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Canons of the Musical Offering

Tony Phillips of the American Mathematical Society has posted a most interesting study in which these canons are used to illustrate the mathematics of elementary functions.

How the "Offering" Came to Be

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

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