RE: [harmonic_entropy] Digest Number 115

That looks intriguing, Paul. I obviously missed the introduction, but I will
certainly have a closer look at this issue. By the way: I finally got to add
something to the linear temperament section on my website. Please let me
know your opinion.

Heinz

-----Original Message-----
From: harmonic_entropy@yahoogroups.com
[mailto:harmonic_entropy@yahoogroups.com]
Sent: Monday, December 03, 2001 3:42 AM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Digest Number 115

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There are 3 messages in this issue.

Topics in this digest:

1. Re: Fun with Matlab
From: klaus schmirler <KSchmir@...>
2. Re: Fun with Matlab continued
From: klaus schmirler <KSchmir@...>
3. Re: Fun with Matlab continued
From: "Paul Erlich" <PERLICH@...>

________________________________________________________________________
________________________________________________________________________

Message: 1
Date: Mon, 03 Dec 2001 01:03:23 +0100
From: klaus schmirler <KSchmir@...>
Subject: Re: Fun with Matlab

Paul Erlich schrieb:
>
> /harmonic_entropy/files/Erlich/fun.gif
>
> My guess that a triad l:m:n occupies an area proportional to
> (l*m*n)^
> (1/3) seems to be borne out pretty well, nay?

What a great chart!

Obviously you selected a string of ratios that keeps the fifth
just for the diagonal. What happens along the other spokes? and
what are the large triangular areas, where the new spokes start?
In fact, what are the large areas directly surrounding the major
chord? Did you put 6:5:4 in the hub or did it end up there by
itself; in other words, is there just one hub in the middle of
it all, and that's 6:5:4?

Who, by the way, are the Voronoi? Some Star Trek creatures (I
don't have TV, I'm washing the rabio)? And is it possible to
make such a graph one-dimensional for dyads?

(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)

in awe

klaus

________________________________________________________________________
________________________________________________________________________

Message: 2
Date: Mon, 03 Dec 2001 01:24:51 +0100
From: klaus schmirler <KSchmir@...>
Subject: Re: Fun with Matlab continued

Also, do you get more cells in the same space if you allow a
higher limit for l*m*n or is the structure itself finite?

klaus

________________________________________________________________________
________________________________________________________________________

Message: 3
Date: Mon, 03 Dec 2001 05:03:41 -0000
From: "Paul Erlich" <PERLICH@...>
Subject: Re: Fun with Matlab continued

--- In harmonic_entropy@y..., klaus schmirler <KSchmir@z...> wrote:
> Also, do you get more cells in the same space if you allow a
> higher limit for l*m*n or is the structure itself finite?
>
> klaus

The former. The cells shrink to zero, but the _ratios between their
areas_ is what appears to be the same, and what would be key to
having a meaningful triadic harmonic entropy function.

________________________________________________________________________
________________________________________________________________________

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

I'll reply on the main tuning list.

-----Original Message-----
From: heinz.bohlen@... [mailto:heinz.bohlen@...]
Sent: Monday, December 03, 2001 11:17 AM
To: harmonic_entropy@yahoogroups.com
Subject: RE: [harmonic_entropy] Digest Number 115

That looks intriguing, Paul. I obviously missed the introduction, but I will
certainly have a closer look at this issue. By the way: I finally got to add
something to the linear temperament section on my website. Please let me
know your opinion.

Heinz

-----Original Message-----
From: harmonic_entropy@yahoogroups.com
[mailto:harmonic_entropy@yahoogroups.com]
Sent: Monday, December 03, 2001 3:42 AM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Digest Number 115

To unsubscribe from this group, send an email to:
harmonic_entropy-unsubscribe@egroups.com

------------------------------------------------------------------------

There are 3 messages in this issue.

Topics in this digest:

1. Re: Fun with Matlab
From: klaus schmirler <KSchmir@...>
2. Re: Fun with Matlab continued
From: klaus schmirler <KSchmir@...>
3. Re: Fun with Matlab continued
From: "Paul Erlich" <PERLICH@...>

________________________________________________________________________
________________________________________________________________________

Message: 1
Date: Mon, 03 Dec 2001 01:03:23 +0100
From: klaus schmirler <KSchmir@...>
Subject: Re: Fun with Matlab

Paul Erlich schrieb:
>
> /harmonic_entropy/files/Erlich/fun.gif
>
> My guess that a triad l:m:n occupies an area proportional to
> (l*m*n)^
> (1/3) seems to be borne out pretty well, nay?

What a great chart!

Obviously you selected a string of ratios that keeps the fifth
just for the diagonal. What happens along the other spokes? and
what are the large triangular areas, where the new spokes start?
In fact, what are the large areas directly surrounding the major
chord? Did you put 6:5:4 in the hub or did it end up there by
itself; in other words, is there just one hub in the middle of
it all, and that's 6:5:4?

Who, by the way, are the Voronoi? Some Star Trek creatures (I
don't have TV, I'm washing the rabio)? And is it possible to
make such a graph one-dimensional for dyads?

(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)

in awe

klaus

________________________________________________________________________
________________________________________________________________________

Message: 2
Date: Mon, 03 Dec 2001 01:24:51 +0100
From: klaus schmirler <KSchmir@...>
Subject: Re: Fun with Matlab continued

Also, do you get more cells in the same space if you allow a
higher limit for l*m*n or is the structure itself finite?

klaus

________________________________________________________________________
________________________________________________________________________

Message: 3
Date: Mon, 03 Dec 2001 05:03:41 -0000
From: "Paul Erlich" <PERLICH@...>
Subject: Re: Fun with Matlab continued

--- In harmonic_entropy@y..., klaus schmirler <KSchmir@z...> wrote:
> Also, do you get more cells in the same space if you allow a
> higher limit for l*m*n or is the structure itself finite?
>
> klaus

The former. The cells shrink to zero, but the _ratios between their
areas_ is what appears to be the same, and what would be key to
having a meaningful triadic harmonic entropy function.

________________________________________________________________________
________________________________________________________________________

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

To unsubscribe from this group, send an email to:
harmonic_entropy-unsubscribe@egroups.com

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/