Haven't heard from Fermilab

Hi Manuel,

Since you did such a good job computing all those dyadic harmonic
entropy curves, would you like to participate in calculations of
triadic harmonic entropy? A typical calculation could require almost
a trillion exponentiations, so some fast computing power (like yours,
I presume) would come in handy.

Anyone else interested can let me know as well.

-Paul

Hi Paul,

Maybe, but I haven't got time to write software for it.
If you give me compilable sources I'll see what I can do but
a trillion ...
This machine is already several years old, so I presume a recent
Pentium to be faster. And I need it for compilation too.

Manuel

Thanks Manuel . . . I'll try to find a simplifying approximation to the
problem . . . . no luck so far when trying such approximations in the dyad
case . . .

--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/harmonic_entropy/topicId_339.html#341

> Thanks Manuel . . . I'll try to find a simplifying approximation to
the
> problem . . . . no luck so far when trying such approximations in
the dyad
> case . . .

How could there possibly be a simplification of such a complex
problem???

_____ ____ ___ _ __
Joseph

Joseph wrote,

>How could there possibly be a simplification of such a complex
>problem???

I think there could be. For example, the dyadic harmonic entropy curve,
which required a million exponentiations to calculate, might be approximable
in terms of a small number of Gaussians. Some mathematician might be able to
work this out.

What I was initially thinking was that ignoring the "tails" of the bell
curve should reduce the number of calculations by, say, a factor of a
thousand -- but my preliminary experiments in the dyadic case indicate that
ignoring the tails leads to disastrous results . . .

Dan wrote,

>What about looking at this ass backwards... by that I just mean that
>Helmholtz and Partch both had far 'simpler' approaches that yielded
>very good models of what your computationally intensive dyadic
>harmonic entropy curves showed, so how about a best guess as to what a
>similarly 'simple' model might be for triads (etc.)? Something that
>one would guess would be in the right ballpark anyway...

Well, it would be monotonically related to geometric mean for the simplest
triads, which would be the local minima, and then it would be a smooth
surface parachuting upward from, and connecting, those minima . . . the
problem is determining how simple is simple. For example, in the dyadic
case, it seems that a standard deviation assumption of 0.6% implied a
geometric mean of about 10 as the dividing line between "simple" (local
minima with entropy value monotonically related to geometric mean) and
"complex" (falling on the smooth curve parachuting upward from, and
connecting, those minima) . . . but I don't know how I would have determined
that without going through the harmonic entropy calculation. Similarly, I'm
interested in a correct triadic computation so that I can see what certain
assumptions about standard deviation imply about "simplicity" and
"complexity" . . .