 | ||
The Art of Fugue (or The Art of the Fugue; German: Die Kunst der Fuge), BWV 1080, is an incomplete work of unspecified instrumentation by Johann Sebastian Bach (1685–1750). Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.
Contents
- Structure
- Instrumentation
- The Unfinished Fugue
- Harpsichord
- Organ
- Piano
- String quartet
- Orchestra
- Other
- References
This work consists of 14 fugues and 4 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 word "contrapunctus" is often used for each fugue.
Structure
The Art of Fugue is based on a single subject ( play on piano or play on organ ):
which each canon and fugue employs in some variation.
The work divides into seven groups, according to each piece's prevailing contrapuntal device; in both editions, these groups and their respective components are generally ordered to increase in complexity. In the order in which they occur in the printed edition of 1751 (without the aforementioned works of spurious inclusion), the groups, and their components are as follows.
Simple fugues:
1. Contrapunctus I: 4-voice fugue on principal subject, play principal subject or play whole contrapunctus 2. Contrapunctus II: 4-voice fugue on principal subject, accompanied by a 'French' style dotted rhythm motif, play principal subject 3. Contrapunctus III: 4-voice fugue on principal subject in inversion, employing intense chromaticism, play principal subject 4. Contrapunctus IV: 4-voice fugue on principal subject in inversion, employing counter-subjects, play principal subjectCounter-fugues, in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:
5. Contrapunctus V: Has many stretto entries, as do Contrapuncti VI and VII, play principal subject 6. Contrapunctus VI, a 4 in Stylo Francese: This adds both forms of the theme in diminution, (halving note lengths), with little rising and descending clusters of semiquavers in one voice answered or punctuated by similar groups in demisemiquavers in another, against sustained notes in the accompanying voices. The dotted rhythm, enhanced by these little rising and descending groups, suggests what is called "French style" in Bach's day, hence the name Stylo Francese. play principal subject 7. Contrapunctus VII, a 4 per Augmentationem et Diminutionem: Uses augmented (doubling all note lengths) and diminished versions of the main subject and its inversion.Double and triple fugues, employing two and three subjects respectively:
8. Contrapunctus VIII, a 3: Triple fugue, with three subjects, having independent expositions, play principal subject 9. Contrapunctus IX, a 4 alla Duodecima: Double fugue, with two subjects occurring dependently, and in invertible counterpoint at the 12th, play principal subject 10. Contrapunctus X, a 4 alla Decima: Double fugue, with two subjects occurring dependently, and in invertible counterpoint at the 10th, play principal subject 11. Contrapunctus XI, a 4: Triple fugue, employing the three subjects of Contrapunctus VIII in inversion, play subjectMirror fugues, in which a piece is notated once and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:
12. Contrapunctus XII, a 4 13. Contrapunctus XIII, a 3Canons, labelled by interval and technique:
14. Canon per Augmentationem in Contrario Motu: Canon in which the following voice is both inverted and augmented. 15. Canon alla Ottava: Canon in imitation at the octave 16. Canon alla Decima in Contrapunto alla Terza: Canon in imitation at the tenth 17. Canon alla Duodecima in Contrapunto alla Quinta: Canon in imitation at the twelfthThe Unfinished Fugue:
18. Fuga a 3 Soggetti (Contrapunctus XIV): 4-voice triple fugue (not completed, but likely to have become a quadruple fugue: see below), the third subject of which is based on the BACH motif, B♭ – A – C – B♮ ('H' in German letter notation). play motif .Instrumentation
Both editions of the Art of Fugue are written in open score, where each voice is written on its own staff. This has led some to conclude that the Art of Fugue was intended as an intellectual exercise, meant to be studied more than heard. The renowned keyboardist and musicologist Gustav Leonhardt, argued that the Art of Fugue was probably intended to be played on a keyboard instrument (and specifically the harpsichord). Leonhardt's arguments included the following:
- It was common practice in the 17th and early 18th centuries to publish keyboard pieces in open score, especially those that are contrapuntally complex. Examples include Frescobaldi's Fiori musicali (1635), Samuel Scheidt's Tabulatura Nova (1624), works by Johann Jakob Froberger (1616–1667), Franz Anton Maichelbeck (1702–1750), and others.
- The range of none of the ensemble or orchestral instruments of the period corresponds to any of the ranges of the voices in The Art of Fugue. Furthermore, none of the melodic shapes that characterize Bach's ensemble writing are found in the work, and there is no basso continuo.
- The fugue types used are reminiscent of the types in The Well-Tempered Clavier, rather than Bach's ensemble fugues; Leonhardt also shows an "optical" resemblance between the fugues of the two collections, and points out other stylistic similarities between them.
- Finally, since the bass voice in The Art of Fugue occasionally rises above the tenor, and the tenor becomes the "real" bass, Leonhardt deduces that the bass part was not meant to be doubled at 16-foot pitch, thus eliminating the pipe organ as the intended instrument, leaving the harpsichord as the most logical choice.
However, opponents of Leonhardt's theory such as Reinhard Goebel argue that:
- The Art of Fugue is not completely playable on a keyboard. Contrapunctus XII and XIII, for instance, cannot be played on a single keyboard without making awkward jumps or neglecting the main theme, especially on the keyboard instruments of Bach's day, such as the harpsichord or the early pianoforte, both of which lacked a sustain pedal. This is something Bach would never have allowed to happen. (Although Leonhardt notes that there are similarly 'unplayable' passages in The Well-Tempered Clavier.)
- The absence of the basso continuo is only logical since a fugue for string quartet wouldn't have one by default.
There is also the possibility that The Art of Fugue was not intended for one single (type of) instrument, but instead for whatever instruments were at hand. This hypothesis is given weight by the modern recording and concert history of the work: it is variously performed by string quartets, wind quartets, solo keyboardists, and orchestras.
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, and to the "scientific" meaning that Bach attributed to counterpoint.