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Message: 2475 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 23:35:57

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: dkeenanuqnetau

--- In tuning-math@y..., "clumma" <carl@l...> wrote:


>>> I realized this ambiguity after I posted.  I meant,
>>> any given linear temp. taken to any given number of
>>> notes.
>> 


>> That doesn't quite do it. You meant:
>> 
>> .. that the number of o-tonal chords is the same as the number 
>> of u-tonal chords in any linear temp. taken to any number of 
notes.
> 


> You took out the "given"??



Put 'em back if you like, but there doesn't seem to be any ambiguity 
now without them, or am I missing something?
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Message: 2476 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 00:07:19

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: dkeenanuqnetau

--- In tuning-math@y..., "clumma" <carl@l...> wrote:


> Dave, didn't you once show that the number of o- and
> u-tonal chords must be the same in any linear temp.,
> of any number of notes?



Hmm. I don't think I showed it. I just claimed it was obvious when you 
look at a linear tempered tuning as chains of generators, at least in 
the single-chain case.

The utonal chord pattern on the chains must always be the mirror image 
of the otonal. If the tuning has a point of reflective symmetry (not 
necessarily at a note) then there will be the same number of otonal as 
utonal.

With multiple chains they must be considered to be arranged uniformly 
around the surface of a cylinder (with the chains parallel to the axis 
of the cylinder). If the tuning has a point of reflective symmetry in 
this geometry, then there will be the same number of otonal as utonal.

Miracle-tempered Vitale 19 is not a linear temperament since it is not 
contiguous on the chain. But it is symmetrical on the chain so it has 
equal o and u.
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Message: 2477 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 00:12:58

Subject: Re: One way to block web advertising

From: dkeenanuqnetau

--- In tuning-math@y..., "clumma" <carl@l...> wrote:


> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:


>> I'm using the Guidescope proxy service. It's working for me.
>> See  * [with cont.]  (Wayb.)
> 


> Doesn't seem to block the ads in the messages... any suggestions
> to get it to work?



It's blocking them for me. I just see a piece of text saying 
"ADVERTISEMENT".

I'm still using an old version.
guide: version 2000/10/09-19:20:21
Guidescope Proxy(TM) 0.98
I don't know if that has anything to do with it. 

Doesn't it have a way for you to manually tell it you don't want to 
see a certain ad again? It's been a while since I installed it.
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Message: 2478 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 02:52:58

Subject: Re: One way to block web advertising

From: clumma


>It's blocking them for me.  I just see a piece of text saying 
>"ADVERTISEMENT".

Hmm.  Cool.

>Doesn't it have a way for you to manually tell it you don't
>want to see a certain ad again? It's been a while since I
>installed it.



Maybe it has something to do with the firewall I'm behind.
Anyway, I've recently decided I shouldn't have to run software
to stop ads (and something about sending all my http trafic
through some company's server in New Jersey raises a red flag).
Instead, I'll just send an angry e-mail to yahoo, and eventually
quit using their service.

I'm really tired of ads.  I don't have any deep philosophical
thing to say here, for once.  I'm just tired of seeing them.

-Carl
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Message: 2479 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 04:51:36

Subject: Re: the 75 "best" 7-limit ETs below 100,000-tET

From: genewardsmith

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:



















> Hey guys. This is _tuning_ math remember. It's a serious stretch of 
my 
> imagination to think that ETs above 2000 have anything to do with 
> tuning, let alone 100,000!



These high numbers have their uses, and Paul seems to have discovered 
something of considerable number-theoretic interest, so give us a 
break, please.
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Message: 2481 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 11:26:39

Subject: Re: Well . . .

From: paulerlich

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:


> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> 


>> I don't know what's going on here, but it sure reminds me of the 
>> Riemann zetafunction!
> 


> It implies things about the zeta function, and I want to post about 
> it to sci.math.research; am I correct in thinking that you are the 
> one who discovered this?



It's pretty safe to assume that.



> I also am wondering if you are going to sic 
> Matlab's FFT on the 5-limit also.



You mussed have mist it.
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Message: 2482 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 11:30:50

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:


> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
>> Hey Dave,
>> 


>> Continuing our conversation from the tuning list, I plugged in 
the 
>> unison vectors 243:245 and 224:225 into Graham's temperament 
finder, 
>> and got Graham's MAGIC temperament. Graham gives a generator of 
>> 380.39 cents. The 19-tone MOS would have 7 otonal and 7 utonal 
>> tetrads, with a maximum error of 5+ cents.
>> 
>> How many tetrads did your MIRACLE Vitale 19 have, Dave? (by which 
I 
>> mean Rami Vitale's scale, without 21/16, 63/32, 8/7, 12/7, and 
>> Miraclized.)
> 


> It has 5 otonal and 5 utonal 7-limit tetrads with max error of 2.7 
c.



Now -- if you think of this as a linear temperament where _only_ 
224:225 is tempered out, I bet you can reduce that error even further.

But: maybe you want those extra tetrads that MAGIC gives you. I 
would. (Clearly I'm using a _subjective_ goodness measure, but I 
would want to impose that _after_ I had a nice _flat_ survey.)
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Message: 2483 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 11:32:43

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: paulerlich

--- In tuning-math@y..., "clumma" <carl@l...> wrote:


> Dave, didn't you once show that the number of o- and
> u-tonal chords must be the same in any linear temp.,
> of any number of notes?
> 
> -Carl



Huh? Compare 7-meantone with 7-chain-of-minor thirds.
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Message: 2484 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 11:36:50

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: paulerlich

I wrote,



> Now -- if you think of this as a linear temperament where _only_ 
> 224:225 is tempered out



"linear" should read "planar"
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Message: 2485 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 13:02:43

Subject: A theory

From: paulerlich

Since 612 is the "tuning of schismas", any near-multiple of 612 will 
be more likely to have the schisma vanish, and thus to do 5-limit 
well, than non-near-multiple of 612. This is similar to how the 
diatonic semitone produces a bit of periodicity in the smaller 5-
limit ETs, with peaks at 19 and 22, 31 and 34, 41 and 43, 53 and 55.

So . . . there must be some very significant 7-limit comma lurking at 
about 1/1664 octave. This is the Breedsma, which equals exactly one 
step of 1663.89978-tET.
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Message: 2486 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 18:28:08

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: clumma


>> >ave, didn't you once show that the number of o- and
>> u-tonal chords must be the same in any linear temp.,
>> of any number of notes?
>> 
>> -Carl
> 


> Huh? Compare 7-meantone with 7-chain-of-minor thirds.



I realized this ambiguity after I posted.  I meant,
any given linear temp. taken to any given number of
notes.

-C.
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Message: 2487 - Contents - Hide Contents

Date: Fri, 14 Dec 2001 18:32:04

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: clumma


> If the tuning has a point of reflective symmetry (not necessarily
> at a note) then there will be the same number of otonal as utonal.



Symmetry with respect to what?  If it doesn't have to be a note,
any continuous single-generator chain will have it.

-Carl
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Message: 2489 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 21:01:39

Subject: Re: (free) Proxomitron blocks Yahoo Ads

From: genewardsmith

--- In tuning-math@y..., J Gill <JGill99@i...> wrote:



> Using the DEFAULT settings of Proxomitron:
> 
> NO MORE YAHOO ADS in the messages!



I did that also, but I had to list yahoo.groups as a place where I did not want to see image files. It works, however, and it was easy.
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Message: 2490 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 21:49:43

Subject: Re: the 75 "best" 5-limit ETs below 2^17-tET

From: genewardsmith

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:


> --- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:


>> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:



> badness = steps^(3/2)*sqrt((err(3/2)^2 + err(5/3)^2 + err(5/4)^2)/3)
> 
> I tried both ignoring consistency and setting badness to infinity for
> inconsistent ETs; either way, the pattern (power spectrum of
> 1/badness) looked about the same.



Consistency matters only to the bad ets, so it isn't going to make a difference.
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Message: 2491 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 00:34:59

Subject: Vitale 19 (was: Re: Temperament calculations online)

From: clumma


>>>> > realized this ambiguity after I posted.  I meant,
>>>> any given linear temp. taken to any given number of
>>>> notes.
>>> 


>>> That doesn't quite do it. You meant:
>>> 
>>> .. that the number of o-tonal chords is the same as the number 
>>> of u-tonal chords in any linear temp. taken to any number of 
>>> notes.
>> 


>> You took out the "given"??
> 


> Put 'em back if you like, but there doesn't seem to be any
> ambiguity now without them, or am I missing something?



You said, "that doesn't quite do it"....

Anyway, without the givens, one could read... "all linear
temperaments have the same number of o- and u-tonal chords",
as Paul seems to have done.

-Carl
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Message: 2493 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 15:35:50

Subject: Re: A theory

From: paulerlich

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:


> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:
> 


>> Since 612 is the "tuning of schismas", any near-multiple of 612 will 
>> be more likely to have the schisma vanish, and thus to do 5-limit 
>> well, than non-near-multiple of 612. 
> 


> It's not likely to have the schisma vanish; quite the reverse. What


it *is* going to do is to represent the schisma as a certain number of
steps with great accuracy.

Oops -- that's what I meant!



> 


>> So . . . there must be some very significant 7-limit comma lurking at 
>> about 1/1664 octave. This is the Breedsma, which equals exactly one 
>> step of 1663.89978-tET.
> 


> You seem to be on to something, but why just the breedsma? This


still seems to require more explanation.

You bet!
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Message: 2494 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 15:37:11

Subject: Re: Badness with gentle rolloff

From: paulerlich

--- In tuning-math@y..., "clumma" <carl@l...> wrote:


>>> Sorry, Gene, but I'm not following where you're getting these
>>> exponents.  Is there a simple rule or reason I'm missing?
>>> 
>>> -Carl
>> 


>> It has to do with Diophantine approximation theory. Have you read 
>> Dave Benson's course notes?
> 


> I've looked at them.  What I could understand looked mundane,
> and what I couldn't looked like it required quite a bit more
> math than I know.  Is there a section of the Benson which is
> particularly helpful here?
> 
> -Carl



Well, he does mention the Diophantine approximation exponent for
N-term ratios.
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Message: 2495 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 15:42:07

Subject: Re: the 75 "best" 5-limit ETs below 2^17-tET

From: paulerlich

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:


> --- In tuning-math@y..., "paulerlich" <paul@s...> wrote:


>> Assuming a "critical exponent" of 3/2 for this case (is that right?)
> 


> Correct, but could you give the exact definition of badness you are
using?



badness = steps^(3/2)*sqrt((err(3/2)^2 + err(5/3)^2 + err(5/4)^2)/3)

I tried both ignoring consistency and setting badness to infinity for
inconsistent ETs; either way, the pattern (power spectrum of
1/badness) looked about the same.



>I also could not find the FFT data you said you posted.



I simply mentioned that the result looked about the same as the
7-limit case but with the peak at 612 . . . if you like I can post the
graph when I get back to the office . . .
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Message: 2496 - Contents - Hide Contents

Date: Sat, 15 Dec 2001 16:18:31

Subject: Re: Some commas and Paul's chart

From: paulerlich

The reason the schisma and the breedsma may be showing up as so
important is that they're far smaller than any simpler commas in their
respective limits. So most of the good ETs go along for a while
treating them as if they don't exist, but once they are treated as a
finite number of steps in the ETs, a whole new standard of 5- or
7-limit accuracy is attained.

Perhaps we should look more closely at the lower periods in the FFT,
all of which are kind of squished toward the left in the graph that I
posted . . . the first example of this kind of phenomenon in 5-limit
would be 15:16, about 1/11 octave, producing high points in the
5-limit ET graph wherever it's a near-integer number of steps: 1
(12-tET), 2 (19-tET, 22-tET), 3 (31-tET, 34-tET), 4 (41-tET, 43-tET),
5 (53-tET, 55-tET).

Clearly we're on the path to a full (or fuller) understanding of the
patterns that have been known for decades, if not centuries, in the
graph of ET quality, and have typically been regarded as random noise,
aside from instances where the sum of two good ETs is a good ET.
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Message: 2497 - Contents - Hide Contents

Date: Sun, 16 Dec 2001 13:30:28

Subject: inverse of matrix --> for what?

From: monz

As Paul stated recently in a Tuning List post, the
three unison-vectors 50:49, 64:63, and 245:243 define
22-EDO tuning.

Rewriting those as a (3^x)*(5^y)*(7^z) matrix, we get:

matrix   
| 0  2 -2 |
|-2  0 -1 |
|-5  1  2 |

Using Microsoft Excel's "minverse" function, as explained
in Graham's webpage:
Matrix tutorial * [with cont.]  (Wayb.)

decimal inverse   
| 0.045454545 -0.272727273 -0.090909091 |
| 0.409090909 -0.454545455  0.181818182 |
|-0.090909091 -0.454545455  0.181818182  |

Excel's "mdeterm" function gives 22 as the determinant of
the original matrix.  Multiplying the inverse of the matrix
by the determinant gives the inverse as fractional parts of 22:
  
fractional inverse   
| 1 -6 -2 | *  1
| 9 -10 4 |   --
|-2 -10 4 |   22


My questions: what does this inverse explain?
What purpose does it serve?

You all know that I prefer dealing with exact fractional numbers,
if they exist, rather than approximate floating-point decimals.
So why is this fractional inverse matrix useful?

Do these integers tell us something about 22-EDO?
Or about 22-EDO's representation of the prime-factors?

????



love / peace / harmony ...

-monz
Yahoo! GeoCities * [with cont.]  (Wayb.)
"All roads lead to n^0"


 



_________________________________________________________

Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.]  (Wayb.)
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Message: 2498 - Contents - Hide Contents

Date: Sun, 16 Dec 2001 13:31:34

Subject: Re: formula for meantone implications?

From: monz

Hi J,

Thanks for the explanation and corrections.


- monz



> From: unidala <JGill99@xxxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Sunday, December 16, 2001 7:28 AM
> Subject: [tuning-math] Re: formula for meantone implications?
>
>
> J Gill: If (to characterize what you are doing) there is a necessity 
> for the (independent variable) domain (in X) to result in *two* 
> values of the (dependent variables) ranges (in Y and in Z), then it 
> is not describable as a "function" (where there cannot be a "one to 
> two" correspondence between the independent variable (X) and either 
> of the independent variables (Y and Z).
>
> <etc. -- snip>




 



_________________________________________________________



Do You Yahoo!?

Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.]  (Wayb.)
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Message: 2499 - Contents - Hide Contents

Date: Sun, 16 Dec 2001 13:49:24

Subject: Re: formula for meantone implications?

From: monz


> From: monz <joemonz@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Sunday, December 16, 2001 1:31 PM
> Subject: Re: [tuning-math] Re: formula for meantone implications?
>
>
> Hi J,
> 
> Thanks for the explanation and corrections.
> 
> 
> - monz




It seems to work OK, but I'm still confused.  What I'm looking
for is a way to mathematically define the implied ratios, with
the requirement that when the meantone pitch is *exactly* midway
between two ratios, both ratios must be given as answers.



-monz


 



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Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.]  (Wayb.)
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