>>>>> "Phil" == Phil Taylor <[EMAIL PROTECTED]> writes:
Phil> Yes and no. the expression "well-tempered" comes from the
Phil> title of Bach's two volumes of preludes and fugues. (...)
>>> No, I think most people these days believe that Bach's Well-tempered
>>> keyboard was not equal tempered.
>>
>> as far as I know it was well tempered following a system developed by a
>> man called werckmeister. In systems like this you chose a number of
>> consecutive fifths wich are about just intonation and divide the
>> divergence between 12 just intonated fifths and the octave between the
>> other fifths. As I remember, this specific system also includes a
>> correction for the thirds.
Phil> I stand corrected. However, if the system used involved distributing
Phil> the accumulated error from twelve perfect fifths among all the notes,
Phil> the result will surely be an equally-tempered scale, even though it's
Phil> mathematical basis is different?
Not if the error isn't distributed equally among all the fifths.
I play recorder with a harpsichord which is usually tuned to some kind
of seventeenth or eighteenth century tuning. As is usual, the
harpsichord will "transpose", by shifting the keyboard over by one
string, so that if the scale were equal tempered, the instrument could
play at either A440 or A415. But when it plays at A440, what it's
really doing relative to the way it was tuned is playing in the key of
C# (if the piece is in C). I bought my A415 recorders because the
difference between playing in C and playing in C# on an instrument in
one of these tunings is not at all academic or obscure; the C# sounds
pretty lousy.
--
Laura (mailto:[EMAIL PROTECTED] , http://www.laymusic.org/ )
(617) 661-8097 fax: (801) 365-6574
233 Broadway, Cambridge, MA 02139
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