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I got started on this work – fine as it is on its own merits – as a result of starting on another one. Dating probably from late in Bach's career, it begins with a somber fantasia emphasizing two distinct motives, a rising sixth (heard at the outset) and a descending "sighing" idea (listen for it first in the pedal at 1:00). This gives way, at 4:40 in the present track, to a splendid fugue with – speculatively – a very interesting relationship to that "other work" I'm presently making MIDI sequences for. Let's examine it.
Structure of this fugue
This is one of Bach's relatively few da capo fugues, with an A-B-A form (also found in the gigantic Wedge fugue, BWV 548). It begins at 4:40 with this succinct subject:
At 6:16, the B section starts with a second subject in rising chromatic half notes against powerfully propulsive accompanying material derived from episodic figures in the A section:
I've always found this B section almost without peer in the Bach oeuvre for sheer drive. The subject begins to appear in rising fragments traded off between voices, and an increasingly active pedal (7:10-7:20) leads to a passage reminscent of the trills near the end of the Passacaglia & Fugue (7:30) that heralds the return of A (7:36).
The recapitulation has been criticized for its somewhat perfunctory nature, and indeed it seems to arrive rather quickly at the pedal point leading to the final cadence. No matter: it is still a magnificent piece.
The Royal Theme
Another well-documented work from Bach's late career is the Musical Offering (BWV 1079), which has its genesis in a visit Bach paid to Frederick II of Prussia in 1747. The king gave Bach the following formidable theme upon which to improvise a fugue:
This Bach did, to everyone's amazement but not to his own satisfaction. He went away and later presented Frederick with a set of two fugues, ten canons, and a trio sonata based on this "Royal Theme" and titled Muzikalisches Opfer (Musical Offering), inscribed with a rather flattersome entreaty to the King to accept it.
The part of the Musical Offering improvised for the King is likely the opening three-part fugue, which Bach titled Ricercar a 3. And here, as I started working on the MIDI sequence for the Ricercar, is where things got interesting.
The Internet is filled with ill-documented chaff, so I would like to state up front that I'm an astronomer, not a musicologist, so what follows is not scholarly research by a DMA but speculation by a Bach lover.
Key assumption: Bach wrote BWV 537 before his visit to Frederick. (That's not a statement of fact, but an assumption.)
Observation 1: The contours of the two subjects of the BWV 537, taken together, seem to me to bear a striking resemblance to the contour of the Royal Theme, made all the easier to see since the two works happen to be in the same key.
The first part of BWV 537 subject 1 is a close mirror of the start of the Royal Theme, while the final part is loosely similar to the return to the tonic at the end of the Theme. In between is Frederick's descending chromatic fifth, to which the second subject of 537 provides the inverted foil of a rising chromatic fourth.
Observation 2: Bach's Ricercar a 3 employs accompanying material virtually identical to that in the B section of the 537 fugue. Here is just one of numerous instances, with the Royal Theme highlighted in red and the rotating accompanying material in blue:
Compare with the second figure in the Structure of this Fugue section above.
Now imagine Bach's sitting at the harpsichord in Frederick's splendid court, presented with a seemingly diabolical melody upon which to perform that most difficult of tasks: contrapuntal improvisation. Would the similarity to a previously composed work have not jumped out of his vast store of musical memory and provided guidance as he played his first treatment of the Royal Theme? While I do not know for certain, the similarities are sufficient to make me to wonder if Bach, when presented with a theme seemingly designed to stump him, couldn't help but smile to himself. Of course he wouldn't duplicate 537, and certainly he didn't need a crutch to amaze his listeners with his performing and improvisational ability. But with previous experience as a guide, perhaps he launched into his performance for the King knowing he had it made.
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