The Art of Fugue – a pinnacle of polyphony Commentary by ...
Canons From the Art of Fugue
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02/12/2014 Canons from the Art of Fugue http://www2.nau.edu/tas3/artoffuguecanons.html 1/5 Site ©1996 Timothy A. Smith Author BACH Courses Canons from the Art of Fugue Background: Die Kunst der Fuge contains four canons which are among Bach's longest and formally complex. True to the cyclical conception of which they are part, each of the four develops aspects of fugal writing that are difficult to maintain in canon. While from head to tail a strict canon at the octave, the Canon alla Ottava , for example, contains fugal expositions of the subject at the dominant, again at the dominant in contrary motion , and at the tonic in contrary motion. Invertible counterpoint at the 10th and 12th characterize the canons alla Decima and Duodecima, respectively, while the former contains a meandering diminution of the subject in its coda. The Canon per Augmentationem in contrario Motu continues its invertible counterpoint (at the 8va ) while developing the subject, as its title implies, by means of augmentation and contrary motion . It is possible that the inspiration for these four canons came from Bach's own Fuga Canonica in Epidiapente which he had earlier composed for the Musical Offering , and to which they bear a marked resemblance. Canon 1: The Canon alla Ottava explores fugal technique in its reiteration of the head motive at the level of the dominant and in contrary motion. This canonic "subject" is the melodic inversion of the main theme of the Art of Fugue.
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Canons
Transcript of Canons From the Art of Fugue
02/12/2014 Canons from the Art of Fugue
http://www2.nau.edu/tas3/artoffuguecanons.html 1/5
Site ©1996 Timothy A. Smith
Author BACH Courses
Canons from the Art of Fugue
Background:
Die Kunst der Fuge contains four canons which are among Bach's longest and formally complex. True to the cyclical conception ofwhich they are part, each of the four develops aspects of fugal writing that are difficult to maintain in canon.
While from head to tail a strict canon at the octave, the Canon alla Ottava, for example, contains fugal expositions of the subject atthe dominant, again at the dominant in contrary motion, and at the tonic in contrary motion. Invertible counterpoint at the 10th and12th characterize the canons alla Decima and Duodecima, respectively, while the former contains a meandering diminution of thesubject in its coda. The Canon per Augmentationem in contrario Motu continues its invertible counterpoint (at the 8va) whiledeveloping the subject, as its title implies, by means of augmentation and contrary motion.
It is possible that the inspiration for these four canons came from Bach's own Fuga Canonica in Epidiapente which he had earliercomposed for the Musical Offering, and to which they bear a marked resemblance.
Canon 1: The Canon alla Ottava explores fugal technique in its reiteration of the head motive at the level of the dominant andin contrary motion. This canonic "subject" is the melodic inversion of the main theme of the Art of Fugue.
02/12/2014 Canons from the Art of Fugue
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Formally, the Canon alla Ottava is the least complicated in that its high voice consistently represents the leader, and its lowvoice, the follower. The colored sections in the following picture represent analogous units.
Canon 2: The subject of this Canon alla Decima consists of the unadorned Die Kunst theme in contrary motion.
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The second, third, and fourth canons of the Art of Fugue each divide neatly into two sections. In section one of this canon (mm.133), the lower voice leads while the upper voice follows a 10th higher (canon at the 10th). After a short bridge passage (mm.
02/12/2014 Canons from the Art of Fugue
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3440), there is an exchange of registers in which the follower, this time in the lower voice, imitates not a 10th lower, but at theoctave. Thus sections one and two exemplify double counterpoint at the 10th. The colored sections in the following picture linkanalogous units.
Canon 3: The subject of this Canon alla Duodecima consists of Die Kunst's main theme with complete upper and lowerneighbor diminutions of each factor in an ascending triad outlining the rising P5 of the theme's head motive.
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The formal organization of this canon is identical to that of its predecessor. Other than the substantial change of affect in headmotives, the primary innovation of Canon No. 3 is that its follower imitates at the interval of the 12th (8va+5th higher) ratherthan the 10th. The low voice takes the lead in section one whereafter the high voice follows a 12th higher, exemplifying thefugal principle of "real" answer. Midway through the canon these registers are exchanged but with the follower echoing theleader, not a 12th lower, but at the octave (double counterpoint at the 12th). The colored sections in the following picture link
02/12/2014 Canons from the Art of Fugue
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analogous units.
Canon 4: The subject of this Canon per Augmentationem in contrario Motu is a disjunct variation of the Die Kunst theme.
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This canon ranks among the most complicated in Bach's oeuvre. While simple in terms of formtwo sections in doublecounterpointthe canon's follower is in contrary motion AND rhythmic augmentation to its leader! Bach manages to sustainthis display of contrapuntal fireworks for fiftytwo measures whereafter he causes the voices to exchange registers and do itagain in double counterpoint at the 8va (mm. 53109)! This procedure is quickly recognized, aurally, in the two places wherethe leader executes ascending chromatics in eighths (which are answered, of course, by descending chromatics in quarters). Thecolored sections in the following picture represent analogous units.
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