You wrote:
 
>... ... ... ...
>>
>> And, what about the "French Overture," which was written in C-Minor,
>> but published in B-Minor, and is now performed in both?  Isn't there
>> a difference in the 'feel' of those two keys?  (But, if there is a
>> different feel to the two keys, and if the story about Bach's
allowing
>> it to be published in B-Minor is correct, didn't Bach care?)
>>
>> Varda
>
>Of course we have no way of knowing what Bach *really* thought, but it
fits
>well with my conception of him that  he didn't really care -- he
wouldn't
>have had the time :-)
>
>The subject of temperaments is fascinating.  Some years ago Wendy
Carlos wrote
>a very interesting paper on the subject, published in the Computer
Music
>Journal.  The salient points (from memory, and it was a long time ago):
>You can define a measure of "goodness" of a tempered scale in numeric
terms
>by calculating the theoretical differences in frequency between the
scale
>and perfect intervals (this is sort of a distance function in a vector
>space, if that helps).  She then did a computer study to analyze equal
>temperament scales with different numbers of notes -- the twelve tone
>equal tempered scale is actually an amazingly good fit -- much better
than
>an 11 note or 13 note scale.  That is, a twelve-tone scale comes
"pretty
>close" to many perfect intervals.  There are other scales with many
more
>notes with better fits, though, and she composed a piece in a tuning
with
>something over 200 notes per octave, if I remember correctly.  A very
>interesting piece...
>
>
After what I just wrote, it occurs to me that given that Bach did have
and use a transposing harpsichord, that device might be at the heart of
two versions a half-tone apart.
 
Joseph Spencer