Re: Wonder Scale optimizations and Scala CALCULATE/LEASTSQUARE

Hello, there, Manuel, and today I tested the CALCULATE/LEASTSQUARE
feature a bit more.

One thing I found with our Wonder Scale optimization problem is that
while giving everything a weight of 1.0 (8/7, 3/2, 12/7, 9/7), or
giving a weight of 2.0 to the 3/2 and 12/7 and 1.0 to the others,
produced the same result, the result changed when I tried other
weighings, as expected.

Giving a weight of 2.0 to the 3/2 (because of its role along with the
4/3 as the most complex stable interval in a Gothic or typical
neo-Gothic style) and 1.0 to everything else pulled the result a bit
toward 233.985 cents, as expected.

Giving a weight of 2.0 only to the 9/7 -- taking this as the most
"shallow valley" or ratio most sensitive to fine tuning in order to
maximize its degree of concord as an "unstable but relatively
blending" interval -- I found that the generator was also pulled, now
by a smaller amount, toward the wide direction, again as expected.

Paul, I'm not sure if this the same question you were raising, and I'd
emphasize that my crude algebra and cruder calculus might at best let
me report these results which appear to me as expected, and let others
form a more informed judgment, maybe by trying to replicate the
experiment.

Again, Manuel, thanks for your very user-friendly tutorial on this
feature.

Most appreciatively,

Margo

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> Paul, I'm not sure if this the same question you were raising

Not exactly. I suggested that giving weight a to both 3:2 and 7:6,
and giving weight b to both 7:9 and 7:4, would give the same result,
regardless of the values of a and b.