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Updated as more discovered. Last updated 26th March 2025
Whether Bach intended for Contrapunctus number 14 (Fuga a 3 soggetti) to be left unfinished as an exercise for future composers or not is likely to be something we will never know. But at least 70 composers since then have tried their hand at a completion. I was surprised to see that, beyond limited discussions of small numbers of these (e.g. Indra Hughes’s thesis p.77, brief analyses of a few in Walter Kolneder’s epic volumes) or youtube playlists, there are relatively few places that they are collected.
[Update 15/4/23: I have been made aware of an excellent website by Yasuhiko Nakajima, devoted to the Art of Fugue, with a page listing various completions here. I am grateful to a reader of this blog, J.C, for alerting me to this website. I have added in some additional completions and links to YN’s website below]
[Update 23/01/24: I have discovered another Japanese website by Katsutoshi Watanabe which includes a few more completions, available on Youtube, of which I was previously unaware. This is also worth visiting as he provides many more links to recordings than the ones I provide below, if you interested in hearing a range of performances]
In a rough categorisation, we have performances that (a) simply finish off with a brief coda, (b) use the existing “torso” as a jumping off point for their own composition e.g.. by extending the existing triple fugue, or (c) introduce the principal theme as a 4th theme. Within (c) there are those that simply quote it in combination with the other 3 themes or those that (not exclusively) give it a full exposition, combine it with the others according to Goncz’s permutation matrix, follow Hughes’ proposed completion (including inversions of the themes), or those that complete a quadruple fugue in their own manner.
Where possible, I have linked to recordings of each fugue (mostly on youtube). Where I do not have access to the score or a written description, I have tried to count the bars of the completion but admit this is mostly going to be inaccurate.
Jan Overduin has performed 8 completions here
0:00……….. Michael Ferguson 4:59……….. Zoltán Göncz 10:20……… Penny Johnson 12:37……… Kevin Korsyn 16:18……… Davitt Moroney 18:20……… David Schulenberg 20:36……… Francis Tovey 24:42………Helmut Walcha,
(see below for further details regarding these)
Completions that utilise the principal theme
Hitotsubashi University Chamber Music Club link, completion (~8 bar completion, quotes the principal theme, rather than using it as a 4th subject)
Mitch Boucher link, completion (10 bar completion with one quotation of the principal theme, although not in combination with other themes)
Vyacheslav Gryaznov link; completion (16 bar completion, quoting the principal theme in combination)
Bernard Fouccroulle link; completion (25 bar completion, including one combination with the principal theme)
Matthieu Camillieri link; completion
J. Todd Frazier score, midi (30 bar completion)
Davitt Moroney link; completion (30 bar completion, contains two quadruple combinations with the principal theme). Franss-Wilfrid von Promnitz, previously included here as a separate completion, records Moroney’s (Available on Spotify or for purchase).
Lorenzo Ghielmi link; completion. (30 bar completion) and more recent organ version here.
Kees van Houten/Leo van Doeselaar link; completion (33 bar completion, with two quadruple combinations – performance by Netherlands Bach Society – see my separate post)
Tillman Hoppstock: link; completion (35 bar completion, score)
Bernard Labadie link; completion (36 bar completion, adapted from Moroney)
Penny Johnson link; completion. (39 bar completion, score)
Richard Troeger link, completion (40 bar completion)
David Schulenberg link completion at 06:30 (41 bar completion. 4th theme enters as cantus firmus without its own exposition. Further discussion in his book, The Keyboard Music of J.S. Bach)
Danil Trifonov link; completion (41 bar completion)
Samuel Kummer. Available on Spotify or for purchase. (44 bar completion)
Reinhard Febel link; continuation (not really sure if this can be called a completion: there is (re)statement of the 4 themes but not much else)
Lionel Rogg link; completion (46 bars added)
Lenny Cavallaro link; completion (47 bar completion based on Indra Hughes’ proposals)
Claudi Meneghin link; completion (48 bar completion, follows Goncz’ permutation matrix and then all inverted themes in combination)
Colin MacKnight link; completion (49 bar completion)
Hugo Riemann link to Nakajima’s page on this completion (49 bar completion)
Riverstun music without score; score without music (51 bar completion, utilising Indra Hughes’ proposals and Goncz’s permutation matrix)
Maria Scharwieß link to completion only (~51 bar completion, contains separate exposition of principal theme)
Yasuhiko Nakajima link (includes exposition of principal theme)
Joseph Groocock score only (53 bar completion)
Neil Halliday link, completion (~55 bar completion, adaptation of Tovey’s completion, encorporating ideas from Indra Hughes and Geir Eskland)
Paul Binski link; completion (58 bar completion)
Christiaan Ingelse link; completion (59 bar completion)
Kevin Korsyn link; completion (61 bars added, includes exposition of 4th theme alongside counter-subject, utilises permutation matix)
Helmut Walcha link; completion. (71 bars added, contains one quadruple combination with the principal theme)
Douglas M. Green (74 bars) – mentioned by Walter Kolneder
Donald Tovey link (organ); completion; completion alone (piano) (78 bar completion), YN
Thierry Escaich link; completion (78 bar completion)
Gianluca Cagnani link; completion. (~85 bar improvised completion)
Brian Ciach link; completion (89 bar completion, link to website with score)
James Iliffe score and notes (94 bar completion)
Adel V Heinrich score only (96 bar completion)
Michael Ferguson link; completion (98 bar completion)
Eduard Melkus (109 bar completion) – mentioned in Walter Kolneder’s summary. There is a recording, but I have not been able to track this down.
Zoltan Goncz link; completion (111 bar completion, utilising the permutation matrix)
Geir øyvind Eskeland link, slower version with score (111 bar completion)
Theo Nederpelt 113 bar completion with exposition of 4th theme. Available in score and CD with his book: J.S.Bachs meesterwerk Die Kunst der Fuge – een menselijk document
Malcolm Ledger Version 1: link; completion (additional 117 bars, with no separate exposition of 4th theme)
Oscar Gottlieb Blarr link to article only (126 bar completion)
Thomas Daniel score only (133 bar completion)
Tudor Saveanu link, link with score, completion, completion with score (135 bar completion, utilises the permutation matrix) [another version]
Paul Guggenheim (137 bar completion, but book is only available for purchase for >$150)
Erich Bergel link; completion (142 bar completion, includes exposition of 4th theme)
Kalevi Aho link; completion (144 bar completion)
Karl Hermann Pillney. link; completion. (144 bar completion). This album (booklet) features three completions by Pillney, Tovey and Aho, as well as other workings of the BACH theme is for purchase here.
Yngve Jan Trede link; completion. (145 bar completion, utilises the permutation matrix)
Samuel Karsko link to website with performance (completion begins at 09:30), discussion and score (149 bar completion, NB this site disappeared very quickly and is only accessible on the Wayback Machine!)
Henrik Dyhr link; completion (151 bar completion)
Malcolm Ledger Version 2: link; completion (additional 200 bars, with individual exposition for 4th theme)
Kenneth Amis: link to where an mp3 can be downloaded, completion starts at 07:35
Dai Bo: link; completion
Mario Ruffini: completion.
John Cleaveland: link
Nikolaus Matthes link, completion
Ferruccio Busoni link; original three voice combination onwards; entry of 4th subject (672 bar completion, within a large Fantasia with multiple sections)
Completions that do not utilise the principal theme
Klangspiegel link (just a prolongation of the final note)
Fabio Bonizzoni link. (simply ends with D major cadence, a tierce de picardie)
Lydia Maria Blank link (two additional chords)
Luciano Berio link; completion. version with score (very short conclusion)
Mike Magatagan link, completion (27 bar completion including re-exposition of 2nd theme but no 4th theme)
Caue Muratt Link
Bernhard Martin score only (40 and 51 bar completions)
Thomas Jung link; completion; score (50 bar completion)
Alexandre Pierre François Boëly (1785-1856) link; completion (60 bar completion, the new additions made by Boëly actually start from an earlier point: P200 had not yet been discovered/circulated) see YN’s analysis
Volkhardt Preuss link; score (adds 71 bars but still ends up unfinished)
Rudolf Barshai link; completion (86 bar completion)
Kimiko Ishizaka link; completion
Jon Lord link; completion
William Malloch link; completion (no idea what is happening in this completion, here is a review of the album and William Malloch himself in an interview about the AoF)
The Diasneb link; completion.
Maurits Reynen link; completion (Alternate version: link; completion)
Michael Finnissy link (piece starts from the introduction of the BACH theme); continuation (132 bars)
Nils Viggo Bentzon & Jan Maegaard. I have not yet managed to track these piece or any further information about it down, but a recording of their 39 and 74 bar completions was made on organ by Eva Feldbaek
Walter Steffens. Op.39: AD FUGAM. Ein Schluss zu Bachs „Kunst der Fuge“ für Streicher und Solo-Klarinette, E 1980 – UA 1980, Braunschweig (Festl. Tage für neue Kammermusik, Ltg. Uwe Praekelt), Dauer: 12’ – also am unable to find a recording or score for this piece.
– Halfofthealphabet
