On Tue, 01 Jun 1999 10:32:36 "David B. Klein"
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> Bach composed 10 concertos for 1 harpsichord, 3 concertos for 2
> harpsichords, 2 concertos for 3 harpsichords, and 1 concerto for 4
> harpsichords. What is the strongest mathematical conclusion that I can draw
> from this relation?
>
> David Klein
This could open up a whole new area of musicology.
1. By far the strongest mathematical conclusion is that
Bach wrote 16 concertos for n harpsichords, where n is a
positive integer <=4.
2. From any reasonable extrapolation, one can infer that
the probability of some dusty library yielding a Bach
concerto for five harpsichords is small - perhaps
because there were only 4 harpsichords at Cothen, or
only 4 competent players to play all those fast notes;
or maybe there wasn't enough room on the platform.
3. Intriguing results are obtained if one abandons the
integer restriction on the number of harpsichords. Thus
one might infer that Bach wrote about 6 concertos for one
and a half harpsichords (using, say, an instrument which had
been hammered so much that only half the notes worked).
However, I believe that JSB was too much of a perfectionist
to bother with such a hybrid (which would have severely
cramped his style). In any case it would lead to
endless bickering between the players as to who was
going to play the dud harpsichord.
4. Is your data reliable? What about Brandenburg 5, with
flute, violin and harpsichord playing all the tricky bits?
Does this count as a third of a concerto for harpsichord?
Most self-respecting players would not bother to learn that
big cadenza in the first movement unless they thought they
were playing at least a bit of a harpsichord concerto - and
were being paid accordingly.
----------------------
Donald Davison
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