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Message: 10350 - Contents - Hide Contents

Date: Sat, 21 Feb 2004 03:24:12

Subject: Re: JIP

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> /root/tentop.htm * [with cont.]  (Wayb.)
> 
> 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.

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.
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Message: 10351 - Contents - Hide Contents

Date: Sat, 21 Feb 2004 03:25:35

Subject: Re: Who's Val, anyway?

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> 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!)?



Either that, or we could get Graham to change his name to Val.
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Message: 10353 - Contents - Hide Contents

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 * [with cont.]  (Wayb.)
>> 


>> 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 - Contents - Hide Contents

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

Subject: cool voronoi/delaunay applet

From: Paul Erlich

Voronoi/Delaunay Applet * [with cont.]  (Wayb.)
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Message: 10356 - Contents - Hide Contents

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 * [with cont.]
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Message: 10357 - Contents - Hide Contents

Date: Sat, 21 Feb 2004 07:26:20

Subject: Re: JIP

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:



> So does it measure pitch or not?



It maps monzos to pitches.
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Message: 10358 - Contents - Hide Contents

Date: Sat, 21 Feb 2004 07:34:35

Subject: Re: poincare duality

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> I think Mathworld could use your help with this one, Gene:
> 
> Poincar  Duality -- from MathWorld * [with cont.] 



It's a little succinct, isn't it? Actually, if I did write something 
it would be for Wikipedia. I started out thinking about adding 
something on the Riemann-Siegel zeta function, just so I could refer 
to it, and ended up deciding that some more important special 
functions were missing. So I added the Jacobi theta function and 
defined Jacobi and Weierstrass elliptic functions in terms of it, 
just as I always thought was the best method, added a Dedekind eta 
function, a j invariant, and a Dirichlet eta function. In all of 
which I managed to lose sight of my original goal of relevance to 
music, but the encyclopedia is much improved in the area of special 
functions relevant to number theory.
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Message: 10359 - Contents - Hide Contents

Date: Sat, 21 Feb 2004 07:53:39

Subject: Re: poincare duality

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> I think Mathworld could use your help with this one, Gene:
> 
> Poincar  Duality -- from MathWorld * [with cont.] 



By the way, there's a discussion of this page

Exterior power - Wikipedia, the free encyclopedia * [with cont.]  (Wayb.) =

Exterior power - Wikipedia, the free encyclopedia * [with cont.]  (Wayb.)

on the corresponding talk page ("discuss this page.") I was thinking 
of writing something on the wedge product which could actually be 
understandable by non-mathematicians, and Charles was not too keen on 
the idea. However, I see that immediately afterward he moved material 
from the Grassmann algebra page to this one, giving it an entire new 
introductory section, and thereby making it more concrete, just as we 
had discussed. I'd be interested if people here could tell me if it 
makes any sense to them, and how much.



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Message: 10360 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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 - Contents - Hide Contents

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: 10373 - Contents - Hide Contents

Date: Tue, 24 Feb 2004 22:03:00

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

From: Gene Ward Smith

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



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Message: 10374 - Contents - Hide Contents

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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