Bach J. S. , Trio Sonata and Canon Perpetuus from the musical offering for Flute, Violin and Basso Continuo
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Bach wrote and published this set shortly after visiting Frederick the Great of Prussia in 1747, and based on a theme the King purportedly devised. All of the pieces in the set are based on the same theme.
The three- and 6-part ricercars are considered among the summits of Bach's contrapuntal writing. The trio sonata of this set is also among his finest chamber works. The other pieces (canons) are perhaps more academic, but still fascinating.
Analysis of Several Canons
Canon 1. a 2 cancrizans
The first canon of the Musical Offering is a "crab": it employs Frederick's
royal theme with a second canonic voice stating the theme simultaneously backward.
Canon 2. a 2 Violini in unisono
This is a simple unison canon for two violins with the royal theme appearing in an independent line below the canonic voices.
Canon 3. a 2 per Motum contrarium
In the third movement the canonic voices are instructed to move in contrary motion (per Motum contrarium), while the royal theme is stated in the highest voice.
Canon 4. a 2 per Augmentationem contrario Motu
Bach's inscription, Notulis crescentibus crescat Fortuna Regis refers to rhythmic augmentation of the follower: "As the notes increase may the fortunes of the King do likewise." The upside down clef signals the follower to move in the opposite direction of the leader.
Canon 5. a 2 per Tonus
In canon #5 the royal theme appears in the highest voice, while the canonic voices are separated by the interval of a perfect 5th. Bach's allegorical notation, Ascendenteque Modulatione ascendat Gloria Regis, alludes to a modulating spiral in which each repetition of the canon rises in pitch by a whole step ("As the keys ascend so may the glory of the king also ascend"). Stefan Scheller cites this canon as an example of an acoustical illusion in which the scale may be made to appear to rise when it really does not.