As an antidote to all the math entries I've been doing lately, I'll talk about a curious set of pieces I discovered recently: J.S. Bach's Musical Offering. There is a fascinating backstory behind its enigmatic title and the "Royal Theme" on which it is based:
(Here is a decent recording of the Ricercar a 3 from the set, where in the beginning the Royal Theme is stated on its own.)
The official story is that Frederick the Great invited Bach to visit him in his residence. Upon arrival, the king showed Bach one of the very first pianofortes and invited him to improvise on the theme above. According to accounts, Bach impressed the audience—many of whom were composers themselves—with his impromptu fugue. Two weeks later, Bach sent the king a set of pieces based on the Royal Theme—including the improvised fugue as he remembered it—entitled Musikalisches Opfer, or Musical Offering. This is the account you will find in most music references or textbooks.
What most accounts don't mention is the fiendish difficulty of the task King Frederick set before Bach. When it comes to counterpoint, some themes are harder to use than others; however, the Royal Theme is suspiciously resistant to any sort of contrapuntal treatment, as if it were designed to be as hard as possible to build on. What is also not mentioned is that King Frederick was specific in his request: he wanted Bach to improvise a three-voice fugue on the theme. Not an easy task to do even when not improvising, Bach still managed to do it well enough to dazzle the audience. However, the king then requested Bach to do a six-voice fugue on the theme, a nearly impossible request under any circumstances. Even Bach's own Well-Tempered Clavier contained at most a five-voice fugue. Bach reluctantly admitted defeat, citing lack of preparation, instead improvising on a presumably easier theme of his own choosing, now lost to us. However, Bach was a proud man, and he did include a six-voice fugue in The Musical Offering, as if to prove to King Frederick that he was indeed up to the challenge after all.
(Evening in the Palace of Reason is the informative and entertaining account from which I first learned about the story behind this piece. If you're interested in learning more about the lives of Bach or Frederick the Great and their fateful meeting, I cannot recommend this book highly enough.)
What is also not usually mentioned is King Frederick's musical ability. While he was familiar with music, having played the flute in his youth, it is hard to believe that he managed to craft a theme complex enough to stump Bach. The most likely suspect is Bach's son, C.P.E. Bach, who was the king's court musician at the time. Schoenberg takes this position and also offers an explanation for the peculiar title of the set:
He knew what to do and what not to do in order to produce a theme which would not lend itself to any [contrapuntal treatment]. For this reason I believe that he, Philipp Emanuel, was the originator of the Royal Theme.…But Johann Sebastian must have recognized the bad trick. That he calls his 'Offering', a Musikalische Opfer is very peculiar, because the German word Opfer has a double meaning: 'offering', or rather 'sacrifice' and 'victim'—Johann Sebastian knew that he had become the victim of a 'grand seigneur's' joke.
—Arnold Schoenberg, from the essay "Bach" in Style and Idea
If you've read Gödel, Escher, Bach you may remember that The Musical Offering plays a significant role in the book. In particular, there are the "riddle canons": short snippets of music accompanied by enigmatic Latin titles or inscriptions intended to be "solved" by the player and developed into full-fledged pieces. The most famous one is the crab canon where the snippet is intended to be played simultanously backwards, the only other clue besides the title being the backwards clef and key signature at the end of the piece.
For more information about The Musical Offering, you can look at the Wikipedia article or the E2 article, which also contains another analysis of the riddle canons. This Piano Society thread on Bach (Google cache link as the original appears to be down) contains recordings of two movements from the set, including the one linked above with the Royal Theme. If your interest is piqued enough to want to buy a recording of the full set, I listen to and can recommend this 1999 recording by Le Concert des Nations.
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