Tuning-Math Digests messages 10325 - 10349

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Message: 10325

Date: Tue, 17 Feb 2004 19:30:17

Subject: Re: top23

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

> This looks reasonable.  Let's go back to the top 23 from Gene's 
>114...

Gene was using the L_infinity norm of the wedgie there, but never 
explained why. I used the L_1 norm because that gives you the (hyper)
taxicab cross-sectional area of the periodicity unit of the 
temperament in the Tenney lattice. I'll assume that Gene had some 
reason for using L_infinity . . . It seems that in all the cases 
we've looked at, only 7-limit linear's wedgie is "rich" enough so 
that L_infinity and L_1 don't give virtually identical results . . .


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Message: 10326

Date: Wed, 18 Feb 2004 18:04:34

Subject: Re: top23

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> > --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> > 
> > > This looks reasonable.  Let's go back to the top 23 from Gene's 
> > >114...
> > 
> > Gene was using the L_infinity norm of the wedgie there, but never 
> > explained why.
> 
> It was one of the two obvious choices, and since a linear 
temperament 
> is always two vals wedged together, I picked a val-based definition.

I don't get it. Why would a val-based definition lead you to use the 
L_infinity norm?


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Message: 10347

Date: Sat, 21 Feb 2004 02:54:35

Subject: JIP

From: Paul Erlich

/root/tentop.htm *

If the JIP is not a point in the original space it operates on, then 
it probably shouldn't be referred to as a point. Rather, it seems to 
measure pitch, so why not refer to it as PITCH or something? (You 
probably asked me if I preferred that already but I had even less 
idea what it meant then.)


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Message: 10348

Date: Sat, 21 Feb 2004 03:06:03

Subject: Who's Val, anyway?

From: Paul Erlich

I sympathize with the confusion over the term "Val". You have named 
its dual after our friend Monz. Graham's approach has always been, I 
think, to work with these directly, so why not refer to them with the 
term "Breed" (which happens to be descriptive as well!)?


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