The Art of Fugue, BWV 1080

The Art of Fugue, or The Art of the Fugue (Die Kunst der Fuge), 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.

Structure

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:

• 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 (counter-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, (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.
• Contrapunctus 7, a 4 per Augment[ationem] et Diminut[ionem]: 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:

• 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 [forma inversa and recta]
• Contrapunctus inversus 13 a 3 [forma recta and inversa]

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 [in] 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[punctus] 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:

• [Contrapunctus 14] Fuga a 3 Soggetti: four-voice triple fugue (not completed by Bach, but likely to have become a quadruple fugue: see below), the third subject of which begins with the BACH motif, B♭–A–C–B♮ ('H' in German letter notation).

Fuga a 3 Soggetti

Fuga a 3 Soggetti ("fugue in three subjects"), also called the "Unfinished Fugue" and Contrapunctus 14, was contained in a handwritten manuscript bundled with the autograph manuscript Mus. ms. autogr. P 200. 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." ("While working on this fugue, which introduces the name BACH [for which the English notation would be B♭–A–C–B♮] in the countersubject, the composer died.") 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.

Music

Ishizaka made her debut as a composer on March 19, 2016, with her performance of Bach's The Art of the Fugue featuring her own completion of the final fugue. In 2017, she then recorded a version, including her completion, and released it under a Creative Commons license, available for download in audiophile quality from her website.