Bach Canon per Augmentationem in Contrario Motu Arranged for Cello Duo
Arranged by Hans Erik Deckert
Title: Canon per Augmentationem in Contrario Motu (for Cello Duo)
Composer: Johann Sebastian Bach
Edited By: Hans Erik Deckert
Instrumentation: Violoncello Ensemble
Johann Sebastian Bach’s last work The Art of Fugue (1749-50) was only rediscovered in the 1920s. Although printed shortly after Bach’s death it received little attention and was treated more as a study in fugal composition. After its rediscovery by Wolfgang Graeser this work was given its first performance on 26th June 1927 in the Thomaskirche in Leipzig directed by Karl Straube, 178 years after it had been composed! Now this masterpiece from Bach’s musical legacy has been recognized as being unparalleled in the history of music. Erich Schwebsch, the musicologist, has characterised it as a dizzying mathematical construction full of multiple movement, form, symmetry, transformation and analogy: as “resounding cosmology”. Graeser himself called it “probably the most colossal work of occidental music”.
The Art of Fugue consists of 14 mostly four-part fugues (the final quadruple fugue is unfinished), as well as the four two-part canonic fugues. The latter are placed together in a group directly before the final fugue. The principal subject of The Art of Fugue:The four two-part canonic fugues alone constitute an unfathomable testimony to Bach’s polyphony. Four completely independent variations on the subject provide the basis for these canons.
The first canon Canon alla Ottava – here the consequent (i.e the following imitating voice) enters at the interval of an octave – has a dance-like character by being in triple time. The basis is the inverted subject:
The second canon Canon alla Duodecima in Contrapunto alla Quinta – the consequent enters at the interval of a fifth – is like a vigorous dispute between two adversaries. The subject is the foundation for this rhythmic vitality:
In the third canon Canon alla Decima in Contrapunto alla Terza – the consequent enters at the interval of a third – we encounter tranquillity and motion in stoic equilibrium. Here the inverted subject is linked to a syncopated rhythm:
In the fourth canon, Canon per Augmentationem in Contrario Motu, the consequent imitates on the one hand through the doubling of all note values (augmentation = enlargement), as well as through the exact inversion of all the intervals (Contrario Motu = contrary motion). Bach kept working intermittently on this little masterpiece before it attained its ultimate form. Even his signature “B A C H” can be recognized in bars 11 and 37 in the first two demisemiquavers (32nd notes) of the 6th and 7th quavers (8th notes) of both bars. Due to this augmentation, the consequent (initially in bar 3 in the bass, then in bar 29 in the descant) can only play for half the length of the other voice. Because of this, the reversal of roles starts in bar 27. Bach’s spirituality is intensely manifest in this canon. Here we see a diversity of melody and rhythm enriched by chromaticism, producing two completely separate sides of a dialogue which, although poles apart, are united by his inconceivable mastery. This is the pinnacle of canonic artistry. The principal subject of The Art of Fugue lays the foundation for this work of genius:
In the 4 canons, Erich Schwebsch has perceived an affinity to the four temperaments. Above I have indicated the relationship to the respective temperaments.
The Art of Fugue was originally written for a keyboard instrument and has been performed in many arrangements since then. In this arrangement of the four two-part canonic fugues for two cellos, the upper voice has simply been transposed down an octave.
-Hans Erik Deckert (translated by P. Sanders)