Tuning-Math Digests messages 10353 - 10377

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Message: 10353

Date: Sat, 21 Feb 2004 03:30:55

Subject: Re: JIP

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> > /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. 
> 
> It's a vector in a normed vector space, and these are sometimes 
> called points if you are thinking of the geometry involved.

Thinking about the geometry involved, I understand that for any given 
value returned by JIP, there is an n-1 dimensional hyperplane in 
Tenney space.

> > Rather, it seems to 
> > measure pitch, so why not refer to it as PITCH or something? 
> 
> I did call it SIZE, which I recall you didn't like. Anyway, I don't 
> think your remark makes much sense--it's just as much a point as 
> something in the Tenney space.

I'm smiling, but I don't think there's any hope of us ever writing a 
paper together.

So does it measure pitch or not?


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Message: 10355

Date: Sat, 21 Feb 2004 03:51:03

Subject: cool voronoi/delaunay applet

From: Paul Erlich

Voronoi/Delaunay Applet *


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Message: 10356

Date: Sat, 21 Feb 2004 05:13:55

Subject: poincare duality

From: Paul Erlich

I think Mathworld could use your help with this one, Gene:

Poincar  Duality -- from MathWorld *


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Message: 10360

Date: Mon, 23 Feb 2004 03:07:03

Subject: Re: JIP

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> 
> > So does it measure pitch or not?
> 
> It maps monzos to pitches.

So when it operates on monzos (which would seem to be the understood 
role of a functional in Tenney space), it returns the pitch. This 
seems like a basic thing you'd want to inform the reader of . . .



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Message: 10363

Date: Tue, 24 Feb 2004 16:48:09

Subject: creepy numbers

From: Paul Erlich

Though it's not tuning-related, I thought Gene or someone might be 
able to "explain" this strange phenomenon:

(999999/127000)^2 = 62.00000000006200 . . . .

?


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Message: 10364

Date: Tue, 24 Feb 2004 18:13:42

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

Paul wrote on 5 Jan:
>Now, for all primes r,
>If p contains any factors of r, the r-rungs in the lattice (which
>have length log2(r)) are shrunk from
>cents(r)
>to
>cents(r) - log2(r)*cents(p/q)/log2(p*q).
>If q contains any factors of 2, they are instead stretched to
>cents(r) + log2(r)*cents(p/q)/log2(p*q).

Sorry for being so behind. I noticed that this TOP tempering
can be easily done with Scala. First you need to set the prime
weights to the reciprocal of their log2, like this:

SET HARMCONST 2 1.0
SET HARMCONST 3 0.69092975
SET HARMCONST 5 0.43067656
SET HARMCONST 7 0.35620719
etc., primes not in the comma don't have to be set of course.

Then do PROJECT/TEMPER/WEIGHTED <comma(s)>

>No, it's simply limited to temperaments of codimension 1.

It doesn't have to be, the above command takes any number of
commas and tempers them out simultaneously.

I'll make an extra option for the PROJECT/TEMPER command so
that the SET HARMCONSTs can be omitted.

Manuel


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Message: 10365

Date: Tue, 24 Feb 2004 17:25:41

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" 
<manuel.op.de.coul@e...> wrote:
> 
> Paul wrote on 5 Jan:
> >Now, for all primes r,
> >If p contains any factors of r, the r-rungs in the lattice (which
> >have length log2(r)) are shrunk from
> >cents(r)
> >to
> >cents(r) - log2(r)*cents(p/q)/log2(p*q).
> >If q contains any factors of 2, they are instead stretched to
> >cents(r) + log2(r)*cents(p/q)/log2(p*q).
> 
> Sorry for being so behind. I noticed that this TOP tempering
> can be easily done with Scala. First you need to set the prime
> weights to the reciprocal of their log2, like this:
> 
> SET HARMCONST 2 1.0
> SET HARMCONST 3 0.69092975
> SET HARMCONST 5 0.43067656
> SET HARMCONST 7 0.35620719
> etc., primes not in the comma don't have to be set of course.
> 
> Then do PROJECT/TEMPER/WEIGHTED <comma(s)>

Huh!

> >No, it's simply limited to temperaments of codimension 1.
> 
> It doesn't have to be, the above command takes any number of
> commas and tempers them out simultaneously.

Really?? Wow. What do you get for 5-limit 12-equal TOP?


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Message: 10366

Date: Tue, 24 Feb 2004 19:00:44

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

>Really?? Wow. What do you get for 5-limit 12-equal TOP?

(1195.378, 1894.637, 2797.035)

Manuel


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Message: 10367

Date: Tue, 24 Feb 2004 19:06:31

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

Not sure that you expected that answer though.
If I temper out the syntonic comma and the schisma the
result is better:

(1200.051, 1901.874, 2785.782)

Manuel


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Message: 10368

Date: Tue, 24 Feb 2004 18:29:28

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" 
<manuel.op.de.coul@e...> wrote:
> 
> >Really?? Wow. What do you get for 5-limit 12-equal TOP?
> 
> (1195.378, 1894.637, 2797.035)
> 
> Manuel

That's not correct. For one thing, it's not equal!

1195.378/12 = 99.6148
1894.637/19 = 99.7177
2797.035/28 = 99.8941

For another thing, the diesis doesn't vanish:

<1195.378 1894.637 2797.035|7 0 -3> = -23.459


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Message: 10369

Date: Tue, 24 Feb 2004 18:33:03

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" 
<manuel.op.de.coul@e...> wrote:
> 
> Not sure that you expected that answer though.
> If I temper out the syntonic comma and the schisma the
> result is better:
> 
> (1200.051, 1901.874, 2785.782)
> 
> Manuel

The syntonic comma isn't being tempered out at all here:

<1200.051 1901.874 2785.782|-4 4 -1> = 21.51

And this certainly isn't an equal temperament!


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Message: 10370

Date: Tue, 24 Feb 2004 18:44:01

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" 
<manuel.op.de.coul@e...> wrote:

> It doesn't have to be, the above command takes any number of
> commas and tempers them out simultaneously.

So at best, there seems to be an error in this procedure.


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Message: 10371

Date: Tue, 24 Feb 2004 21:23:50

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

>That's not correct. For one thing, it's not equal!

Yes, sorry, I forgot again how to use my own program!
The code is correct, but I gave it the wrong parameters.
It should have been (1200.6171 1900.9770 2801.4398).
Step is 100.051421.

Manuel


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Message: 10372

Date: Tue, 24 Feb 2004 21:52:47

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

31-equal TOP is this, identical for 5-limit and 7-limit:
(1201.6366 1899.3611 2790.8979 3372.3350)

Manuel


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Message: 10374

Date: Wed, 25 Feb 2004 18:22:00

Subject: Re: non-1200: Tenney/heuristic meantone temperament

From: Manuel Op de Coul

Gene wrote:
>> 31-equal TOP is this, identical for 5-limit and 7-limit:
>> (1201.6366 1899.3611 2790.8979 3372.3350)

>I get 1201.4675

I don't see how that can be correct. Your twelfth will be
1899.094. Then (1901.955 - 1899.094) / (1201.4675 - 1200.0) =
1.95 which is not log2(3)/log2(2) = 1.585.

Manuel


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