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"All work and no play:" Graupner's five thousand inversions

Think of the most twisted and crazed Jack Nicholson expression from the poster to the Stanley Kubric film The Shining. That's how I picture Christoph Graupner. Better yet, cut to the scene in the movie where the plot turns: The wife, played by Shelley Duvall, frantically finds that her husband is insane; she discovers he has typed hundreds of pages of nothing but the repeated sentence "All work and no play makes Jack a dull boy," instead of the book manuscript he has been obsessed with. All while Penderecki's Polymorphia plays in the background.

Now I have to admit that my imagination can go a bit overboard sometimes, and Christoph Graupner did produce some truly beautiful work. He was a highly competent composer, clearly not crazy. Then what made me think this way? It is this: Graupner wrote a canon which he claims has 5626 solutions; he came up with a short melody that, frankly, is full of holes, and he went on to fill seven hundred pages with five thousand, six hundred and twenty-six (5626) different four-voice configurations of that melody in counterpoint with itself. That many solutions to his highly reactive, half empty and repetitive phrase.

To be clear, this is Christoph Graupner, the brilliant prodigy who studied with Kuhnau, Bach's predecessor as Kantor of the Thomasschule in Leipzig. (Incidentally, all three of these composers wrote canons.) Graupner could easily have taken Kuhnau's job instead of Bach, and almost did, but instead used the job offer to get a pay raise in Darmstadt. (You can read about all of this in Grove's Dictionary of Music and Musicians.) Graupner showed no signs of being the slightest bit loony.

What is this puzzling volume? Let's take a closer look, thanks to the labor of the Ländesbibliothek and Universitätsbibliothek Darmstadt ( Here is one randomly-chosen page containing solutions 3530 through 3537.

one of many hunreds of pages from the manuscript

Notice that there are no transformations applied to the subject other than transposition. No retrograde, contrary motion, augmentation, or so on.

Perhaps I've been extremely unlucky and dropped my finger into the book at the one point where the one or two extremely rare errors occur. It will require a person with more time than I have to definitively declare this project a musical failure, but all indications so far, especially the musical subject, have inclined me to think so.

For the time being we can say that the enterprise was much less than perfect. While the disagreeing accidentals may simply represent an oversight in editing, the fourths do not (measures 5 and 10). And glancing across the page I did select reveals a quagmire of cross relations.

Notice the numerical annotations in the right margin of the manuscript page beside each solution. In this case, "3516." These appear to be references to "sister" solutions, related in some way. Investigation shows that the referenced solutions are still different from their brothers. In our case, solution 3516 shares the problem of clashing accidentals as the solution we examined.

In inversion 3516 similar though soluble complications arise with the accidentals added to the tenor part. If all F's are sharped, then clashes and cross relations are avoided, but the unprepared fourths with the bass occur in the same spot. Inverting the alto and bass parts could solve this, but presumably that inversion is already counted.

I don't know how many pages there are in total -- likely over 700 (5626 ÷ 8 per page) -- or whether the solutions occupy more than one volume. The digital archive at Darmstadt has three large PDF files posted with several hundred pages each, the last ending with solution number 3792. I take it on faith that the 5626? solutions are all somewhere.

What kind of motivation stokes such industry? Where is the musicality?

Let's be fair

Graupner was an immaculate calligrapher. In fact he was employed by Kuhnau as a copyist. His graceful hand contributes tomes to the Darmstadt manuscript collection. Yet this album of canon solutions is as hurriedly written as imaginable; the quarter notes are not even filled in. (White-notation!) The accidentals are not proofread. Clearly this compendium was not intended for public eyes. Nor was it prepared for publication.

Perhaps Graupner had in mind to use the best of these solutions in a polymorphous canon such as the one by the Count de Ligniville in his Stabat Mater. In a canon such as this, knowing the myriad combinations made available by a motive would be paramount.

polymorphous canon by de Ligneville

On the other hand, that project would not require such a thorough or exhaustively documented investigation of the available permutations. More likely in my mind, the work was completed in order to influence amateur musicians. This is still the age of alchemy, of the mingling of mathematics, numerology and music, and of Mizler's Society for Musical Sciences of which Telemann was a member, and Bach would later be. Perhaps Graupner saw the solutions as a route to membership in this group, or as a resume item in general. Looking at the canonic subject, one notices that its composition seems mathematically, not gesturally generated.

The Guiness Book of World Records was not yet in publication, but yet another explanation for the existence of Graupner's rather unmusical labors might be to shatter the record set by George Waterhouse in the late sixteenth century with his 1163 canons on the plainchant Miserere. To me this seems the most plausible explanation for such extreme emphasis on quantity over quality. Waterhouse's canons were never published, and neither would Graupner have had the impetus to do so with his collection.

In retrospect it is tempting to see every extant jotting as a composer's message to posterity, an entry in the ledger of history, but sometimes things persist despite the lack of effort to preserve them. What choice did Graupner have in recording his idea other than to use his great skill as copyist to furiously produce it, still unedited? It certainly would not fit on a Post-it sticky note.


So I'll close my anti-tirade as it settles down as to series of apologies for an ostentatious premise, conceding that in truth Christoph Graupner did not go mad; he simply wasted a bit of time just as we all do. I wish I could find an image of his likeness to replace my daydream from The Shining, but I'm having very little luck tracking one down, and am afraid none exist.

I will also have to apologize for passing judgment on the quality of the canon, but as the history of canon goes, this is a rather early example of the kind of superlative digression that gives the discipline a bad name. There are two requirements in creating a canon:

1. follow the rule

2. create music

The rule (literally 'canon') constitutes a challenge that tests the limits of contrapuntal and competence. The rule challenges the composer to know those limits. It is the first of two steps, the second step being a worthwhile musical creation. No wise composer relies on an assumed forgiveness on the part of the solver. In fact it is only the assumption that no problem will exist in the solution that allows the correct solution to be found among numerous inadequate contenders.

Bach strove to do just the opposite: his motivation was to elevate the rulemaking with well-crafted composition. Not to exalt the mere adherence to the rule, but to follow through with the second step. The fact that he did brings us to consider these things.


For further reading;

P. Cahn: ‘Christoph Graupners Kanons als Versuch einer systematischen Imitationslehre’, Musiktheorie, i (1986), 129–37

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