"Paul H. Erlich" schrieb:

> >and
> >what are the large triangular areas, where the new spokes
> start?
>
> The last triad in a particular linear series before you hit
> the l*m*n <= 1
> million limit.
so close to the 3rd root of a million? and amounting to
augmented triads?

>
> >In fact, what are the large areas directly surrounding the
> major
> >chord?
>
> The voronoi cell simply contains all points in the plane that
> are closer to
> a particular point in a set than to any other point in the
> set. In this
> case, the set is l,m,n such that l:m:n is in lowest terms and
> l*m*n <= 1
> million.
Well, I hope that most of my questions amount to: What changes
from one point to the other? do you have the cubic roots of a
million in the center and approximations, getting worse in
various ways, extending from it?

> >Who, by the way, are the Voronoi? Some Star Trek creatures (I
> >don't have TV, I'm washing the rabio)?
>
> I hope it's not infectious!
I caught it from John Lennon...

> >(the reason i'm getting lively suddenly instead of reading
> along
> >in silent awe or incomprehension is that i often wondered
> >whether it is possible to express and/or quantize the fact
> that
> >the lower-number ratios (odd, no fancy recombinations
> allowed)
> >are surrounded by obvious empty spaces and remain that way as
> >you up the limit.) (one sentence)
>
> Klaus, that's THE WHOLE IDEA of harmonic entropy, from the
> very beginning.
> Of course one-dimensional graphs don't excite a lot of people!

If this means that the curves in the diagrams I have seen so far
represent the space around an interval, then I'm not thinking
totally different from the rest of the world after all. This
would also mean that things like the Tenney harmonic distance
are not related to this at all. (I used to think - still do -
of the "space around a ratio" as relating to "harmonic
plausibility", and a variant of Tenney's distance as "melodic
plausibility". Of course, I just couldn't see a way to quantify
this.)

klaus