned Musician'' by Christoph Wolff, ISBN 0-393-04825-X.
6. a midi file can be found here
7. University of Auckland News, Volume 37, Issue 9 (May 25, 2007)
8. The thesis is available online: http://hdl.handle.net/2292/392
9. Score published by Carus-Verlag [CV 18.018]. http://www.carus-verlag.com/index.php3?selSprache=1&BLink=KKArtikel&ArtNummer=1801800
10. 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.
11. Partial performances on organ (''Contrapuncti I–IX'') and piano (''I, II, IV, IX, XI, XIII inversus,'' and ''XIV'').
12. 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.
13. Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.

Dr. Serban Nichifor: "The Art of Fugue" version for 2 guitars quartets; performers: Calin Grigoriu, Gabriel Brosteanu, Radu Miculita,Hanelore Mocanu, Radu Corbos, Andra Stanciu, Zsolt Bara and Tudor Niculescu-Mizil; National University of Music Bucharest (Romania), 23.03.2007

Joachim Stange-Elbe (klangspiegel): "The Art of Fugue" version for synthesizers; 37. Würzburger Bachtage, church St. Johannis Würzburg (Germany), 27.11.2005

Media

See also

★ List of compositions of Johann Sebastian Bach

★ Bach compositions printed during the composer's lifetime

★ Unfinished symphony

External links

★ Piano Society: JS Bach - A biography and various free recordings in MP3 format, including art of fugue

★ Web-essay on ''The Art of Fugue''

★ Introduction to ''The Art of Fugue''

★ ''Die Kunst der Fuge'' (scores and MIDI files) on the Mutopia Project website

★

★ ''The Art of Fugue'' as MIDI files

★ Image of the ending of the final fugue at external site

★ Contrapunctus XIV (the reconstructed quadruple fugue) – Carus-Verlag

★ Contrapunctus II as interactive hypermedia at the BinAural Collaborative Hypertext