The Art of Fugue
This work consists of fourteen fugues and four canons in D minor, each using some variation of a single principal subject, and generally 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 single musical subject.
The earliest extant source of the work is an autograph manuscript possibly written from 1740 to 1746, usually referred to by its call number as Mus.
Papa hat 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.
Unlike the fugues written in the primary autograph, the Fuga is presented in a two-stave keyboard system, instead of with individual staves for each voice.
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[2] of the first mirror fugue, Contrapunctus XIII; 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 anomalous character of the published order and the Unfinished Fugue, have engendered a wide variety of theories which attempt to restore the work to the state originally intended by Bach.
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.
This account is disputed by modern scholars, as the manuscript was written in Bach's own handwriting, and thus dates to a time before his deteriorating health and vision prevented him from writing, in their view probably 1748–1749.
[9] Several musicians and musicologists have 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,[10] David Goode, Lionel Rogg, and Davitt Moroney (1989), conductor Rudolf Barshai (2010),[11] pianist Daniil Trifonov (2021) and composer / conductor Nikolaus Matthes (2025)[12] Ferruccio Busoni's Fantasia contrappuntistica is based on Contrapunctus XIV, but it develops Bach's ideas to Busoni's own purposes in Busoni's musical style, rather than working out Bach's thoughts as Bach himself might have done.
[13] Loïc Sylvestre and Marco Costa reported a mathematical architecture of The Art of Fugue, based on bar counts, which shows that the whole work could have been conceived on the basis of the Fibonacci series and the golden ratio.
[14] Dominic Florence proposes that a concept he calls "opposition" governs all the methods that Bach uses in Contrapuncti 1, 2, 3, and 5 to create variety.
These include changes in "melody (contrary motion), polyphony (contrapuntal inversion), harmony (dissonance), [rhythmic] density (texture), rhythm (syncopation), and tonality (modulation}".
He concludes that "Analyses of fugues should focus on continuous, dynamic, organic processes that evolve over time, rather than on the static and discontinuous dismemberment into strictly delineated sections.
"[15] In 1984, the German musicologist Hans Heinrich Eggebrecht suggested a possible religious interpretation of The Art of Fugue, which he agreed was impossible to prove: that the work illustrated in musical terms the Christian doctrine of redemption by God's grace alone, sola gratia, rather than by any action an individual can take.
