The Art of Fugue - The Unfinished Fugue

The Unfinished Fugue

Contrapunctus XIV breaks off abruptly in the middle of the third section at bar 239. The autograph carries a note in the handwriting of Bach's son Carl Philipp Emanuel Bach saying "Über dieser Fuge, wo der Name 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.

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 might 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.

A number of musicians and musicologists have conjectured completions of Contrapunctus XIV, notably music theoretician Hugo Riemann, musicologists Donald Tovey and Zoltán Göncz, organists Helmut Walcha, David Goode and Lionel Rogg, and Davitt Moroney. Ferruccio Busoni's Fantasia Contrappuntistica is based on Contrapunctus XIV, but is more a work by Busoni than by Bach.

In 2007, New Zealand organist and conductor Indra Hughes completed a doctoral thesis about the unfinished ending of Contrapunctus XIV, proposing that the work was left unfinished not because Bach died, but as a deliberate choice by Bach to encourage independent efforts at a completion.

Douglas Hofstadter's book Gödel, Escher, Bach discusses the unfinished fugue and Bach's supposed death during composition as a tongue-in-cheek illustration of Austrian logician Kurt Gödel's first incompleteness theorem. To be more specific, the idea in that theorem is that the very power of a "sufficiently powerful" formal mathematical system can be exploited to "undermine" the system, by leading to statements that assert such things as "I cannot be proven in this system". Because of this twisty kind of self-reference, such assertions are true but unprovable. In Hofstadter's discussion, Bach's great compositional talent is used as a metaphor for a "sufficiently powerful" formal system; however, Bach's insertion of his own name "in code" into the fugue is not, even metaphorically, a case 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.

A book entitled "Bach: Essays on His Life and Music" includes an article about the unfinished fugue, stating that Bach never intended to write the rest of the fugue on the last sheet of music paper used for the fugue because of the unalignment of the bottom staves. It also says that because of the above-mentioned reason, Bach wrote the rest of the fugue on another sheet of music paper, called "fragment x" that would have completed, or almost completed, the fugue. However, even if there is a fragment x, it has been lost.