Okay, it’s been a while since my last post. I was originally going to put the following in bits and pieces up on Timbledown Annex, but then realized it needed a bit more space and consolidation. WARNING: The following may only interest music geeks, but if you’re not one, stick with it, you may glean something interesting from it.

Not all of the music Johann Sebastian Bach wrote has made its way down to us. Some pieces are missing in their entirety. One in particular only exists as a fragment – Contrapunctus XIV from The Art of Fugue. There’s two incomplete versions that have survived: one was published as a fragment, and the other, slightly longer by six measures, is on manuscript paper in JSB’s own hand. (Click on the image below to see a larger version.)

The little handwritten note on the page was added later by his son Carl Philipp Emanuel (the following is taken from Wikipedia):

“Über dieser Fuge, wo der Nahme B A C H im Contrasubject angebracht worden, ist der Verfasser gestorben.” (“At the point where the composer introduces the name BACH (which in English notation is B♭-A-C-B♮) in the countersubject to this fugue, the composer died.”)

Nice story, but most scholars don’t buy it.

At any rate, the piece has been a puzzler for academics, composers and musicians ever since. How to perform it, for one. Glenn Gould did it once as written, breaking off abruptly where the published version does, at measure 233.

The above is the second half of the Gould performance – part 1, in all its hummy, eccentric Gouldian goodness, is here. Despite its oddity, I like this version; it seems to say, in a different way, what CPE tried to in his scribble on his dad’s score. Despite a long and fruitful career, JS had so much more to give us, but his work was interrupted by death, symbolized in Gould’s lifted hand at the incomplete measure, which seems to be a mixture of hiding his face in shock and grief, and placing a hand over his mouth to stifle a gasp. Yeah, I know, Gould didn’t intend all that, but that’s what I got out of it.

The other question has been, WWJSD? A number of people have taken a crack at finishing Contrapunctus XIV, but in 1991, Zoltán Göncz, a Hungarian scholar and composer, decided that the clues to how the piece would have ended were to be found in the piece itself, in the other parts of The Art of Fugue, and in JSB’s other work. After careful examination, he worked out a solution that extrapolates the three-part fugues into a four-part fugue that into the end.

You can read an article about his solution here. It’s actually quite readable for a supposedly academic paper, and follows his reasoning clearly, at least for me.

What’s that? Can’t be bothered to read the article? Want to watch a video instead? Here you are, then.

Part 1 (curse YouTube’s 10 minute clip time limit!). This is all Bach. The chart below is Göncz’s analysis, where he shows the themes (numbers) and which voice (top to bottom: soprano, alto, tenor, bass) is playing it at that point. Göncz put heavy borders around the sections where each new theme is introduced, and the pattern of the introduction. (If you read the article, there’s a nifty chart that, along with the text, helps to clarify this.)

And Part 2. At about the 2:00 mark, you’ll see a vertical dotted line on the score, which marks where JSB’s handwritten manuscript left off, at the end of measure 239. The next screen has a measure number: 240. From here on, it’s all Göncz. He’s taken the patterns in the three heavy bordered boxed sections, superimposed them on each other, and used them to create a new grid where the fourth fugue theme is fitted in the spaces left by the other three. Now all four voices each have a go at a theme, and all of them pass the themes around between each other. (Upside-down numbers mean the theme has been inverted – notes go up where they went down, and vice versa. This is not unique to Göncz, it’s something Bach and other composers did frequently.)

What I love about watching these is being able to see where the themes are introduced and where they recur, and to be able to follow all the voices as they unfold in the manuscript. It’s like “follow the bouncing ball”, but with four balls, and imaginary ones at that. For those who don’t read music (I read it just enough to get me in trouble), I’d be curious to know if it’s as interesting. Feel free to put your feedback in the comments.

As a final note (pardon the pun), one scholar recently suggested that ol’ JS deliberately left the work unfinished, as a challenge to future composers. The sneak. Well, deliberate or not, Contrapunctus XIV has certainly been a challenge, and will continue to be, no doubt, for centuries to come. Who knows, maybe Johann’s version will turn up in a dusty attic someday, but I think the crafty codger just did it to mess with us.