Bwv 1080 Art of the Fugue Keyboard Reduction

Musical work by Johann Sebastian Bach

Title page of the first edition, 1751

The Art of Fugue , or The Fine art of the Fugue (High german: Die Kunst der Fuge), BWV 1080, is an incomplete musical work of unspecified instrumentation by Johann Sebastian Bach. Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.

This work consists of fourteen fugues and 4 canons in D small, each using some variation of a single principal bailiwick, and generally ordered to increase in complexity. "The governing idea of the work", as put by Bach specialist Christoph Wolff, "was an exploration in depth of the contrapuntal possibilities inherent in a single musical subject field."^[i] The word "contrapunctus" is ofttimes used for each fugue.

Sources [edit]

Mus. ms. autogr. P 200 [edit]

The championship page of Mus. ms. autogr. P 200, which bears the title Die / Kunst der Fuga / di Sig.o Joh. Seb. Bach. / (in eigenhändiger Partitur).

The earliest extant source of the work is an shorthand manuscript possibly written from 1740 to 1746, usually referred by its call number every bit Mus. ms. autogr. P 200 in the Berlin State Library. Begetting the championship Die / Kunst der Fuga [sic] / di Sig[nore] Joh. Seb. Bach, which was written by Bach'south son-in-law Johann Christoph Altnickol, followed by (in eigenhändiger Partitur) written by Georg Poelchau [de], the autograph contains twelve untitled fugues and two canons arranged in a different order than in the first printed edition, with the absence of Contrapunctus 4, Fuga a 2 clav (ii-keyboard version of Contrapunctus thirteen), Catechism alla decima, and Canon alla duodecima.

The autograph manuscript presents the then-untitled Contrapuncti and canons in the following order: [Contrapunctus 1], [Contrapunctus 3], [Contrapunctus 2], [Contrapunctus 5], [Contrapunctus ix], an early on version of [Contrapunctus 10], [Contrapunctus 6], [Contrapunctus vii], Catechism in Hypodiapason with its 2-stave solution Resolutio Canonis (entitled Canon alla Ottava in the first printed edition), [Contrapunctus 8], [Contrapunctus 11], Canon in Hypodiatesseron, al roversio [sic] e per augmentationem, perpetuus presented in two staves and then on one, [Contrapunctus 12] with the inversus class of the fugue written direct below the rectus grade, [Contrapunctus thirteen] with the same rectus–inversus format, and a two-stave Catechism al roverscio et per augmentationem—a second version of Canon in Hypodiatesseron.

Mus. ms. autogr. P 200, Beilage [edit]

Bundled with the primary autograph are three supplementary manuscripts, each affixed to a composition that would announced in the first printed edition. Referred to every bit Mus. ms. autogr. P 200/Beilage 1, Mus. ms. autogr. P 200/Beilage 2, and Mus. ms. autogr. P 200/Beilage 3, they are written nether the title ~~Die~~ Kunst / der Fuga / von J.Southward.B.

Mus. ms. autogr. P 200, Beilage 1 contains a last preparatory revision of the Canon in Hypodiatesseron, under the title Canon p[er] Augmentationem contrario Motu crossed out. The manuscript contains line break and page break information for the engraving procedure, most of which was transcribed in the beginning printed edition. Written on the acme region of the manuscript is a note written by Johann Christoph Friedrich Bach: "N.B. Der seel. Papa hat auf dice Platte diesen Titul stechen lassen, Canon per Augment: in Contrapuncto all octava, er hat es aber wieder ausgestrichen auf der Probe Platte und gesetzet wie forn stehet" ("Northward.B. The late father had written on the copper plate the following title, Catechism per Augment: in Contrapuncto all octava, just had strucken it out once more on the proof sheet and restored the title as it was formerly".

Mus. ms. autogr. P 200, Beilage 2 contains two-keyboard arrangements of Contrapunctus 13 inversus and rectus, entitled Fuga a 2. Clav: and Alio modo Fuga a 2 Clav. in the first printed edition respectively. Like Beilage 1, the manuscript served as a preparatory edition for the get-go printed edition.

Mus. ms. autogr. P 200, Beilage 3 contains a fragment of a three-subject fugue, which would exist later on chosen Fuga a three Soggetti in the first printed edition. Unlike the fugues written in the primary shorthand, the Fuga is presented in a two-stave keyboard system, instead of five individual staves for each voice. The fugue abruptly breaks off on the fifth folio, specifically on the 239th measure and ends with the note written by Carl Philipp Emanuel Bach: " Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben ." ("At the signal where the composer introduces the name BACH [for which the English notation would be B ♭ –A–C–B ♮ ] in the countersubject to this fugue, the composer died.") The following folio contains a list of errata by Carl Philipp Emanuel Bach for the first printed edition (pages 21–35).

Commencement and second printed editions [edit]

The first printed version was published nether the title Die / Kunst der Fuge / durch / Herrn Johann Sebastian Bach / ehemahligen Capellmeister und Musikdirector zu Leipzig. in May 1751, slightly less than a year afterwards Bach's death. In improver to changes in the society, annotation, and textile of pieces which appeared in the autograph, it contained two new fugues, ii new canons, and three pieces of ostensibly spurious inclusion. A 2d edition was published in 1752, simply differed only in its addition of a preface by Friedrich Wilhelm Marpurg.

In spite of its revisions, the printed edition of 1751 contained a number of glaring editorial errors. The majority of these may exist attributed to Bach's relatively sudden death in the midst of publication. Three pieces were included that practice non appear to have been office of Bach's intended order: an unrevised (and thus redundant) version of the 2d double fugue, Contrapunctus 10; a two-keyboard arrangement^[two] of the start mirror fugue, Contrapunctus XIII; and an organ chorale prelude on " Vor deinen Thron tret ich hiermit " ("Herewith I come before Thy Throne"), derived from BWV 668a, and noted in the introduction to the edition every bit a recompense for the work's incompleteness, having purportedly been dictated by Bach on his deathbed.

The dissonant character of the published order and the Unfinished Fugue have engendered a wide variety of theories which attempt to restore the work to the country originally intended by Bach.

Structure [edit]

The Art of Fugue is based on a single subject, which each canon and fugue employs in some variation:

$\relative c'' { \set Staff.midiInstrument = #"church organ" \clef treble \key d \minor \time 4/4 d,2 a' | f d | cis d4 e | f2~ f8 g f e | d4 }$

The work divides into seven groups, according to each piece's prevailing contrapuntal device; in both editions, these groups and their respective components are by and large ordered to increase in complication. In the club in which they occur in the printed edition of 1751 (without the aforementioned works of spurious inclusion), the groups, and their components are as follows.

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Elementary fugues:

Contrapunctus I: 4-voice fugue on main subject
Contrapunctus II: iv-voice fugue on principal subject, accompanied by a 'French' style dotted rhythm
Contrapunctus III: iv-voice fugue on principal subject in inversion, employing intense chromaticism
Contrapunctus Four: 4-phonation fugue on principal subject area in inversion, employing counter-subjects

Stretto Fugues (Counter-fugues), in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:

Contrapunctus V: Has many stretto entries, as practice Contrapuncti Vi and VII
Contrapunctus VI, a iv in Stylo Francese: This adds both forms of the theme in diminution,^[iii] (halving note lengths), with little rise and descending clusters of semiquavers in i voice answered or punctuated by like groups in demisemiquavers in another, confronting sustained notes in the accompanying voices. The dotted rhythm, enhanced by these piddling ascent and descending groups, suggests what is called "French manner" in Bach'south twenty-four hours, hence the name Stylo Francese.^[4]
Contrapunctus Vii, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and macerated versions of the main subject and its inversion.

Double and triple fugues, employing ii and 3 subjects respectively:

Contrapunctus VIII, a 3: Triple fugue, with three subjects, having contained expositions
Contrapunctus Nine, a 4 alla Duodecima: Double fugue, with two subjects occurring dependently, and in invertible counterpoint at the 12th
Contrapunctus X, a 4 alla Decima: Double fugue, with ii subjects occurring dependently, and in invertible counterpoint at the 10th
Contrapunctus XI, a 4: Triple fugue, employing the 3 subjects of Contrapunctus VIII in inversion

Mirror fugues, in which a piece is notated one time and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:

Contrapunctus XII, a 4
Contrapunctus Thirteen, a 3

Canons, labeled by interval and technique:

Canon per Augmentationem in Contrario Motu: Catechism in which the following voice is both inverted and augmented.
Canon alla Ottava: Canon in imitation at the octave
Catechism alla Decima in Contrapunto alla Terza: Canon in imitation at the tenth
Canon alla Duodecima in Contrapunto alla Quinta: Canon in imitation at the twelfth

The Unfinished Fugue:

Fuga a three Soggetti ("Contrapunctus XIV"): 4-voice triple fugue (not completed by Bach, but likely to have go a quadruple fugue: see below), the third subject of which begins with the BACH motif, B ♭ –A–C–B ♮ ('H' in German letter notation).

Instrumentation [edit]

Both editions of the Art of Fugue are written in open up score, where each vocalization is written on its own staff. This has led some to conclude^[5] that the Art of Fugue was intended every bit an intellectual exercise, meant to be studied more than than heard. The renowned keyboardist Gustav Leonhardt argued that the Art of Fugue was intended^[half-dozen] to be played on a keyboard instrument, and specifically the harpsichord. Leonhardt'southward arguments included the following:^[7]

Information technology was common exercise in the 17th and early 18th centuries to publish keyboard pieces in open score, especially those that are contrapuntally complex. Examples include Frescobaldi's Fiori musicali (1635), Samuel Scheidt's Tabulatura Nova (1624), works by Johann Jakob Froberger (1616–1667), Franz Anton Maichelbeck (1702–1750), and others.
The range of none of the ensemble or orchestral instruments of the period corresponds to whatsoever of the ranges of the voices in The Art of Fugue. Furthermore, none of the melodic shapes that characterize Bach'due south ensemble writing are found in the work, and there is no basso continuo.
The fugue types used are reminiscent of the types in The Well-Tempered Clavier, rather than Bach's ensemble fugues; Leonhardt also shows an "optical" resemblance betwixt the fugues of the two collections, and points out other stylistic similarities between them.
Finally, since the bass voice in The Art of Fugue occasionally rises above the tenor, and the tenor becomes the "real" bass, Leonhardt deduces that the bass part was not meant to be doubled at 16-foot pitch, thus eliminating the piping organ as the intended musical instrument, leaving the harpsichord as the well-nigh logical pick.

It is now generally accepted by scholars that the work was envisioned for keyboard.^[eight] Despite disagreements on how (and whether) information technology was intended to exist played, The Art of Fugue continues to be performed and recorded past many unlike solo instruments and ensembles.

Fuga a iii Soggetti [edit]

The final page of Contrapunctus Fourteen

Fuga a 3 Soggetti ("fugue in iii subjects"), as well referred to as the "Unfinished Fugue", was independent in a handwritten manuscript arranged with the autograph manuscript Mus. ms. autogr. P200. It breaks off abruptly in the middle of its third department, with an only partially written measure out 239. This autograph carries a note in the handwriting of Carl Philipp Emanuel Bach, stating "Über dieser Fuge, wo der Name B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben." ("While working on this fugue, which introduces the name BACH [for which the English notation would be B ♭ –A–C–B ♮ ] in the countersubject, the composer died.") This account is disputed by modern scholars, as the manuscript is clearly written in Bach's own hand, and thus dates to a time before his deteriorating health and vision would accept prevented his ability to write, probably 1748–1749.^[9]

Attempts at completion [edit]

A number of musicians and musicologists have composed conjectural completions of Contrapunctus Fourteen which include the 4th subject, including musicologists Donald Tovey (1931), Zoltán Göncz (1992), Yngve January Trede (1995), and Thomas Daniel (2010), organists Helmut Walcha,^[x] David Goode, Lionel Rogg, and Davitt Moroney (1989), conductor Rudolf Barshai (2010)^[xi] and Daniil Trifonov (2021). Ferruccio Busoni's Fantasia contrappuntistica is based on Contrapunctus Xiv, but it develops Bach's ideas to Busoni'southward ain purposes in Busoni's musical style, rather than working out Bach's thoughts as Bach himself might take washed.^[12] Other completions that do not incorporate the fourth subject including those by the French classical organist Alexandre Pierre François Boëly and pianist Kimiko Douglass-Ishizaka.

Significance [edit]

In 2007, New Zealand organist and usher Indra Hughes completed a doctoral thesis about the unfinished ending of Contrapunctus XIV, proposing that the work was left unfinished non because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.^[13] ^[14]

Douglas Hofstadter'due south volume Gödel, Escher, Bach discusses the unfinished fugue and Bach's supposed death during composition equally a tongue-in-cheek illustration of Austrian logician Kurt Gödel'south commencement incompleteness theorem. According to Gödel, the very ability of a "sufficiently powerful" formal mathematical system can be exploited to "undermine" the system, past leading to statements that assert such things as "I cannot be proven in this arrangement". In Hofstadter's give-and-take, Bach's great compositional talent is used as a metaphor for a "sufficiently powerful" formal system; nonetheless, Bach'southward insertion of his ain proper name "in lawmaking" into the fugue is not, fifty-fifty metaphorically, a instance of Gödelian self-reference; and Bach's failure to finish his self-referential fugue serves as a metaphor for the unprovability of the Gödelian assertion, and thus for the incompleteness of the formal system.

Sylvestre and Costa^[15] reported a mathematical compages of The Art of Fugue, based on bar counts, which shows that the whole piece of work was conceived on the basis of the Fibonacci series and the golden ratio. The significance of the mathematical architecture can probably be explained by considering the part of the work as a membership contribution to the Correspondierende Societät der musicalischen Wissenschaften [de], and to the "scientific" meaning that Bach attributed to counterpoint.

Notable recordings [edit]

Harpsichord [edit]

Gustav Leonhardt (1953, 1969)
Isolde Ahlgrimm (1953, 1967)
Davitt Moroney (1985)^[16]
Robert Hill (1987, 1998)^[17]
Ton Koopman with Tini Mathot (1994), on two harpsichords
Bradley Brookshire (2007) includes an additional CD-ROM with score to follow forth as MP3s play
Matteo Messori (2008) alternating three harpsichords (after Taskin, Harrass and Hildebrandt)
Lorenzo Ghielmi on a Silbermann piano and harpsichord with Vittorio Ghielmi and "Il Suonar Parlante" viols quartet (2009)

Organ [edit]

Helmut Walcha (1956, 1970)^[16]
Glenn Gould (1962) incomplete^[xviii]
Lionel Rogg (1970)^[19]
Marie-Claire Alain (1974, Rotterdam)
Herbert Tachezi [de] (1977) on the Jürgen Ahrend and Gerhard Brunzema [de] organ in St. Johann (Oberneuland) [de], Bremen
Wolfgang Rübsam (1992)
Marie-Claire Alain (1993)
Louis Thiry (1993) on the Silbermann organ of St Thomas' Church building, Strasbourg
André Isoir (1999)^[xx] Some movements performed as a duet with Pierre Farago, on the Grenzing organ of Saint-Cyprien in Périgord, France
Hans Fagius (2000) on the Carsten Lund organ of Garnisons Church Copenhagen, Denmark
Kevin Bowyer (2001) on the Marcussen organ of Saint Hans Church, Odense, Denmark
Régis Allard (2007)
George Ritchie (2010) on the Richards, Fowkes & Co organ of Elevation Presbyterian Church in Scottsdale, Arizona (This recording includes as a bonus track an alternative have of the final unfinished fugue with the completion by Helmut Walcha)
Joan Lippincott (2012)

Piano [edit]

Richard Buhlig and Wesley Kuhnle (1934)
Glenn Gould, incomplete^[xviii]
Charles Rosen (1967)
Grigory Sokolov (1982)
Zoltán Kocsis (1984)
Yūji Takahashi (1988)
Evgeni Koroliov (1991)
Tatiana Nikolayeva (1992)
Anton Batagov (1993)
Joanna MacGregor (1996)
Pierre-Laurent Aimard (2008)
Zhu Xiao-Mei (2014)^[21]
Angela Hewitt (2014)
Kimiko Douglass-Ishizaka (2017)^[22]
Daniil Trifonov (2021)

Cord quartet [edit]

Quartetto Italiano (1985)^[23]
Juilliard String Quartet (1987)^[24]
Emerson String Quartet (2003)
Vittorio Ghielmi and "Il Suonar Parlante" viols quartet (2009) with Lorenzo Ghielmi on a Silbermann piano and harpsichord

Orchestra [edit]

Arthur Winograd by Winograd String Orchestra (ca 1952)
Hermann Scherchen with Orchestre de la RTSI (1965)^[25]
Karl Ristenpart with Chamber Orchestra of the Saar (1965)
Karl Münchinger with Stuttgart Chamber Orchestra (1965, 1985 live)
Neville Marriner with Academy of St Martin in the Fields (1974)
Lukas Foss with I Soloisti di Pickup (1977) orchestrated past William Malloch
Jordi Savall with Hesperion 20 (1986)
Erich Bergel with Cluj Philharmonic Orchestra (1991)^[16]
Rinaldo Alessandrini with Concerto Italiano (1998)
Stuttgart Chamber Orchestra (2002)
Rachel Podger with Brecon Bizarre (2017)

Other [edit]

Milan Munclinger with Ars Rediviva (1959, 1966, 1979)
Fine Arts String Quartet and New York Woodwind Quintet (1962)
Yūji Takahashi (incomplete) electronic version (1975)
Musica Antiqua Köln (managing director Reinhard Goebel) for string quartet/harpsichord and diverse such instrumental combinations (1984)
Canadian Contumely for contumely quintet (1990)
Amsterdam Loeki Stardust Quartet for recorder quartet (1998)
Phantasm (director: Laurence Dreyfus) for viola da gamba four-part consort (1998)
Pittsburgh Symphony Orchestra Brass (1998)
Fretwork for Espoused of Viols (2002)
József Eötvös for two eight-string guitars (2002)
Walter Riemer [de] first version on fortepiano (2006)^[26]
An electronic version, Laibachkunstderfuge, by Neue Slowenische Kunst industrial band Laibach (2008)
Vulfpeck (founder Jack Stratton) for talk box (2016)^[27]

Notes and references [edit]

^ Johann Sebastian Bach, the Learned Musician by Christoph Wolff, p. 433, ISBN 0-393-04825-Ten.
^ The printed indication of "a 2 Clav." and the counterpoint of the added voices practice not appear to follow Bach'southward practice, evidencing that the parts were likely included by the editors of the printed edition to eternalize the piece of work.
^ Helmut Walcha, "Zu meiner Wiedergabe", in Die Kunst Der Fuge BWV 1080, St Laurenskerk Alkmaar 1956 (Archiv Production, Polydor International 1957), Insert pp. five–eleven, at p. 7.
^ Anon. (n.d.). "The Art of Fugue – Types of Fugues, Office ane". American Public Media. Retrieved 28 April 2012.
^ Anon. (n.d.). "The Art of Fugue – Bach's Concluding Harpsichord Work: An Argument – Did Bach intend Fine art of Fugue to be performed?". American Public Media.
^ "images of front end and dorsum covers; The Art of Fugue – Bach'south Last Harpsichord Piece of work: An Argument (1952)" (PDF).
^ The Art of Fugue Gustav Leonhardt's 1969 liner notes for Harmonia Mundi HM thirty 950 XK: Johann Sebastian Bach, Die Kunst der Fuge [1969], 3–8.; also for Deutsche Harmonia Mundi's CD edition 77013-2-RG (an extensive summary of his 1952 The Art of Fugue – Bach's Last Harpsichord Piece of work: An Argument)
^ David Schulenberg. "Expression and Actuality in the Harpsichord Music of J.South. Bach". The Journal of Musicology, Vol. 8, No. iv (Autumn, 1990), pp. 449–476
^ Run into e.g. the word in Johann Sebastian Bach, the Learned Musician by Christoph Wolff, ISBN 0-393-04825-X.
^ Walcha's conclusion to the last Contrapunctus has been recorded by Walcha himself, in his Stereo recording of the complete organ works by Bach for Archiv (1956-1971); and by Walcha'due south pupil, George Ritchie, in the documentary moving picture Desert Fugue (2010).
^ "The Fine art of Fugue". Rudolf Barshai Memorial . Retrieved half dozen February 2021.
^ See Donald Tovey's comments in A Companion to the Fine art of Fugue (2013 Dover reprint, ISBN 0-486-49764-X, page 177 footnote).
^ University of Auckland News, Volume 37, Issue nine (May 25, 2007) Archived September 26, 2007, at the Wayback Motorcar
^ The thesis is bachelor online: http://hdl.handle.net/2292/392
^ Loïc, Sylvestre; Costa, Marco (2011). "The Mathematical Architecture of Bach's The Art of Fugue". Il Saggiatore musicale. 17: 175–196.
^ ^a ^b ^c The recordings past Walcha (1970) and Moroney include both their completion of Contrapunctus Fourteen and the unfinished original, while Bergel's includes only his attempt.
^ Robert Hill: Recordings of Musical Offering & Art of Fugue, bach-cantatas.com
^ ^a ^b Fractional performances on organ (Contrapuncti I–Ix) and piano (I, Ii, IV, Ix, 11, XIII inversus, and XIV).
^ 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.
^ André Isoir: Recordings of Musical Offer and Fine art of Fugue, bach-cantatas.com
^ Published by Accentus Music: CD – J. S. Bach Kunst der Fuge – Zhu Xiao-Mei, Piano, No. ACC 30308
^ "video".
^ Paolo Borciani and Elisa Pegreffi with Tommaso Poggi and Luca Simoncini, as Quartetto Italiano, CD Nuova Era 7342, recording 1985.See [1]
^ "J.S.Bach – Juilliard Cord Quartet – die Kunst der Fuge (1992, CD)".
^ Except the canons, which are played past harpsichordist Kenneth Gilbert on the recording.
^ "J. S. Bach: The Art of the Fugue – Die Kunst der Fuge, BWV 1080". www.niederfellabrunn.at.
^ Jack Stratton: Contrapunctus IX (talkbox) on YouTube

External links [edit]

Full discography of The Art of Fugue, bach-cantatas.com
Discography
Johann Sebastian Bach / L'art de la fugue / The Fine art of the Fugue – Jordi Savall, Hesperion Twenty – Alia Vox 9818
Piano Society: JS Bach – A biography and diverse costless recordings in MP3 format, including Art of Fugue
Web-essay on The Fine art of Fugue
Introduction to The Art of Fugue
Die Kunst der Fuge (scores and MIDI files) on the Mutopia Project website
The Fine art of Fugue: 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
Malina, János: The Ultimate Fugue, The Hungarian Quarterly, Wintertime 2007
Contrapunctus XIV (reconstruction): Function 1/2, Part ii/two (YouTube video)
Contrapunctus XIV: Completion (in quarter-comma meantone) (YouTube video)
Contrapunctus II as interactive hypermedia at the BinAural Collaborative Hypertext
Synthesized realization and assay of The Fine art of Fugue past Jeffrey Hall
Hughes, Indra (2006). "Accident or Design? New Theories on the unfinished Contrapunctus 14 in JS Bach'southward The Art of Fugue, BWV 1080", The University of Auckland PhD thesis
"Johann Sebastian Bach'southward The Art of Fugue", article Uri Golomb, published in Goldberg Early Music Mag
Ars Rediviva: Audio Recordings Library, The Art of Fugue, Contrapunctus VIII
Description of documentary picture show Desert Fugue
Electronic realization by Klangspiegel
Completion of Contrapunctus Xiv by Paul Freeman
Bach, Alphametics and The Art of Fugue
"Le concert d'Irena Kosikova a fait un tabac", La Dépêche du Midi, eleven August 2014 (in French)

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Source: https://en.wikipedia.org/wiki/The_Art_of_Fugue