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Glenn Gould - J.S. Bach - The Art of the Fugue - Last Fugue Bach's last and not completed fugue. The Unfinished Fugue A handwritten manuscript of the piece known as the Unfinished Fugue is among the three bundled with the autograph manuscript P200. It breaks off abruptly in the middle of its third section, with an only partially written measure 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.“ (“At the point 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.“) 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 have prevented his ability to write, 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“, on which the composer attempted to work out the counterpoint between the four subjects. The 2016 completion by pianist Kimiko Douglass-Ishizaka rejects the fourth subject theory, opting instead to develop the extant materials in the fugue to completion. A number of musicians and musicologists have composed conjectural completions of Contrapunctus XIV, notably Boëly, 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 2001 Luciano Berio arranged the contrapunctus for orchestra; while Berio did not complete the fugue in the usual sense, he produced a performing version that allows the composition to fade away gracefully. 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. According to Gödel, 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“. 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. Sylvestre and Costa reported a mathematical architecture 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 golden ratio. The significance of the mathematical architecture can probably be explained by considering the role 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. Source: Wikipedia.
