Tuning-Math Digests messages 8854 - 8878

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Message: 8854

Date: Tue, 23 Dec 2003 22:38:33

Subject: plot of 5-limit commas

From: Paul Erlich

I plotted all 5-limit commas for which

tenney complexity [TC] < 30
and
tenney-based heuristic error [(n-d)/TC/log(TC)] < 0.001
and
the comma is not a higher power of some other comma

Yahoo groups: /tuning-math/files/Paul/waterfall1.gif *

who can explain the "woof" and "warp", or curved 'grid', apparent in 
this plot?

here is the plot with the ratios of the commas written in:

Yahoo groups: /tuning-math/files/Paul/waterfall2.gif *

the size of the font used for each comma was 16^(1-epimericity)
where the epimerity is tenney based and equal to log(n-d)/log(n*d).

one can easily imagine the epimericity 'contours' running across this 
plot, though i wasn't able to show them as easily as i thought i 
would . . .

anyway, i hope herman miller, at least, takes a look at this!


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Message: 8856

Date: Tue, 23 Dec 2003 23:39:44

Subject: Re: epimorphism

From: Manuel Op de Coul

>Manuel, you are wrong. This is indeed a torsional block. The four
>determinants are 20, 32, 46, and 56 -- obviously these are all
>multiples of 2, so we have torsion!

Drag, you're right. Why is it that when you know there's a bug in
the code you can spot it immediately, when otherwise it remains unnoticed.

Manuel


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Message: 8857

Date: Tue, 23 Dec 2003 22:42:14

Subject: Re: epimorphism

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" 
<manuel.op.de.coul@e...> wrote:
> 
> >Manuel, you are wrong. This is indeed a torsional block. The four
> >determinants are 20, 32, 46, and 56 -- obviously these are all
> >multiples of 2, so we have torsion!
> 
> Drag, you're right. Why is it that when you know there's a bug in
> the code you can spot it immediately, when otherwise it remains 
unnoticed.
> 
> Manuel

so now can you find a *real* counterexample?


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Message: 8860

Date: Wed, 24 Dec 2003 21:21:32

Subject: Re: epimorphism

From: Manuel Op de Coul

Paul wrote:
>so now can you find a *real* counterexample?

I guess not...

I've uploaded a new release with the torsion and epimorphism
bugs fixed, updated Sagittal symbols, improved periodicity
block dialog, and smaller improvements.
http://www.xs4all.nl/~huygensf/software/Scala_Setup.exe - Ok *

Manuel


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Message: 8861

Date: Wed, 24 Dec 2003 21:19:23

Subject: Re: plot of 5-limit commas

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> 
> > who can explain the "woof" and "warp", or curved 'grid', apparent 
> in 
> > this plot?
> 
> I'd start by taking ratios of commas along lines, and see if there 
is 
> a single high-quality comma behind the line.

No; the lines are essentially single numerators in one direction, and 
single denominators in the other.


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Message: 8862

Date: Wed, 24 Dec 2003 14:42:57

Subject: definitions

From: Carl Lumma

Gene,

If you could collect all your definitions, "scale", "tuning",
"notation", etc. and put them on xenharmony.org or Wikipedia
I would be enthralled.

-Carl



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Message: 8868

Date: Fri, 26 Dec 2003 06:16:03

Subject: Re: Attention Gene

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> > Yahoo groups: /tuning-math/message/8269 *
> > 
> > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> > wrote:
> > > --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" 
> > <gwsmith@s...> 
> > > wrote:
> > > > After fixing my program, here is what I am getting for 
Prooijen 
> > and
> > > > geometric 11-limit reductions:
> > > > 
> > > > ! red72_11pro.scl
> > > > Prooijen 11-limit reduced scale
> > > > 72
> > > > !
> > > > 81/80
> > > > 64/63
> > > 
> > > Gene -- why isn't this 45/44?
> 
> I guess I'm using the wrong definition of Prooijen complexity.

It's called 'expressibility', and it's simply (the log of) the "ratio 
of" (or, imprecisely speaking, "odd-limit") measure of the ratio.

Definitions of tuning terms: ratio of, (c) 2003 by Joe Monzo *

Searching Small Intervals *

Since log(45)<log(63), you must indeed have the wrong definition.


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Message: 8872

Date: Fri, 26 Dec 2003 08:32:43

Subject: Re: Attention Gene

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> 
> > Since log(45)<log(63), you must indeed have the wrong definition.
> 
> log(11*45)>log(63), which is what I think I used.

I thought I had already straightened you out on that particular 
misunderstanding.



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Message: 8873

Date: Sat, 27 Dec 2003 20:52:20

Subject: Re: 5-limit, 12-note Fokker blocks

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> The Duodene is well-known as a 5-limit, 12-note Fokker block;
> I 
> decided to check on whether Scala knows of four other examples, and 
> got this.

Scala has many others, including Marpurg's Monochord #1, Ramos/Ramis, 
etc . . . see the Gentle Introduction to Fokker Periodicity Blocks.


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