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J S Bachã¢ââ¢s Most Comprehensive Example of Contrapuntal Writing Is His Art of Fugue

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Musical work by Johann Sebastian Bach

Title page of the starting time edition, 1751

The Art of Fugue , or The Art of the Fugue (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 piece of work consists of fourteen fugues and four canons in D minor, each using some variation of a single main subject, and mostly 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 unmarried musical subject."[ane] The word "contrapunctus" is often used for each fugue.

Sources [edit]

Mus. ms. autogr. P 200 [edit]

The title 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 autograph manuscript perhaps written from 1740 to 1746, ordinarily referred by its call number every bit Mus. ms. autogr. P 200 in the Berlin Land Library. Bearing the championship Die / Kunst der Fuga [sic] / di Sig[nore] Joh. Seb. Bach, which was written by Bach's 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 beginning printed edition, with the absence of Contrapunctus four, Fuga a two clav (ii-keyboard version of Contrapunctus 13), Canon alla decima, and Catechism alla duodecima.

The autograph manuscript presents the and so-untitled Contrapuncti and canons in the post-obit order: [Contrapunctus 1], [Contrapunctus 3], [Contrapunctus 2], [Contrapunctus five], [Contrapunctus 9], an early version of [Contrapunctus x], [Contrapunctus half-dozen], [Contrapunctus 7], Catechism in Hypodiapason with its two-stave solution Resolutio Canonis (entitled Catechism alla Ottava in the first printed edition), [Contrapunctus 8], [Contrapunctus xi], Canon in Hypodiatesseron, al roversio [sic] eastward per augmentationem, perpetuus presented in two staves then on i, [Contrapunctus 12] with the inversus grade of the fugue written straight below the rectus grade, [Contrapunctus 13] with the same rectus–inversus format, and a ii-stave Canon al roverscio et per augmentationem—a second version of Catechism in Hypodiatesseron.

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

Arranged with the chief autograph are iii supplementary manuscripts, each affixed to a composition that would appear in the first printed edition. Referred to as Mus. ms. autogr. P 200/Beilage ane, Mus. ms. autogr. P 200/Beilage 2, and Mus. ms. autogr. P 200/Beilage three, they are written under the title Dice Kunst / der Fuga / von J.S.B.

Mus. ms. autogr. P 200, Beilage 1 contains a concluding preparatory revision of the Canon in Hypodiatesseron, under the title Canon p[er] Augmentationem contrario Motu crossed out. The manuscript contains line interruption and page break information for the engraving process, nearly of which was transcribed in the kickoff printed edition. Written on the top region of the manuscript is a annotation written by Johann Christoph Friedrich Bach: "Due north.B. Der seel. Papa lid auf die 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" ("N.B. The late father had written on the copper plate the following title, Canon per Augment: in Contrapuncto all octava, simply had strucken it out again on the proof sheet and restored the title every bit it was formerly".

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

Mus. ms. autogr. P 200, Beilage three contains a fragment of a three-subject fugue, which would be after called Fuga a 3 Soggetti in the first printed edition. Unlike the fugues written in the chief autograph, the Fuga is presented in a two-stave keyboard arrangement, instead of 5 individual staves for each vocalism. The fugue abruptly breaks off on the fifth folio, specifically on the 239th measure and ends with the annotation written by Carl Philipp Emanuel Bach: " Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben ." ("At the bespeak where the composer introduces the name BACH [for which the English notation would exist B ♭ –A–C–B ♮ ] in the countersubject to this fugue, the composer died.") The post-obit page contains a list of errata by Carl Philipp Emanuel Bach for the first printed edition (pages 21–35).

First and second printed editions [edit]

The first printed version was published under the championship Die / Kunst der Fuge / durch / Herrn Johann Sebastian Bach / ehemahligen Capellmeister und Musikdirector zu Leipzig. in May 1751, slightly less than a year after Bach's expiry. In addition to changes in the club, notation, and cloth of pieces which appeared in the shorthand, it contained two new fugues, two new canons, and three pieces of ostensibly spurious inclusion. A second edition was published in 1752, merely differed only in its addition of a preface past 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 be attributed to Bach'south relatively sudden death in the midst of publication. Three pieces were included that do not appear to have been part of Bach's intended order: an unrevised (and thus redundant) version of the second double fugue, Contrapunctus X; a two-keyboard arrangement[two] of the first mirror fugue, Contrapunctus 13; 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 as a recompense for the work's incompleteness, having purportedly been dictated by Bach on his deathbed.

The dissonant character of the published gild and the Unfinished Fugue accept engendered a broad diversity of theories which attempt to restore the work to the state 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 generally ordered to increase in complexity. In the gild in which they occur in the printed edition of 1751 (without the aforementioned works of spurious inclusion), the groups, and their components are every bit follows.

Simple fugues:

  • Contrapunctus I: 4-voice fugue on primary field of study
  • Contrapunctus Ii: 4-voice fugue on chief subject, accompanied by a 'French' style dotted rhythm
  • Contrapunctus Iii: 4-voice fugue on principal subject in inversion, employing intense chromaticism
  • Contrapunctus IV: 4-voice fugue on principal subject 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 do Contrapuncti 6 and Seven
  • Contrapunctus Half-dozen, a 4 in Stylo Francese: This adds both forms of the theme in diminution,[3] (halving annotation lengths), with little rise and descending clusters of semiquavers in one voice answered or punctuated by similar groups in demisemiquavers in another, against sustained notes in the accompanying voices. The dotted rhythm, enhanced by these little rising and descending groups, suggests what is chosen "French style" in Bach's day, hence the name Stylo Francese.[4]
  • Contrapunctus Seven, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all annotation lengths) and diminished versions of the main subject and its inversion.

Double and triple fugues, employing 2 and three subjects respectively:

  • Contrapunctus VIII, a iii: Triple fugue, with three subjects, having contained expositions
  • Contrapunctus 9, a 4 alla Duodecima: Double fugue, with ii subjects occurring dependently, and in invertible counterpoint at the 12th
  • Contrapunctus X, a iv alla Decima: Double fugue, with 2 subjects occurring dependently, and in invertible counterpoint at the 10th
  • Contrapunctus 11, a iv: Triple fugue, employing the three subjects of Contrapunctus Eight in inversion

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

  • Contrapunctus XII, a 4
  • Contrapunctus Xiii, a three

Canons, labeled past interval and technique:

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

The Unfinished Fugue:

  • Fuga a three Soggetti ("Contrapunctus Fourteen"): four-voice triple fugue (non completed by Bach, merely likely to take become a quadruple fugue: meet below), the 3rd subject of which begins with the BACH motif, B ♭ –A–C–B ♮ ('H' in German language letter notation).

Instrumentation [edit]

Both editions of the Art of Fugue are written in open score, where each voice is written on its ain staff. This has led some to conclude[5] that the Art of Fugue was intended as an intellectual exercise, meant to be studied more than heard. The renowned keyboardist Gustav Leonhardt argued that the Art of Fugue was intended[6] to be played on a keyboard instrument, and specifically the harpsichord. Leonhardt'due south arguments included the following:[vii]

  1. Information technology was common practice in the 17th and early 18th centuries to publish keyboard pieces in open up score, specially those that are contrapuntally complex. Examples include Frescobaldi's Fiori musicali (1635), Samuel Scheidt's Tabulatura Nova (1624), works past Johann Jakob Froberger (1616–1667), Franz Anton Maichelbeck (1702–1750), and others.
  2. The range of none of the ensemble or orchestral instruments of the period corresponds to whatsoever of the ranges of the voices in The Fine art of Fugue. Furthermore, none of the melodic shapes that narrate Bach's ensemble writing are found in the piece of work, and there is no basso continuo.
  3. The fugue types used are reminiscent of the types in The Well-Tempered Clavier, rather than Bach'southward ensemble fugues; Leonhardt also shows an "optical" resemblance between the fugues of the two collections, and points out other stylistic similarities between them.
  4. Finally, since the bass vocalism in The Fine art of Fugue occasionally rises higher up the tenor, and the tenor becomes the "existent" bass, Leonhardt deduces that the bass function was non meant to be doubled at sixteen-foot pitch, thus eliminating the pipe organ every bit the intended instrument, leaving the harpsichord every bit the most logical choice.

It is now generally accustomed past scholars that the work was envisioned for keyboard.[8] Despite disagreements on how (and whether) it was intended to exist played, The Fine art of Fugue continues to be performed and recorded by many different solo instruments and ensembles.

Fuga a three Soggetti [edit]

The final page of Contrapunctus Fourteen

Fuga a 3 Soggetti ("fugue in three subjects"), also referred to as the "Unfinished Fugue", was contained in a handwritten manuscript bundled with the autograph manuscript Mus. ms. autogr. P200. Information technology breaks off abruptly in the center of its third department, with an only partially written measure 239. This autograph carries a annotation 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 language annotation 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 ain manus, and thus dates to a time before his deteriorating wellness and vision would have prevented his ability to write, probably 1748–1749.[9]

Attempts at completion [edit]

A number of musicians and musicologists accept composed conjectural completions of Contrapunctus XIV which include the fourth subject, including musicologists Donald Tovey (1931), Zoltán Göncz (1992), Yngve Jan Trede (1995), and Thomas Daniel (2010), organists Helmut Walcha,[ten] David Goode, Lionel Rogg, and Davitt Moroney (1989), conductor Rudolf Barshai (2010)[11] and Daniil Trifonov (2021). Ferruccio Busoni's Fantasia contrappuntistica is based on Contrapunctus Xiv, simply information technology develops Bach's ideas to Busoni'due south own purposes in Busoni's musical fashion, rather than working out Bach's thoughts equally Bach himself might have washed.[12] Other completions that do not incorporate the quaternary subject including those past the French classical organist Alexandre Pierre François Boëly and pianist Kimiko Douglass-Ishizaka.

Significance [edit]

In 2007, New Zealand organist and conductor Indra Hughes completed a doctoral thesis nearly the unfinished ending of Contrapunctus Xiv, proposing that the piece of work was left unfinished not because Bach died, simply as a deliberate choice by Bach to encourage independent efforts at a completion.[thirteen] [fourteen]

Douglas Hofstadter's book Gödel, Escher, Bach discusses the unfinished fugue and Bach'southward supposed decease during composition equally a natural language-in-cheek illustration of Austrian logician Kurt Gödel's first incompleteness theorem. Co-ordinate to Gödel, the very ability of a "sufficiently powerful" formal mathematical system can exist exploited to "undermine" the arrangement, by leading to statements that affirm such things as "I cannot be proven in this arrangement". In Hofstadter's discussion, Bach's bang-up compositional talent is used as a metaphor for a "sufficiently powerful" formal arrangement; nevertheless, Bach'due south insertion of his ain name "in code" into the fugue is not, fifty-fifty metaphorically, a case of Gödelian self-reference; and Bach'due south 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 arrangement.

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

Notable recordings [edit]

Harpsichord [edit]

  • Gustav Leonhardt (1953, 1969)
  • Isolde Ahlgrimm (1953, 1967)
  • Davitt Moroney (1985)[xvi]
  • 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 along as MP3s play
  • Matteo Messori (2008) alternating three harpsichords (after Taskin, Harrass and Hildebrandt)
  • Lorenzo Ghielmi on a Silbermann pianoforte and harpsichord with Vittorio Ghielmi and "Il Suonar Parlante" viols quartet (2009)

Organ [edit]

  • Helmut Walcha (1956, 1970)[16]
  • Glenn Gould (1962) incomplete[18]
  • Lionel Rogg (1970)[xix]
  • 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, Strasbourg
  • André Isoir (1999)[xx] Some movements performed every bit 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 building Copenhagen, Kingdom of 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 Pinnacle Presbyterian Church in Scottsdale, Arizona (This recording includes equally a bonus track an alternative take of the terminal unfinished fugue with the completion by Helmut Walcha)
  • Joan Lippincott (2012)

Pianoforte [edit]

  • Richard Buhlig and Wesley Kuhnle (1934)
  • Glenn Gould, incomplete[18]
  • 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)

String quartet [edit]

  • Quartetto Italiano (1985)[23]
  • Juilliard Cord 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 Bedroom Orchestra (1965, 1985 alive)
  • Neville Marriner with Academy of St Martin in the Fields (1974)
  • Lukas Foss with I Soloisti di Pickup (1977) orchestrated by William Malloch
  • Jordi Savall with Hesperion Xx (1986)
  • Erich Bergel with Cluj Combo Orchestra (1991)[sixteen]
  • Rinaldo Alessandrini with Concerto Italiano (1998)
  • Stuttgart Sleeping accommodation Orchestra (2002)
  • Rachel Podger with Brecon Baroque (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 (director Reinhard Goebel) for cord quartet/harpsichord and various such instrumental combinations (1984)
  • Canadian Brass for contumely quintet (1990)
  • Amsterdam Loeki Stardust Quartet for recorder quartet (1998)
  • Phantasm (manager: Laurence Dreyfus) for viola da gamba 4-role consort (1998)
  • Pittsburgh Symphony Orchestra Brass (1998)
  • Fretwork for Consort of Viols (2002)
  • József Eötvös for ii 8-string guitars (2002)
  • Walter Riemer [de] first version on fortepiano (2006)[26]
  • An electronic version, Laibachkunstderfuge, by Neue Slowenische Kunst industrial ring Laibach (2008)
  • Vulfpeck (founder Jack Stratton) for talk box (2016)[27]

Come across likewise [edit]

  • Listing of compositions past Johann Sebastian Bach
  • List of compositions by Johann Sebastian Bach printed during his lifetime
  • The Art of Fugue discography

Notes and references [edit]

  1. ^ Johann Sebastian Bach, the Learned Musician by Christoph Wolff, p. 433, ISBN 0-393-04825-Ten.
  2. ^ The printed indication of "a 2 Clav." and the counterpoint of the added voices practise not appear to follow Bach's practice, evidencing that the parts were likely included by the editors of the printed edition to bolster the piece of work.
  3. ^ Helmut Walcha, "Zu meiner Wiedergabe", in Die Kunst Der Fuge BWV 1080, St Laurenskerk Alkmaar 1956 (Archiv Production, Polydor International 1957), Insert pp. 5–xi, at p. 7.
  4. ^ Anon. (n.d.). "The Art of Fugue – Types of Fugues, Part 1". American Public Media. Retrieved 28 April 2012.
  5. ^ Betimes. (due north.d.). "The Art of Fugue – Bach'south Last Harpsichord Work: An Argument – Did Bach intend Art of Fugue to be performed?". American Public Media.
  6. ^ "images of front and back covers; The Art of Fugue – Bach's Last Harpsichord Work: An Argument (1952)" (PDF).
  7. ^ The Art of Fugue Gustav Leonhardt'due south 1969 liner notes for Harmonia Mundi HM 30 950 XK: Johann Sebastian Bach, Die Kunst der Fuge [1969], 3–8.; likewise for Deutsche Harmonia Mundi's CD edition 77013-ii-RG (an extensive summary of his 1952 The Art of Fugue – Bach'south Last Harpsichord Piece of work: An Argument)
  8. ^ David Schulenberg. "Expression and Authenticity in the Harpsichord Music of J.South. Bach". The Journal of Musicology, Vol. 8, No. 4 (Fall, 1990), pp. 449–476
  9. ^ See e.g. the word in Johann Sebastian Bach, the Learned Musician by Christoph Wolff, ISBN 0-393-04825-X.
  10. ^ Walcha'south 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 past Walcha's educatee, George Ritchie, in the documentary moving picture Desert Fugue (2010).
  11. ^ "The Art of Fugue". Rudolf Barshai Memorial . Retrieved half-dozen February 2021.
  12. ^ See Donald Tovey's comments in A Companion to the Art of Fugue (2013 Dover reprint, ISBN 0-486-49764-X, folio 177 footnote).
  13. ^ University of Auckland News, Volume 37, Issue 9 (May 25, 2007) Archived September 26, 2007, at the Wayback Machine
  14. ^ The thesis is available online: http://hdl.handle.net/2292/392
  15. ^ Loïc, Sylvestre; Costa, Marco (2011). "The Mathematical Architecture of Bach's The Fine art of Fugue". Il Saggiatore musicale. 17: 175–196.
  16. ^ a b c The recordings by Walcha (1970) and Moroney include both their completion of Contrapunctus XIV and the unfinished original, while Bergel'south includes only his attempt.
  17. ^ Robert Hill: Recordings of Musical Offering & Art of Fugue, bach-cantatas.com
  18. ^ a b Fractional performances on organ (Contrapuncti I–Nine) and piano (I, 2, IV, Ix, Xi, Xiii inversus, and Fourteen).
  19. ^ The recording, which includes both the unfinished original and Rogg'south completion, in the year of its release won the 1000 Prix du Disque from the Charles Cros Academy.
  20. ^ André Isoir: Recordings of Musical Offering and Art of Fugue, bach-cantatas.com
  21. ^ Published by Accentus Music: CD – J. S. Bach Kunst der Fuge – Zhu Xiao-Mei, Piano, No. ACC 30308
  22. ^ "video".
  23. ^ Paolo Borciani and Elisa Pegreffi with Tommaso Poggi and Luca Simoncini, as Quartetto Italiano, CD Nuova Era 7342, recording 1985.See [1]
  24. ^ "J.S.Bach – Juilliard String Quartet – die Kunst der Fuge (1992, CD)".
  25. ^ Except the canons, which are played by harpsichordist Kenneth Gilbert on the recording.
  26. ^ "J. S. Bach: The Fine art of the Fugue – Die Kunst der Fuge, BWV 1080". www.niederfellabrunn.at.
  27. ^ Jack Stratton: Contrapunctus IX (talkbox) on YouTube

External links [edit]

  • Full discography of The Fine art of Fugue, bach-cantatas.com
  • Discography
  • Johann Sebastian Bach / Fifty'art de la fugue / The Fine art of the Fugue – Jordi Savall, Hesperion Xx – Alia Vox 9818
  • Piano Society: JS Bach – A biography and various free recordings in MP3 format, including Fine art of Fugue
  • Web-essay on The Art of Fugue
  • Introduction to The Art of Fugue
  • Dice Kunst der Fuge (scores and MIDI files) on the Mutopia Projection website
  • The Fine art of Fugue: Scores at the International Music Score Library Project
  • The Fine 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, Winter 2007
  • Contrapunctus XIV (reconstruction): Part 1/2, Part 2/2 (YouTube video)
  • Contrapunctus Xiv: Completion (in quarter-comma meantone) (YouTube video)
  • Contrapunctus Two equally interactive hypermedia at the BinAural Collaborative Hypertext
  • Synthesized realization and analysis of The Art of Fugue past Jeffrey Hall
  • Hughes, Indra (2006). "Blow or Design? New Theories on the unfinished Contrapunctus fourteen in JS Bach's The Art of Fugue, BWV 1080", The University of Auckland PhD thesis
  • "Johann Sebastian Bach'south The Art of Fugue", article Uri Golomb, published in Goldberg Early on Music Magazine
  • Ars Rediviva: Audio Recordings Library, The Fine art of Fugue, Contrapunctus VIII
  • Description of documentary film Desert Fugue
  • Electronic realization by Klangspiegel
  • Completion of Contrapunctus 14 by Paul Freeman
  • Bach, Alphametics and The Art of Fugue
  • "Le concert d'Irena Kosikova a fait un tabac", La Dépêche du Midi, 11 August 2014 (in French)

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

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