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 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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Bach-Werke-Verzeichnis (Bach Works Catalogue) is the numbering system used to identify musical works by Johann Sebastian Bach. ... An unfinished portrait miniature of Oliver Cromwell by Samuel Cooper. ... Bach in a 1748 portrait by Haussmann Places in which Bach resided throughout his life Johann Sebastian Bach (pronounced ) (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together the... In music, a fugue (IPA: ) is a type of contrapuntal composition or technique of composition for a fixed number of parts or voices (referred to as voices, regardless of whether the work is vocal or instrumental). ... In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration (e. ...

Each of the fugues except the final unfinished one (see however below) use the same, deceptively simple, subject in D minor: D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B-flat, C, and D (natural minor scale). ...

Image File history File links No higher resolution available. ...

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": Events Adam Smith is appointed professor of logic at the University of Glasgow March 25 - For the last time, New Years Day is legally on March 25 in England and Wales. ... Counterpoint is a very general feature of music (especially prominent in much Western music) whereby two or more melodic strands occur simultaneously - in separate voices, either literally or metaphorically (if the music is instrumental). ...

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: In music theory, the word inversion has several meanings. ...

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: Stretto (plural: stretti), from the Italian stringere to draw close is a musical term for when a fugue motif is used to accompany itself. ... In music and music theory augmentation is the lengthening or widening of rhythms, melodies, intervals, chords. ... Diminution, from Italian diminuimento, is a musical term used to mean different things in the context of melodies and intervals or chords. ... In music, a fugue (IPA: ) is a type of contrapuntal composition or technique of composition for a fixed number of parts or voices (referred to as voices, regardless of whether the work is vocal or instrumental). ...

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 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 BACH motif. ... Year 1927 (MCMXXVII) was a common year starting on Saturday (link will display full calendar) of the Gregorian calendar. ...

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. Events Adam Smith is appointed professor of logic at the University of Glasgow March 25 - For the last time, New Years Day is legally on March 25 in England and Wales. ...

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. Bach-Werke-Verzeichnis (Bach Works Catalogue) is the numbering system used to identify musical works by Johann Sebastian Bach. ...

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. // Events January 24 - Charles VII Albert becomes Holy Roman Emperor. ...

The unfinished fugue

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. See e.g. the discussion in Johann Sebastian Bach, the Learned Musician by Christoph Wolff, ISBN 0-393-04825-X. Image File history File links Download high resolution version (1024x554, 148 KB) Last, unfinished fugue from art of fugue File links The following pages link to this file: The Art of Fugue ... Image File history File links Download high resolution version (1024x554, 148 KB) Last, unfinished fugue from art of fugue File links The following pages link to this file: The Art of Fugue ... Carl Philipp Emanuel Bach (March 8, 1714 – December 14, 1788) was a German musician and composer, the second of five sons of Johann Sebastian Bach and Maria Barbara Bach. ... Events April 24 - A congress assembles at Aix-la-Chapelle with the intent to conclude the struggle known as the War of Austrian Succession - at October 18 - The Treaty of Aix-la-Chapelle is signed to end the war Adam Smith begins to deliver public lectures in Edinburgh Building of... Events While in debtors prison, John Cleland writes Fanny Hill (Memoirs of a Woman of Pleasure). ... Christoph Wolff (born May 24, 1940) is a German-born musicologist, presently on the faculty of Harvard University. ...

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. Gustav Nottebohm was a pianist, teacher, musical editor and composer. ... Davitt Moroney is a British-born musicologist and harpsichordist. ... A quadruple fugue is a fugue with four voices. ... Carl Philipp Emanuel Bach (March 8, 1714 – December 14, 1788) was a German musician and composer, the second of five sons of Johann Sebastian Bach and Maria Barbara Bach. ...

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 (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. Dr. Hugo Riemann (full name: Karl Wilhelm Julius Hugo Riemann) (July 18, 1849 - July 10, 1919) was a German musicologist. ... Donald Francis Tovey (July 17, 1875 - July 10, 1940) was a British musical analyst, musicologist, writer on music, composer and pianist. ... Helmut Walcha (October 27, 1907 in Leipzig, Germany – August 11, 1991 in Frankfurt am Main, Germany) was a German organist. ... Dante Michaelangelo Benvenuto Ferruccio Busoni (April 1, 1866 – July 27, Italian composer, pianist, music teacher and conductor. ... Glenn Herbert Gould (September 25, 1932 – October 4, 1982) was a Canadian pianist, noted especially for his recordings of the music of Johann Sebastian Bach. ...

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: Zoltán Göncz (born July 23, 1958 in Budapest) is a Hungarian composer who often applies archaic forms (canon, passacaglia) and complex structures in his compositions. ...

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. In music, a fugue (IPA: ) is a type of contrapuntal composition or technique of composition for a fixed number of parts or voices (referred to as voices, regardless of whether the work is vocal or instrumental). ...

Image File history File links No higher resolution available. ...

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. Sine qua non or condicio sine qua non was originally a Latin legal term for without which it could not be (but for). It refers to an indispensable and essential action, condition, or ingredient. ...

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) Score published by Carus-Verlag [CV 18.018] (see External links).

Some notable recordings of the Art of Fugue

See here for a more complete list.

Harpsichord:

• Gustav Leonhardt (1969)
• Davitt Moroney (1985) ^[1]
• Menno Van Delft (1999)
• Sébastian Guillot (2006)

Piano: Gustav Leonhardt (born May 30, 1928) is a Dutch harpsichordist, organist and conductor. ... Davitt Moroney is a British-born musicologist and harpsichordist. ...

• Charles Rosen (1967)
• Tatiana Nikolayeva (1992)
• Walter Riemer (2006), using a fortepiano of Mozart type

Organ: Charles Rosen (born May 5, 1927) is an American pianist and music theorist. ... Tatiana Petrovna Nikolayeva (May 4, 1924–November 13, 1993) was a Russian pianist, composer and teacher. ...

• Helmut Walcha (1956, 1970) ^[1]
• Glenn Gould (1962) incomplete ^[2]
• Lionel Rogg (1970) ^[3]
• André Isoir (1983[?])
• Marie-Claire Alain (1993)

String quartet: Helmut Walcha (October 27, 1907 in Leipzig, Germany – August 11, 1991 in Frankfurt am Main, Germany) was a German organist. ... Glenn Herbert Gould (September 25, 1932 – October 4, 1982) was a Canadian pianist, noted especially for his recordings of the music of Johann Sebastian Bach. ... André Isoir (born July 20, 1935) is a French classical musician known primarily as an organist. ... Marie-Claire Alain is an organist best known for her prolific recording career. ...

• Italian Quartet (1985)
• Juilliard String Quartet (1989)
• Keller Quartet (1997)
• The Stuggart Chamber Orchester (2002)
• Emerson Quartet (2003)

Orchestra : The Italian Quartet (Quartetto Italiano) is a string quartet, founded in 1945. ... The Juilliard String Quartet is a classical music string quartet founded in 1946 at the Juilliard School in New York. ... The Emerson String Quartet is a renowned New York City–based string quartet. ...

• Milan Munclinger with Ars Rediviva (1959, 1966, 1979)
• Hermann Scherchen with Orchestre de la RTSI (1965) ^[4]
• Karl Ristenpart with Chamber Orchestra of the Saar (1965)
• Jordi Savall with Hesperion XX (1986)
• Erich Bergel with Cluj Philharmonic Orchestra (1991) ^[1]
• Karl Münchinger & Stuttgarter Kammerorchester (2001)

Other: This article or section does not cite any references or sources. ... This article or section does not cite any references or sources. ... Hermann Scherchen (June 21, 1891 – June 12, 1966) was a German conductor and arranger. ... Karl Ristenpart (January 26, 1900 – December 24, 1967) was a German conductor born in Kiel, Germany, who studied at the Stern Conservatory in Berlin and in Vienna. ... Jordi Savall i Bernadet (born 1941, in Igualada, Catalonia) is a Spanish viol player and composer. ... Hespèrion XXI is an international Early Music ensemble. ... The Transylvania State Philharmonic Orchestra of Cluj-Napoca has grown to be a valuable institutions of music, having a sustained presence in the Romanian and European cultural space. ...

• 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)

Musica Antiqua Köln is an early music that was founded in 1973 by Reinhard Goebel and fellow students from the Conservatory of Music in Cologne. ... Reinhard Goebel (born 1952) is a German conductor and violinist devoted to early music. ... The saxophone (colloquially referred to as sax) is a conical-bored instrument of the woodwind family, usually made of brass and played with a single-reed mouthpiece like the clarinet. ... This article or section does not adequately cite its references or sources. ... Various recorders The recorder is a woodwind musical instrument of the family known as fipple flutes or internal duct flutes — whistle-like instruments which include the tin whistle and ocarina. ... Various sizes of viol, from Michael Praetorius Syntagma musicum (1618) Early Italian tenor viola da gamba, detail from the painting , by Raphael Sanzio, c. ...

Notes and references

1. ^ ^{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.
2. ^ Partial performances on organ (Contrapuncti I–IX) and piano (I, II, IV, IX, XI, XIII inversus, and XIV).
3. ^ 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.
4. ^ 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 Organ in Katharinenkirche, Frankfurt am Main, Germany The organ is a keyboard instrument played using one or more manuals and a pedalboard. ... Kenneth Gilbert (born December 16, 1931) is a Canadian harpsichordist. ...

Media

Image File history File links The_Art_of_Fugue,_Contrapunctus_I.ogg Contrapunctus I of Bachs The Art of Fugue. ... Software development stages In computer programming, development stage terminology expresses how the development of a piece of software has progressed and how much further development it may require. ...

See also

• List of compositions of Johann Sebastian Bach
• Bach compositions printed during the composer's lifetime
• Unfinished symphony

There are over 1000 known compositions by Johann Sebastian Bach. ... See List of compositions of Johann Sebastian Bach for the complete list of Bach compositions - the present list only lists those compositions by Bach that were printed during his lifetime: since some of these editions got a bit scattered over the BWV catalogue, this list is only intended to provide... Several (classical) composers left fragments of symphonies that for various reasons could be considered incomplete or unfinished. ...

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: Free scores at the International Music Score Library Project.
• 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