thesis...

> From: "Michael Saunders" <michaelsaunders7@hotmail.com>
> Subject: representation, fuzzy logic, optimal tuning, adaptive tuning
>
> yes, exactly. this is where it gets interesting. in rusty, i represent
> intervals (and all other quantities) fuzzily---as functions (valued
> on [0,1]) of goodness (or "appropriateness" or "suitability")
> vs. pitch-distance. so, a perfect fifth, say, might be represented
> by a fairly broad curve peaking at 3/2. in the later sections, you'll
> see how one can define a tuning as a network of fuzzy intervals
> and let my labrynthine optimization algorithm make all those
> compromises in ratio automatically, according to the slack offered
> by the breadth of the curves---if you get my meaning---doing what
> the old tuners used to do by ear and trial-and-error.

I'm sure you've already been forwarded to the Harmonic Entropy list
where you can see curves similar to what you describe (upside down
apparently, creating a local minimum at 3/2 etc). (Not that your
work is off-topic here, its just that that is where some of the
information has been collected).

I've been recently working with the concept of dropping scales onto
such a curve and seeing how they 'want' to tune. Currently my program
only does diatonic scales (though not just 'the' diatonic). The curve
generation has a big influence on the results, and I haven't aurally
correllated some of the results which is necessary to see if I'm
on the right track.

I'll search for the URL to your paper.

Bob Valentine