higher-D Farey, 2.0?

Any insights on the higher-D Farey series stuff?
I'm sure such a thing won't be forgotten, but I
thought I'd stoke the coals...

-Carl

I still need to post "Eureka, part 2" . . . but really, I'm pretty sure we
won't need to define mediants . . . I expect that the validation exercise
for the cuberoot(a*b*c) approximation for "2-widths" or areas will come out
favorably . . . I just need to set it up and run it . . . for days and weeks
and months.

>I still need to post "Eureka, part 2" . . . but really, I'm pretty
>sure we won't need to define mediants . . . I expect that the
>validation exercise for the cuberoot(a*b*c) approximation for
>"2-widths" or areas will come out favorably . . . I just need to
>set it up and run it . . . for days and weeks and months.

You mean, you'll test Tenney dissonance against the voronoi cell
approach?

Processor intensive, eh? Time to consider distributed computing
again? I've got a Pentium 4 at work that just sits all day...
and remember the name of the web site is omenic (entropia.com,
there's also distributed.net).

-Carl

>>I still need to post "Eureka, part 2" . . . but really, I'm pretty
>>sure we won't need to define mediants . . . I expect that the
>>validation exercise for the cuberoot(a*b*c) approximation for
>>"2-widths" or areas will come out favorably . . . I just need to
>>set it up and run it . . . for days and weeks and months.

>You mean, you'll test Tenney dissonance against the voronoi cell
>approach?

No, the validation exercise would simply check that the total "probability"
(i.e., the sum of the products of bell curve height times cuberoot(a*b*c))
is approximately constant across the triadic plane.

>>>I still need to post "Eureka, part 2" . . . but really, I'm pretty
>>>sure we won't need to define mediants . . . I expect that the
>>>validation exercise for the cuberoot(a*b*c) approximation for
>>"2-widths" or areas will come out favorably . . . I just need to
>>>set it up and run it . . . for days and weeks and months.
>
>>You mean, you'll test Tenney dissonance against the voronoi cell
>>approach?
>
> No, the validation exercise would simply check that the
> total "probability" (i.e., the sum of the products of bell curve
> height times cuberoot(a*b*c)) is approximately constant across
> the triadic plane.

Can you give an example?

-Carl

Did you follow the validation exercise I did for the dyad case, using
sqrt(n*d) as the approximation for width?

-----Original Message-----
From: carl@... [mailto:carl@...]
Sent: Monday, August 13, 2001 7:15 PM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Re: higher-D Farey, 2.0?

>>>I still need to post "Eureka, part 2" . . . but really, I'm pretty
>>>sure we won't need to define mediants . . . I expect that the
>>>validation exercise for the cuberoot(a*b*c) approximation for
>>"2-widths" or areas will come out favorably . . . I just need to
>>>set it up and run it . . . for days and weeks and months.
>
>>You mean, you'll test Tenney dissonance against the voronoi cell
>>approach?
>
> No, the validation exercise would simply check that the
> total "probability" (i.e., the sum of the products of bell curve
> height times cuberoot(a*b*c)) is approximately constant across
> the triadic plane.

Can you give an example?

-Carl

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> Did you follow the validation exercise I did for the dyad case,
> using sqrt(n*d) as the approximation for width?

Yes, in fact, I believe it was a comment from me that suggested
it. I know what you want to do now. Dont understand the
(verbal) equation you gave yet, though.

-Carl

It's the same as the dyad case, except now in the triad case, the
approximation will be cuberoot(a*b*c) instead of sqrt(n*d). Got it?

-----Original Message-----
From: carl@... [mailto:carl@...]
Sent: Monday, August 13, 2001 8:55 PM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Re: higher-D Farey, 2.0?

> Did you follow the validation exercise I did for the dyad case,
> using sqrt(n*d) as the approximation for width?

Yes, in fact, I believe it was a comment from me that suggested
it. I know what you want to do now. Dont understand the
(verbal) equation you gave yet, though.

-Carl

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--- In harmonic_entropy@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> It's the same as the dyad case, except now in the triad case, the
> approximation will be cuberoot(a*b*c) instead of sqrt(n*d). Got it?

Yes, I think so. Let's run it!

-Carl