Re: fuzzy etcetera

> From: "Michael Saunders" <michaelsaunders7@hotmail.com>
> Subject: thesis
>
> >From: Robert C Valentine <BVAL@IIL.INTEL.COM>
> >I'm sure you've already been forwarded to the Harmonic Entropy list
> >where you can see curves similar to what you describe
>
> No, I haven't been, but I remember reading about that some time ago.
> My system is centered on the idea of:
> 1. Defining exactly what you mean by certain intervals by
> defining them fuzzily.
> 2. Defining a tuning by connecting the scalar degrees with fuzzy
> intervals, and stating how important each is to you.
> 3. Letting an algorithm find the best compromise, either before the
> performance or in response to which degrees are sounding.
>
> I'd like to see what you think about how my system compares
> with yours. My url is:
> http://members.fortunecity.com/odradek5/pp/rustyprogress.html
>

Thanks, there was something wrong with the PDF link (for me).

> What's yours?

The 'problem' I was trying to solve was finding
'good' tunings for diatonic scales, where good would mainly
be aimed at having many good approximations of small fractions.

Nothing Earth shatterring here, but I wanted to look at a lot
of scales and I wanted to automate the search.

I built a curve where the points of simple small ratios are
minima, with walls rising up from there. Look at Pauls graphs
at the harmonicentropy site and that was what I was going for,
although what I've come up with is far more wiggly and has
many more local minima (it seems to approximate a somewhat
sharper set of ears, but is configurable, which produces
interesting alternative interpretations for what it comes
up with).

Theoretically one would take a diatonic scale with a random
large and small step, drop it on the curve and see where it
settles. But for diatonics, the search space is small enough
that brute force works just fine, just walk through all values
and then see where the local minimum are and why.

Currently, it treats all notes (and modes) with equal
importance, which may not be as limited as it sounds.
For instance, if a 9/8 shows up as a trough that a certain
scale degree aligned with, its probably more indicative
of the strength of the 3/2 it provides in one of the
rotations.

It is still in the 'toy' stage, where I'm not confident
enough in the goodness of its approach to let it generate
the 10 scales to take to a desert island with me. But
it is allowing me to graple with some things I was thinking
about and working out in long hand in a somewhat more
efficient manner. (Only somewhat because, as is usually
the case using computers, you get the data to answer your
original question accompanied by a ton of stuff that,
with luck, prompts better questions and sometimes is
just scruff).

>
> Thanks for the interst,
>

Shore, hope to have something intelligent to say when
I read more in your paper.

Bob

> -m
>

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> Currently, it treats all notes (and modes) with equal
> importance, which may not be as limited as it sounds.
> For instance, if a 9/8 shows up as a trough that a certain
> scale degree aligned with, its probably more indicative
> of the strength of the 3/2 it provides in one of the
> rotations.

You didn't mention the rotations in your explanation of this, so
Michael may be confused. But if I may interject, I did an
optimization over all 42 intervals in the diatonic scale using my
harmonic entropy curve, and what I got was pretty much meantone,
except that the central fifths (G-D, D-A) were tempered slightly more
and the outer fifths (F-C, E-B) slightly less.