Re: Twenty-five non-squirrely well-temperaments

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> For any well-temperament, define the squirrel index as the number of
> consecutive tones around the circle of fifths such that the major
> third above that tone is flatter than the cube root of two (ie, 400
> cents.) Then I will count any well-temperament with a squirrel index
> above five as non-squirrely, on the grounds that the squirrel index
> for Wendell Well is six.
>
This is arguably a necessary condition for "non-squirrely", but not a
sufficient condition. The width of the thirds should occur in orderly
sequence, increasing sequentially as we move up by fifths from the
narrowest and diminishing from the greatest width continuing on
around to the narrowest to complete the cycle.

There are further niceties, some of which I outlined in my answer to
your petition for "desiderata", that we could add to this to
guarantee maximum conformity to the general historical pattern. Well
temperaments after Werkmeister generally conform rather well to the
criteria for a good tuning he outlined in his famous treatise.

As I mentioned earlier, my Natural Synchronous Well doesn't quite
meet this added condition, but the reversal of the D-A sequence by
one cent is aurally not terribly significant if at all. It is the
temeprament I could find that best conforms to the historical pattern
while preserving perfect 1.5 and 2.0 ratios all around and that still
comes out anywhere near the Pythagorean comma on the total tempering
(within 0.0058 cents in that case).