In 1746 Frederick the Great extended an invitation to Johann Sebastian to visit the Prussian court in Berlin. The invitation may have come at the behest of Carl Philip Emanuel, Sebastian's son then in the employ of the king, or it may have been engineered by Count Keyserlingk, Russian ambassador and patron of Bach. In the spring of 1747 the elderly composer arrived in Potsdam where he was received graciously, if not deferentially, as shown by Frederick's (or Carl Philip Emanuel's) calling upon Sebastian as "Old Bach."
The guest was immediately asked to test Frederick's new Silbermann fortepianos and the ensuing display of technique was impressive enough for the emperor to propose a musical subject upon which Bach was requested to improvise a fugue. If contemporary accounts are to be believed, Johann Sebastian improvised at that time two fugues: one for three voices and one for six. Upon his return to Leipzig Bach added to the fugues a strict set of canons and a trio sonata featuring the "royal theme" in the flute part (Frederick's own instrument) which he had engraved and sent to the emperor as a "Musical Offering."
Dedication and ricercar
While it is known today--after its dedication--as the Musical Offering, Bach titled the cycle Regis Jussu Cantio Et Reliqua Canonica Arte Resoluta, an acrostic spelling "ricercar," the old-fashioned precursor of the fugue. Bach also titled the Offering's two fugues by that antique term.
Analysis of Each Canon
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. Make a Möbius strip of this canon and see the animation at strangepaths.com.
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.
Canon 6. Fuga canonica in Epidiapente With ten measures between its leader and follower, the "Canonic fugue with follower at the fifth" is the least recognizable as such. But a canon it is, and a strict one at that. The highest voice is an exact transposition of the middle upward a perfect 5th. While maintaining the canonic structure of this movement Bach yet manages to fashion a full-blown fugue.
Canon 7. Canon perpetuus super Thema Regium Bach's designation of canon #7 as perpetuus, reflects the fact that it has no satisfying ending. Actually any canon that is repeatable may also be considered "perpetual." Notice the unusual use of the bass clef for the canon's follower.
Canon 8. Canon perpetuus The eighth movement is technically not one canon, but two cleverly spliced together in measure 18. The canonic voices of the second half are the vertical mirror image of their counterparts in the first half.
Canon 9. Canon a 2 Quaerendo invenietis The leader reads the ninth canon in the alto clef, right side up, while the follower reads in bass clef, upside down. Like the one before it, this is a mirror canon. In this canon and the next Bach does not indicate the time interval, inviting us to search for it ourselves--Quaerendo invenietis "Seek and ye shall find."
Canon 10. Canon a 4 Again, Bach does not specify the time interval, requiring us instead to "seek it and find"--Quaerendo invenietis.