Fugue Kit

Some Assembly Required!

"Complete" J. S. Bach's final fugue in the Art of Fugue.

Parts Packaged by Otto Steinmayer

For the thinking person, no experience can be more satisfying than to enter the mind of a truly great genius and understand what that person did.  With basic algebra one can work through and understand Einstein's equations of Special Relativity.  With paper, pencil, ruler, and compass, one can illustrate a proposition by Euclid, or by Isaac Newton in his Principia and prove to oneself the soundness of their demonstrations. 

The Art of Fugue turned out to be J.S. Bach's last major project.     There has been much debate concerning what final form Bach intended the work to have taken.  I'll let you read all about that in the Wikipedia article on The Art of Fugue.

There's one fugue that didn't get finished.  Bach's son Carl included it, as Contrapunctus XIV, in the engraved publication and entitled it "Fuga à tre soggetti."  But Carl made a mistake!  This fugue is the only one in the Art  that doesn't include the main subject, or one of its variants.  To make a truly impressive finish, Bach certainly must have desired to introduce the theme subject of the Art.  Plenty of people have fiddled with it, and yes, it fits in.

Here are the three subjects of the unfinished final fugue, in order of appearance:

1) Subject "B"

2)Subject "A"

3) Subject "C"

Yes, the famous "BACH" riff.  All of these fit together.  They're in the fugue from Bach's hand.    Now here's the generating theme of the Art of the Fugue from Contrapunctus I:

Subject "H"
Your job is to take all of these four  themes and put them together.  They do indeed all fit together.  You will have to discover at what point each theme enters vis-à-vis the other three.  They can't all be in the same octave, so you will have find an approriate register for each.  And you will have to compose a few notes of your own to bring the four parts to a satisfying cadence.  In the end, you will have seven bars where all this music is chugging along together, and you will have understood not a little about how Bach went about creating such marvellous counterpoint.

Several musicians have written completions for the Art's final fugue.  To create a full-dress ending would be a task requiring mcu labor, and could not please unless inspiration entered also (wherever inspiration comes from!).    But---to use a metaphor---Bach machined these themes to fit, and unlike metal that rusts, their contours are as clean and the tolerances as fine as they were 260 years ago.  It is within the power of any moderately skilled musician to make them work together.  I think there can be no homage to Bach more sincere than in understanding him the way he wanted to be understood.

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