The Art of Fugue


The Art of Fugue, or The Art of the Fugue, BWV 1080, is an incomplete musical work of unspecified instrumentation by Johann Sebastian Bach. Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.
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 word "contrapunctus" is often used for each fugue.

Mus. ms. autogr. P 200

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. ms. autogr. P 200 in the Berlin State Library. Bearing the title Die / Kunst der Fuga ' / di Sig' Joh. Seb. Bach, which was written by Bach's son-in-law Johann Christoph Altnickol, followed by ' written by, the autograph contains twelve untitled fugues and two canons arranged in a different order than in the first printed edition, with the absence of Contrapunctus 4, Fuga a 2 clav, Canon alla decima, and Canon alla duodecima.
The autograph manuscript presents the then-untitled Contrapuncti and canons in the following order: , , , , , an early version of , , , Canon in Hypodiapason with its two-stave solution Resolutio Canonis, , , Canon in Hypodiatesseron, al roversio ' e per augmentationem, perpetuus presented in two staves and then on one, with the inversus form of the fugue written directly below the rectus form, with the same rectus–''inversus format, and a two-stave Canon al roverscio et per augmentationem—a second version of Canon in Hypodiatesseron''.

Mus. ms. autogr. P 200, Beilage

Bundled with the primary autograph are three supplementary manuscripts, each affixed to a composition that would appear in the first printed edition. Referred to as Mus. ms. autogr. P 200/Beilage 1, Mus. ms. autogr. P 200/Beilage 2, and Mus. ms. autogr. P 200/Beilage 3, they are written under the title Die Kunst / der Fuga / von J.S.B.
Mus. ms. autogr. P 200, Beilage 1 contains a final preparatory revision of the Canon in Hypodiatesseron, under the title Canon p ''Augmentationem contrario Motu crossed out. The manuscript contains line break and page break information for the engraving process, most of which was transcribed in the first printed edition. Written on the top region of the manuscript is a note written by Johann Christoph Friedrich Bach:
Mus. ms. autogr. P 200, Beilage 2 contains two-keyboard arrangements of Contrapunctus 13 inversus and rectus, entitled Fuga a 2. Clav: and Alio modo Fuga a 2 Clav. in the first printed edition respectively. Like Beilage 1, the manuscript served as a preparatory edition for the first printed edition.
Mus. ms. autogr. P 200, Beilage 3 contains a fragment of a three-subject fugue, which would be later called Fuga a 3 Soggetti in the first printed edition. 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. The fugue abruptly breaks off on the fifth page, specifically on the 239th measure and ends with the note written by Carl Philipp Emanuel Bach: "Ueber dieser Fuge, wo der Nahme BACH im Contrasubject angebracht worden, ist der Verfasser gestorben." The following page contains a list of errata by Carl Philipp Emanuel Bach for the first printed edition.

First and second printed editions

The first printed version was published under the title Die / Kunst der Fuge / durch / Herrn Johann Sebastian Bach / ehemahligen Capellmeister und Musikdirector zu Leipzig in May 1751, slightly less than a year after Bach's death. In addition to changes in the order, notation, and material of pieces which appeared in the autograph, it contained two new fugues, two new canons, and three pieces of ostensibly spurious inclusion. A second edition was published in 1752, but differed only in its addition of a preface by Friedrich Wilhelm Marpurg.
In spite of its revisions, the printed edition of 1751 contained a number of glaring editorial errors. The majority of these may be attributed to Bach's relatively sudden death in the midst of publication. Three pieces were included that do not appear to have been part of Bach's intended order: an unrevised version of the second double fugue, Contrapunctus X; a two-keyboard arrangement of the first mirror fugue, Contrapunctus XIII; and an organ chorale prelude on "Vor deinen Thron tret ich hiermit", 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.

Structure

The Art of Fugue is based on a single subject, which each canon and fugue employs in some variation:

\relative c

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, the groups, and their components are as follows.
Simple fugues:
  • Contrapunctus 1: four-voice fugue on principal subject
  • Contrapunctus 2: four-voice fugue on principal subject, accompanied by a 'French' style dotted rhythm
  • Contrapunctus 3: four-voice fugue on principal subject in inversion, employing intense chromaticism
  • Contrapunctus 4: four-voice fugue on principal subject in inversion, employing counter-subjects
Stretto-fugues, in which the subject is used simultaneously in regular, inverted, augmented, and diminished forms:
  • Contrapunctus 5: has many stretto entries, as do Contrapuncti 6 and 7''
  • Contrapunctus 6, a 4 in Stylo Francese: adds both forms of the theme in diminution,, 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.
  • Contrapunctus 7, a 4 per Augment ''et Diminut: uses augmented and diminished versions of the main subject and its inversion.
Double and triple fugues, employing two and three subjects respectively:
  • Contrapunctus 8, a 3: triple fugue with three subjects, having independent expositions
  • Contrapunctus 9, a 4, alla Duodecima: double fugue, with two subjects occurring dependently and in invertible counterpoint at the twelfth
  • Contrapunctus 10, a 4, alla Decima: double fugue, with two subjects occurring dependently and in invertible counterpoint at the tenth
  • Contrapunctus 11, a 4: triple fugue, employing the three subjects of Contrapunctus 8 in inversion
Mirror fugues, in which a piece is notated once and then with voices and counterpoint completely inverted, without violating contrapuntal rules or musicality:
  • Contrapunctus inversus 12 a 4
  • Contrapunctus inversus 13 a 3
Canons, labeled by interval and technique:
  • Canon per Augmentationem in Contrario Motu: Canon in which the following voice is both inverted and augmented. The following voice, running at half-speed, eventually lags the first voice by 20 bars, making the canon effect hard to hear. Three versions have appeared in the autograph Mus. ms. autogr. P 200: Canon in Hypodiatesseron, al roversio e per augmentationem, perpetuus, Canon al roverscio et per augmentationem, and Canon p. Augmentationem contrario Motu, the third of which appears on the second supplemental Beilage.
  • Canon alla Ottava: canon in imitation at the octave; titled Canon in Hypodiapason in Mus. ms. autogr. P 200.
  • Canon alla Decima Contrapunto alla Terza: canon in imitation at the tenth
  • Canon alla Duodecima in Contrapunto alla Quinta: canon in imitation at the twelfth
Alternate variants and arrangements:
  • Contra a 4: alternate version of the last 22 bars of Contrapunctus 10.
  • Fuga a 2 Clav: and Alio modo. Fuga a 2 Clav.: two-keyboard arrangements of Contrapunctus inversus a 3, the forma inversa and recta, respectively.
Incomplete fugue:
  • Fuga a 3 Soggetti'': four-voice triple fugue, the third subject of which begins with the BACH motif, B–A–C–B.

    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 Gustav Leonhardt argued that the Art of Fugue was intended to be played on a keyboard instrument, and specifically the harpsichord. Leonhardt's arguments included the following:
  1. 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, Samuel Scheidt's Tabulatura Nova, works by Johann Jakob Froberger, Franz Anton Maichelbeck, and others.
  2. 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.
  3. 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.
  4. 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.
It is now generally accepted by scholars that the work was envisioned for keyboard.