Re: tuning question

In article <[EMAIL PROTECTED]>,
[EMAIL PROTECTED] (Dale) wrote:

>I'm researching a science fiction story, and have run across yet
>another question that I must needs pose to The Experts (or at least
>The More Informed Than I).
>
>Given a musician with an ear trained to meantone tunings (say circa
>1630), and a properly tuned modern piano in even-temper, could you
>derive a well-temper tuning from the two?

Yes and no:

On the one hand, well-tempered tunings aims at playing well in several
keys, as many as possible, but stick to rational intervals. (The idea goes
back to the Ancient Greeks.) The 12-equal temperament of a modern keyboard
uses the non-rational intervals 2^(k/12). It does not approximate the
interval 5/4 well, the major third (13.7 cents too high), so it must have
sounded bad to those used to good approximations of 5/4.

So that speaks against it. But on the other hand, playing around with an
ET tuning might give some inputs on new WT tunings.

So, summing it up, if somebody in 1630 would have gotten the chance to
play around with an ET tuned piano, they probably have been fascinated
with the fact that it sounds equally bad in all the keys, not the usably
good in all the keys considered playable that the WT aims at achieving.

You could hand the 1630'ies fellows a 9-row cromatic button accordion
tuned in 72-equal (not yet made in our times). Then, using that, they
could produce good approximations of all rational intervals 2, 3, 5, 7,
11, 17, 19, and twice as good of 13 than that of 5 in 12-equal.

  Hans Aberg