Bach clearly saw his final large-scale work, Die Kunst der Fuga (The Art of Fugue) BWV 1080, as his musical testament. In an age where composition was starting to turn away from polyphony (simultaneous co-equal independent voices) to homophony (a leading melody voice with subordinate accompaniment voices), the world last and greatest [primarily] polyphonic composer wanted to show one final time “this is how it’s done”. Unusually for Bach, he made arrangements to have it printed during his lifetime (it was eventually published after his death under the aegis of his second surviving son C. P. E. Bach, himself then more famous than his father).
I have been fascinated with the Art of Fugue since I first heard a version for string orchestra (arranged and conducted by Kurt Redel), and am continuing to collect performances. The score specifies no instruments, just four voices — but the entire work is playable on one keyboard with two hands (as in Tatiana Nikolayeva’s incomparable piano recording). A plethora of performances exist on organ, harpsichord, by string quartet, recorder quartet,…. and indeed full orchestrations by Hermann Scherchen, Rudolf Barshai, and others.
A long-standing mystery is the final, unfinished Contrapunctus XIV, (mis?)labeled “Fuga a 3 soggetti” by C. P. E. Bach. This marvelous triple fugue with three contrasting subjects — the third of which just the name B-A-C-H in German musical notation — ends seemingly in mid-air at bar 239. The original edition has C. P. E. Bach’s claim that J. S. Bach died while writing the last notes: this claim is dismissed by modern scholarship, as the handwriting is clearly Bach’s at a time he could still see tolerably well (hence not in his last few months). Supposedly, Bach dictated one more piece of music on his deathbed (to his amanuensis and son-in-law Altnickol), a chorale setting of “Before Thy Throne I Step Herewith” (BWV 668a).
A couple dozen musicologists and performers have tried their hand at completing the final fugue, ranging from the wild “Fantasia Contrapuntistica” by Busoni to the short and tight completion by harpsichordist Davitt Moroney in his recording (and in his critical edition of the Art of Fugue’s score for Henle Publishers of Munich).
Christoph Wolff, in his book “J. S. Bach, the learned musician”, hypothesizes Bach did complete it, but that the “Fragment X” with the completion went lost in the years between its writing and the first publication of the work. It was first noted in the late 19th century by a German musicologist named G. Nottebohm (1881; cited in Hughes, p. 27) that the three themes can be combined harmoniously with a fourth voice playing the opening theme of the cycle (the subject of Contrapunctus I, D—A—F—D—C#—D-E-F—-GFED). Wolff claims that Bach would have had to stop and work that contrapuntal puzzle out separately.
Today, I stumbled (again) upon the doctoral thesis of New Zealand organist Indra Hughes https://researchspace.auckland.ac.nz/handle/2292/392
He proffers a possibility I had never considered: that Bach deliberately left the fugue ‘unfinished’ as a contrapuntal puzzle, similar to his ‘riddle canons’. After reviewing Bach’s well-known use of number symbolism in his music (especially with numbers involving the Christian Trinity, Bach being a devout Lutheran), he points out that
Bach waited until he was the 14th member to be admitted to the [Mizler] society [of musical science],32 and to commemorate his admission he had his portrait painted with 14 buttons on his waistcoat; in the portrait he is holding the score of the 14th of a set of 14 enigmatic canons (the Goldberg canons BWV 1087).(Hughes, p. 18)
Of course, B+A+C+H = 2+1+3+8 = 14.[*] And then:
The last bar in the manuscript of Contrapunctus 14 is bar 239. To my knowledge no other writers appear to have noticed the fact that 2+3+9 = 14.
I have shown that there are many instances in which Bach associates his name, either through numbers or through musical notes, with something to which he wishes attention to be drawn (or to which he is ascribing significance in his own private way). In the light of the previous discussion, the hypothesis from which this thesis sprang was that it may not be a coincidence that The Art of Fugue ‘runs out’ in a bar whose number is the Bach number. The fact that the tenor part continues by itself, together with the fact that no rests are notated for the alto or bass (another fact that has drawn no comment from other writers) is a clear indication that the music is to continue – to be filled in.35
The final barline is drawn with as much confidence and deliberation as all the other bar lines in this score: the ‘unfinished’ score was not left without a barline. The fact that Bach has chosen this bar – a bar referring to the number 14 as clearly as many other instances of that number – to be the final bar he has written of this work suggests that Bach may be telling us, in his subtle coded way, that there is something significant about this bar. Through the use of the numbers, which refer gematrically to his own name, he is drawing our attention to this final bar.(Hughes, p. 20)
Hughes then goes on to find arguments for this thesis (not all of them convincing), then the remainder of the dissertation mostly consists of a survey and analysis of such existing completions as he could lay hands on at the time of writing. In live performance, he himself uses the short completion by Swiss organist Lionel Rogg.
Perhaps it’s all a classic example of Francis Bacon’s first idol of the mind: the human tendency to see greater order in reality than there really is. But the idea of Bach deliberately doing the equivalent of “the completion is left as an exercise to the reader” not only rhymes with what we know of Bach’s personality, but actually has a precedent in BWV 1087. Se non e vero, e ben trovato. (Giordano Bruno. Freely: “[Even] if it is not true, it is well invented.” or “Even if it ain’t true, it’s a good story.”)
Let me end this post with three longer, but well-invented [ahem] completions:
Zoltán Göncz (completion starts at 10:32) with a rolling score. [NB: the organ is in choir pitch, about a semitone sharp from standard.]
Another, more uptempo, completion on organ, by Colin MacKnight (completion starts at 7:41)
And a pleasant surprise, Rudolf Barshai’s orchestral version (completion starts at 11:51):
Nicht Bach, sondern Meer, sollte er heissen! (Beethoven: “Not Brook [=Bach], but Ocean should have been his last name!”)
[*] Note that in Bach’s time, for gematria (numerology) with Latin letters, only numbers 1-24 were used, as I and J were considered two variants of the same letter, and likewise U and V. As Dr. Hughes points out, it then just also happens that J. S. Bach = 9 + 18 + 2 + 1 + 3 + 8 = 41, or 14 backwards 🙂 This has led some people who tried to complete Contrapunctus XIV to attempt doing it in 41 bars.
ADDENDUM: via German Wikipedia, I found an article by Thomas Wilhelmi, Carl Philipp Emanuel Bachs Avertissement über den Druck der »Kunst der Fuge«, Bach-Jahrbuch 1992, pp. 101–105 in which he describes a 1751 brochure by C. P. E. Bach in which he is trying to attract customers for the printed edition. So much for the claim that keyboard performances of this work are ahistorical 😉
„Da darinnen alle Stimmen durchgehends singen, und die eine mit so vieler Stärcke, als die andere ausgearbeitet ist: So ist iede Stimme besonders auf ihr eigenes Systema gebracht, und mit ihrem gehörigen Schlüssel in der Partitur versehen worden. […] Es ist aber dennoch alles zu gleicher Zeit zum Gebrauch des Claviers und der Orgel ausdrücklich eingerichtet.“
[My translation: Since all the voices sing throughout, and each is worked out with as much strength as the others, each voice is placed on its own stave and given its own clef. […] Nevertheless, everything is expressly arranged at the same time for the use of the piano and the organ.]