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Message: 4000 - Contents - Hide Contents

Date: Mon, 04 Mar 2002 10:16:39

Subject: Re: maple for graph theory

From: genewardsmith

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> What doesn't work? I seem to be able to load the package...
I mean on the computers at SJSU--not installed right, or something.
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Message: 4001 - Contents - Hide Contents

Date: Tue, 5 Mar 2002 00:49:12

Subject: Re: help with ratio/vector algorithm

From: Robert Walker

Hi Monz,

It could be your (int)(expression + 0.5)

In this type of situation sometimes one needs
(int)(expression + 1e-12), or (int)(expression - 1e-12).
- replace 1e-12 by whatever precision you have.

It is usually 1e-14 for double precision arithmetic; one could add
a bit extra so say 1e-12 to have plenty of leeway.

That's because you are looking for the first integer above (or below)
rather than the nearest integer. The nearest integer will sometimes
be above, and sometimes be below. 

Alternatively, find p, do the calculation, and then at the end
after you have calculated p, in a separate step,
check to see if the ratio is below 1. If so, add 1,
or if it is above 2, subtract 1 at the end. 

Robert


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Message: 4002 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 21:05:26

Subject: Re: listing linear temperaments

From: paulerlich

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
>> I took a look at this problem, and it seems to me that starting from >> single ets and using generators from them ought to turn up everything >> of interest if we check everything which makes some sort of sense in >> non-consistent cases (which are the only hard ones.) Making that >> precise and putting it into effect would still make for a big search; >> I would like something like Paul's heuristic to speed that up. >
> What's the status of your heuristic, Paul?
the heuristics are only formulated for the one-unison-vector case (e.g., 5-limit linear temperaments), and no one has bothered to figure out the metric that makes it work exactly (though it seems like a tractable math problem). but they do seem to work within a factor of two for the current "step" and "cent" functions. "step" is approximately proportional to log(d), and "cent" is approximately proportional to (n-d)/(d*log(d)).
>>>> Finally, re the jumping jacks / ideal comma question... what's the >>>> question? How are we defining "most powerful" comma? >>
>> At this point, we aren't. Paul's discovery I suppose could be used >> to do that, if you want to define it in terms of Fourier analysis! >
> Well, I'd certainly like to hear more about this. Are you referring > to the periodicity in the badness curve? You want to run a Fourier > analysis on the wave and see the commas with the biggest peaks?
that seems a bit tangential at this point, since it's related to ets and not linear temperaments. but eventually, the whole business should be unified.
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Message: 4003 - Contents - Hide Contents

Date: Tue, 5 Mar 2002 18:02 +00

Subject: Re: error-free badness

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <200203050710.g257Ad819253@xxxxx.xxxxxx.xxx>
Carl Lumma wrote:

>> but you can always enforce GIGO. > > GIGO?
Garbage In, Garbage Out
>> If a temperament doesn't include a fairly good ET with fewer than >> 100 notes, you could consider that to be badness in itself. >
> Could you go over the your reasoning here?
It goes back to constant structures. It's useful to think about a linear temperament as being like an equal temperament, but with the scale steps unequal. Miracle's good for this, because you can think of it as approximating 31, 41 or 72-equal. With Blackjack, you have to be a lot more aware of the inequality of the intervals, and things like a 9:8 being smaller than a 10:9 or however it works out. So you think of it as a subset of 31-equal, or whatever. Temperaments that aren't mappings of consistent ETs are going to be like Blackjack forever -- no consistent ET you can get a handle on. You can't train musicians to think in terms of so many equal steps. It's harder to guess the relative sizes of two intervals if you can't count scale steps. If the first consistent ET has more than 100 notes, that's also harder to think of, but you can always raise the bar to fit your brain. And you can allow slightly inconsistent temperaments like 46 in, which is an option my program already has. Beyond all this, I'm thinking about how we can add melodic criteria to the search. For example, magic isn't so good in practice because you need 19 notes to get a sensible MOS. There's nothing close to proper in the 7+/-2 range. Miracle has the decimal scale almost in that range, so it works a lot better. The Pelog-type temperament has a 7 note MOS, and so is favoured despite having a relatively poor 5-limit approximation. These small scales will tend not to be consistent, but searching for any remotely sensible mapping with between 5 and 12 notes might be productive. Graham
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Message: 4004 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 21:12:49

Subject: Re: help with ratio/vector algorithm

From: paulerlich

--- In tuning-math@y..., graham@m... wrote:
> In-Reply-To: <004101c1c32d$603c6540$af48620c@d...> > monz wrote: >
>>> ratio r = 2^p * 3^q >>> >>> if q < 0 >>> then p = int((log(3^abs(q)) / log(2)) + 0.5) >>> else p = (int((log(3^abs(q)) / log(2)) + 1.5)) * -1 >>> end if >>> >>> but it's not foolproof: sometimes the exponent of 2 is >>> one less or one more than it should be. i've tried >>> setting up further nested if-statements, to check if >>> the absolute value of p is greater than that of q and >>> adjust accordingly, but there's always an error somewhere. >> >>
>> the errors are occurring because the spreadsheet has to >> check to see if n > d, and i can't figure out how to >> implement that without getting a circular reference. >
> I think =MOD(N20, 1)-N20 does it where N20 is the magnitude of the > original interval in octaves. So you have to substitute that with > log(3^abs(q)) / log(2). > > > Graham
in my periodicity block programs, i have a line that brings all ratios to the octave between 1/1 and 2/1: r=r./2.^(floor(log(r)/log(2)));
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Message: 4005 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 21:07:25

Subject: Re: listing linear temperaments

From: paulerlich

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> Paul wrote...
>> actually, gene already did this back in december. >
> I looked. My eyes! The searching did nothing! > > Paul wrote...
>> i'm making a graph that includes these as well as the ets. >> >> well, i tried to, but the points get too crowded near the >> center for me to label them. >
> F the graph. Let's have a list!
tuning-math messages 1985, 1997, 2009, 2064, 2121, and one more i can't find right now.
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Message: 4006 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 20:58:35

Subject: Re: listing linear temperaments

From: paulerlich

--- In tuning-math@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
>> I wasn't reading the tuning-math very closely back then, but Gene, >> your top 20 is generated by starting with some large number of >> ets
no, i don't think gene approached it this way. he didn't answer this part of your question, though, carl, so you should really get it from the horse's mouth.
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Message: 4007 - Contents - Hide Contents

Date: Tue, 5 Mar 2002 13:17:22

Subject: Re: monz spreadsheet

From: monz

hi Robert and Aaron,

> From: <pitchcolor@xxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, March 04, 2002 12:38 PM > Subject: [tuning-math] monz spreadsheet > > [me, monz] >
>> ratio r = 2^p * 3^q >> >> if q < 0 >> then p = int((log(3^abs(q)) / log(2)) + 0.5) >> else p = (int((log(3^abs(q)) / log(2)) + 1.5)) * -1 >> end if >>
thanks for the suggestions on that topic, but Graham has already given me the solution which works correctly: mod((log(3^abs(q))/log(2)),1) - (log(3^abs(q))/log(2)) -monz _________________________________________________________ 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: 4008 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 17:18:23

Subject: Re: error-free badness

From: Carl Lumma

Thanks for the gloss.  Processing.

>Beyond all this, I'm thinking about how we can add melodic criteria to >the search. For example, magic isn't so good in practice because you >need 19 notes to get a sensible MOS. There's nothing close to proper >in the 7+/-2 range. Miracle has the decimal scale almost in that range, >so it works a lot better. The Pelog-type temperament has a 7 note MOS, >and so is favoured despite having a relatively poor 5-limit >approximation. These small scales will tend not to be consistent, but >searching for any remotely sensible mapping with between 5 and 12 notes >might be productive.
I think this would be a mistake. It's a fine idea to say what the smallest MOS is that contains the map, as you do now, but our idea of what makes an LT good is far better-formed than our idea of what makes a melody good. For example, kleismic has an MOS at 10, or something, which is improper and not good melodically, but there's an 8-tone non-MOS chain which is not MOS and works melodically. -Carl
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Message: 4009 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 21:30:41

Subject: Re: listing linear temperaments

From: paulerlich

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
>
>> I think Gene's using the RMS. >
> Wow. z'that true, Gene?
gene's complexity measures involve "step" and "cent", and "step" is the RMS number of generators in the consonant intervals.
> > More details on Monzo's chart. But Monzo's chart is just a list > of LTs that we eyeballed from Paul's graph. But if what you say > is right about LTs sharing ETs and badness, the eyeballing might > not be so bad afterall. But still, we shouldn't bother with it > any more. We should create a badness-ranked list!
gene gave the top 5 -- search for 'top 5'.
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Message: 4010 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 23:16:34

Subject: a real powerful 11-limit comma

From: paulerlich

151250:151263

anyone seen this before?


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Message: 4011 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 20:53:03

Subject: Re: error-free badness

From: Carl Lumma

>but there's an 8-tone non-MOS chain which is not MOS and works >melodically.
"is proper" was supposed to be in there somewhere -Carl
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Message: 4012 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 20:56:35

Subject: Re: listing linear temperaments

From: Carl Lumma

>>> > think Gene's using the RMS. >>
>> Wow. z'that true, Gene? >
>gene's complexity measures involve "step" and "cent", and "step" is >the RMS number of generators in the consonant intervals.
Wait- is this complexity or badness? I wasn't talking about anything with cents there.
>> More details on Monzo's chart. But Monzo's chart is just a list >> of LTs that we eyeballed from Paul's graph. But if what you say >> is right about LTs sharing ETs and badness, the eyeballing might >> not be so bad afterall. But still, we shouldn't bother with it >> any more. We should create a badness-ranked list! >
>gene gave the top 5 -- search for 'top 5'.
Well, top 5 isn't enough. Also, Gene has given many lists of things, and it isn't clear to me what is supposed to be "the" list. Best I can tell, there isn't one. Which is what this thread is supposed to be about. -Carl
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Message: 4013 - Contents - Hide Contents

Date: Tue, 5 Mar 2002 16:43 +00

Subject: Re: some output from Graham's cgi

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <4.0.1.20020304214213.029dc818@xxxxx.xxx>
Carl Lumma wrote:

> Unison vector input > ------------------- > >> unison vectors >> 36:35 >> 50:49 >> calculated >> unison vectors >> 36:35 >> 50:49 >
> Why do you say "calculated" and then list them again?
Because they aren't always the same. The calculated ones should be the the simplified set. Sometimes they obviously aren't. I know this is a "simultaneous linear Diophantine equations" problem, but that still doesn't tell me how to solve it :-(
>> 0/1, 1886.3 cent generator >
> A bug? Do we always want the "generator" to be the smaller > generator, and the "period" the larger? Anyway, it would be > nice to see the period.
Yes, it's a known bug that I'll tackle one day. This is a valid generator, but not the simplest one. The same way that 3:1 and 8:3 are generators for meantone. The problem is that the generator's chosen before the temperament's optimized.
> Are these optimum generators? Yes. >> basis: >> (0.25, 1.57192809489) >
> Never heard of it.
Then you've learnt something!
>> mapping by period and generator: >> [(4, 0), (0, 1), (3, 1), (5, 1)] >
> I'm up to speed on this. >
>> mapping by steps: >> [(4, 0), (-1, 1), (2, 1), (4, 1)] >
> ? Carried out how far?
This entry looks a bit odd for temperaments generated from unison vectors. It's related to the problem above.
>> highest interval width: 1 > > ?
max()-min() of the second column
>> complexity measure: 4 (8 for smallest MOS) >
>From the map above isn't it 5?
No, it is 4.
>> highest error: 0.027608 (33.129 cents) >
> Why not give rms as well as or instead of this?
Yes, there are a lot of things I could give and this is one of them. I'll write an HTML formatting module sometime. Graham
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Message: 4014 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 22:45:17

Subject: Fwd: Re: listing linear temperaments

From: Carl Lumma

>Date: Tue, 05 Mar 2002 21:15:06 -0800 >To: "dkeenanuqnetau" <d.keenan@xx.xxx.xx> >From: Carl Lumma <carl@xxxxx.xxx> >Subject: Re: listing linear temperaments >
>>> //This is long. May I humbly suggest we do it up old-school, like >>> //in the Classic onelist years, and reply to everything until we >>> //agree on everything? Let's get something export-quality! Dave >>> //Keenan, activate your magic power ring, Voltron is needed once >>> //again! Monz, break out the colored chalks! Paul, I totally >>> //understand you wanting to take a break, and I've always been >>> //behind a book from you, but why not finish the paper on linear >>> //temperamenst first? >>
>> So who wrote this bit with the "//"s and what do you want me to do >> exactly? >
>I wrote it. Pretty cheasy, huh. I just wanted you to participate, >is all. You're the only person I can think of who's sharp enough >to have a chance at understanding the latest temperament stuff who's >still distant enough from it to provide crucial BS control. >
>>> Graham's catalog, "The grooviest 7-limit temperaments", Monzo's >>> lines, and Herman Miller's "Carl's favorite page on the internet" >>> Warped Canons page are huge, huge, huge. But wouldn't it be cool >>> to really get the goat? >>
>> I'm not familiar with this idiom. "Get the goat"? I probably haven't >> been watching enough US TV shows lately. Wait a minute ... I don't >> watch _any_ TV shows. :-) >
>I don't even have a TV. > >I got my idioms mixed, actually. "Gets my goat" is archaic for >"pisses me off". I meant, "get the goose", which is obscure but >means, "really does it properly". >
>> Maybe we don't need to agree on a badness measure. They don't have to >> be ranked in the paper. Just give the reader enough info to make up >> their own mind, or include a table with multiple badness measures. I >> think we can agree that any temperament that has actually been used in >> real life (even if it's only once or only maybe) should be listed. >> Then any temperament that any one of us thinks is at least as good as >> those should be listed. >
>I don't have much to say, since I'm not even after authorship, since I >don't have anything to contribute -- I just want to _read_ the paper. >Personally, I think a list would be best, but agree that explaining the >tools of temperament finding and classification is more important. >
>> If the list is still too small, or you definitely want a top 20, then >> let everyone list their top 15 and we take the union. If that's too >> many then let everyone list their top 14, or if too few, their top 16 >> and so on. Of course you can try to convince people to change their >> lists, but in the end everyone gets their top N. >
>This could work, but I think it looks weaker to say, "here's a list >that we had to vote on", rather than, "here's a list produced by this >formula, and it includes all the historical temperaments". > >From what I've seen, there's no reason the argument over which badness >is best couldn't bear the kind of fruit that the arguments over >dissonance-complexity (tenney) and error (rms) did back in the onelist >days. And even if there isn't a total consensus, just pick one and >mention in the paper that there are other possibilities. >
>> You know, a temperament that is good at 7:9:11s seems a lot more >> interesting to me than one that does 1:3:5:7:9:11:17:19 (and needs >> lots of gens to do it). So I'm dubious about the list-for-every-limit >> idea. But maybe it's just too hard to do otherwise. >
>It's a true point. Limits are just a starting point in line with >classical tuning theory. The paper should give interested people >the start they need on solving for subsets (and Grahams cgi could >also help here). > > >-- You seem to have addressed this just to me, which is fine by me. >Or, if you want this on the list, feel free to forward it there. > >-Carl
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Message: 4015 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 23:29:53

Subject: Re: some output from Graham's cgi

From: Carl Lumma

>>> >asis: >>> (0.25, 1.57192809489) >>
>> Never heard of it. >
>Then you've learnt something! Unfortunately not.
>>> highest interval width: 1 >> >> ? >
>max()-min() of the second column
the 2nd column?
>>> complexity measure: 4 (8 for smallest MOS) >>
>> From the map above isn't it 5? >
>No, it is 4.
Then you're defining complexity differently here than in your last message? -Carl
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Message: 4016 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 20:55:54

Subject: Re: listing linear temperaments

From: Carl Lumma

>>> >ctually, gene already did this back in december. >>
>> I looked. My eyes! The searching did nothing! >
>tuning-math messages 1985, 1997, 2009, 2064, 2121, and one more i >can't find right now.
Thanks, Paul. I've nabbed all these. -C.
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Message: 4017 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 22:43:48

Subject: Fwd: Re: listing linear temperaments

From: Carl Lumma

>X-eGroups-Return: d.keenan@xx.xxx.xx >Date: Wed, 06 Mar 2002 03:06:47 -0000 >From: "dkeenanuqnetau" <d.keenan@xx.xxx.xx> >To: Carl Lumma <carl@xxxxx.xxx> >Subject: Re: listing linear temperaments >User-Agent: eGroups-EW/0.82 >X-Mailer: Yahoo Groups Message Poster >X-Originating-IP: 203.101.241.248 > >--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
>> //This is long. May I humbly suggest we do it up old-school, like >> //in the Classic onelist years, and reply to everything until we >> //agree on everything? Let's get something export-quality! Dave >> //Keenan, activate your magic power ring, Voltron is needed once >> //again! Monz, break out the colored chalks! Paul, I totally >> //understand you wanting to take a break, and I've always been >> //behind a book from you, but why not finish the paper on linear >> //temperamenst first? >
>So who wrote this bit with the "//"s and what do you want me to do >exactly? >
>> A paper. I think it's a great idea. And, the 569 of us who don't >> have a computer set up to do calculations on linear temperaments >> need a list! >> >> Graham's catalog, "The grooviest 7-limit temperaments", Monzo's >lines,
>> and Herman Miller's "Carl's favorite page on the internet" Warped >> Canons page are huge, huge, huge. But wouldn't it be cool to really >> get the goat? >
>I'm not familiar with this idiom. "Get the goat"? I probably haven't >been watching enough US TV shows lately. Wait a minute ... I don't >watch _any_ TV shows. :-) > >Maybe we don't need to agree on a badness measure. They don't have to >be ranked in the paper. Just give the reader enough info to make up >their own mind, or include a table with multiple badness measures. I >think we can agree that any temperament that has actually been used in >real life (even if it's only once or only maybe) should be listed. >Then any temperament that any one of us thinks is at least as good as >those should be listed. > >If the list is still too small, or you definitely want a top 20, then >let everyone list their top 15 and we take the union. If that's too >many then let everyone list their top 14, or if too few, their top 16 >and so on. Of course you can try to convince people to change their >lists, but in the end everyone gets their top N. > >Those without programs (or with limited programs, like me) might be >provided (by those who do have programs, graham and gene) with much >larger lists of temperaments from which to choose, complete with prime >mapping, period, and some kind of optimum generator with errors for >all intervals. > >You know, a temperament that is good at 7:9:11s seems a lot more >interesting to me than one that does 1:3:5:7:9:11:17:19 (and needs >lots of gens to do it). So I'm dubious about the list-for-every-limit >idea. But maybe it's just too hard to do otherwise.
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Message: 4018 - Contents - Hide Contents

Date: Tue, 05 Mar 2002 22:46:10

Subject: Fwd: Re: listing linear temperaments

From: Carl Lumma

>X-Sender: zzdkeena@xx.xxx.xx >X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (32) >Date: Tue, 05 Mar 2002 22:13:09 -0800 >To: Carl Lumma <carl@xxxxx.xxx> >From: David C Keenan <d.keenan@xx.xxx.xx> >Subject: Re: listing linear temperaments > >At 21:15 5/03/02 -0800, you wrote:
>> -- You seem to have addressed this just to me, which is fine by me. > >Not intentionally. >
>> Or, if you want this on the list, feel free to forward it there. >
>Would you please send it. It will be too confusing if the >From: address is me. >-- Dave Keenan >Brisbane, Australia >Dave Keenan's Home Page * [with cont.] (Wayb.)
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Message: 4019 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 11:33 +00

Subject: Re: some output from Graham's cgi

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <200203060919.g269JMN15110@xxxxx.xxxxxx.xxx>
Carl Lumma wrote:

>>>> highest interval width: 1 >>> >>> ? >>
>> max()-min() of the second column >
> the 2nd column? >From this matrix
[(4, 0), (0, 1), (3, 1), (5, 1)] which should be oriented [(4, 0), (0, 1), (3, 1), (5, 1)] the second column is the mapping by generator, and that's what you use for the complexity.
>>>> complexity measure: 4 (8 for smallest MOS) >>>
>>> From the map above isn't it 5? >>
>> No, it is 4. >
> Then you're defining complexity differently here > than in your last message?
I may have forgotten you have to multiply by the number of periods to the equivalence interval. But without that you wouldn't get 5. You must be using the wrong column. Graham
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Message: 4020 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 11:33 +00

Subject: Re: error-free badness

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <a63p45+tjdn@xxxxxxx.xxx>
Me:
>> The Pelog-type temperament has a 7 note MOS, and so is >> favoured despite having a relatively poor 5-limit approximation. > These
>> small scales will tend not to be consistent, Paul: > ?
The smallest 11-limit consistent ET is 22. If we're going to choose temperaments from ET mappings around 7+/-2, they can't be consistent when we get beyond the 9-limit. Graham
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Message: 4021 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 21:48:01

Subject: Re: error-free badness

From: paulerlich

--- In tuning-math@y..., graham@m... wrote:
> In-Reply-To: <a63p45+tjdn@e...> > Me:
>>> The Pelog-type temperament has a 7 note MOS, and so is >>> favoured despite having a relatively poor 5-limit approximation. >> These
>>> small scales will tend not to be consistent, > > Paul: >> ? >
> The smallest 11-limit consistent ET is 22. If we're going to choose > temperaments from ET mappings around 7+/-2, they can't be consistent when > we get beyond the 9-limit.
this is a really strange way of thinking about this. i guess we're on totally different wavelengths. maybe i'm stuck thinking of temperaments in terms of commas -- it seems to be less 'slippery' way, anyhow.
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Message: 4022 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 11:33 +00

Subject: Re: listing linear temperaments

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <200203050710.g257Ae819262@xxxxx.xxxxxx.xxx>
Carl Lumma wrote:

> () document it
Is this the program, the method or the CGI? The first two need doing. I'd rather make the CGI easy enough to use that it doesn't need any other documentation.
> () allow input of identities, not just odd limit
I'm not sure what this means, but I don't think the CGI does it. You can do anything with the original script.
> () return the name of the temperament, if known
Yes, I suppose that should be done. It'll mean I need to keep a list of them somewhere. I wonder if it can be integrated with the catalog.
> () return all fields for each temperament (ie "not unique" or "unique")
You think that's important? It won't be difficult to change.
> My biggest complaint is too many worthy options. But it's better than > not enough! Really shows how spoiled I am.
The odd limit, worst complexity and worst error have to be there. Other things would ideally be guessed by the script, but I don't know how to guess them yet. The defaults should do fine most of the time.
>> What else do you want? >
> Slightly improved cgi stuff (see above) and/or a list.
There are already lists on the site, but I'm not planning to update them now the CGI's there.
> My ideal list would have: > > () Top 20 temperaments, by Gene's favorite badness measure, in each > odd limit from 5 to 17.
You can get close to Gene's badness measure with the CGI, and I am allowing 20 results now, provided the server doesn't kill the script.
> () Show a name, map, rms optimum generator, rms error, simplest commas, > and complexity for each.
Those are all reasonable, and you can expect them by the end of the year. Certainly before I publish anything on dead trees.
> () Make sure the names hold for a given LT if it makes it into the > top 20 of higher and higher limits.
Yes, I'll try and sort that out.
> () Uniqueness level.
Ooh! I can only do this up to 2nd order so far. Would that be okay?
> It would still be nice to report the top 20 to people who aren't going > to learn to use the script.
If people can understand the top 20 but not use the script, there must be something wrong with the script. I'd rather fix it than circumvent it. Still, you're welcome to generate your own lists and put them on your own site. How about if a particular calculation could be referenced by a URL? That might already work, but it could be simplified by allowing the script to substitute default values.
>> 2) Allow custom badness measures. Hopefully this can be done by
> entering >Python expressions in text boxes. I will need to check the > security on >this. The badness as a function of error (RMS or minimax) > and complexity >should be the most useful thing to customize. > > This is a good idea, but it would be the last thing I would spend time > implementing. IMO rms is always better than minimax, and complexity > should be kept separate from badness, and for badness I'll happy to > trust > Gene!
Well, it's implemented now. As there's an ongoing discussion about badness, at least people have something to do test runs with. There isn't a choice of minimax, because it's slower to calculate and isn't always correct anyway. It can't enforce uniqueness either, or know about the simplest MOS, so it doesn't duplicate my static lists.
>> I'm not sure about Gene, but that's how I do it. Raising the cutoff
> -- >not insisting on consistency -- does get you more temperaments, and > this >is an option on the CGI. You'll still miss some because they > aren't >represented by a pair of nearest-prime ETs. > > Nearest-prime? Anyway, all you have to do is show why a temperament > with low badness is bound to appear in multiple ets, as you claim > above, and I'll be happy.
All temperaments will contain multiple ETs, it's only a question of the algorithm being general enough to find them. They aren't always consistent. A lot of the high-ranking temperaments for 17 and higher limits don't include a consistent ET. I don't know if they really are good temperaments or not because I don't have experience of 17-limit, and I don't think anybody does in this way.
>>> What makes some linear temperaments belong to more than one et, out >>> of ets as high as some given number? They would have to share a >>> common generator... Is sharing a common generator related to the >>> un-even distribution of the rationals on the number line (such as >>> makes harmonic entropy work)? >>
>> I'd say ETs belong to linear temperaments rather than the other way >> round. >
> Okay, fine. But I don't see how this answers the question.
It comes from the scale tree. A linear temperament will be a particular branch. It's up to you where you cut it off. Graham
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Message: 4023 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 22:07:39

Subject: Re: some output from Graham's cgi

From: genewardsmith

--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:

> I think Monz and Paul have been calling it octatonic. > > I meant I don't know what basis is. Wasn't it also used in the > context of "MT reduced basis". Makes searching the archives difficult.
If you search for the wedgie you find a posting with the MT reduced basis of <36/35, 50/49>.
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Message: 4024 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 17:26 +00

Subject: Re: some output from Graham's cgi

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <OF57BC8B23.674511F0-ONC1256B74.005DDEBC@xxxxxx.xxxxxxxxx.xx>
Manuel wrote:

> Very nicely made Graham. Do you plan to add the > minimax generators too? Why don't you give a few > more digits for the generators in cents, since you > have plenty for the basis.
I can report the minimax, but I don't plan to sort by it because it'll slow the search down. The cents values are formatted to what's likely to be useful, whereas the basis is the standard stringification of the sequence.
> How about any of you sending me scale files of the > best results, then I add them to the archive and > people can try them? It's also not yet clear to > me what Pajara is, that could be included too.
I might get it to write the Scala files itself when I redo the formatting. Which ones do you think the best are? Pajara's the same as Paultone and Twintone. This should be 22 notes of the RMS optimum: 0.000 52.886 108.814 161.700 217.629 270.515 326.443 379.329 435.257 488.143 544.072 600.000 652.886 708.814 761.700 817.629 870.515 926.443 979.329 1035.257 1088.143 1144.072 1200.000 And the minimax: 0.000 56.178 109.363 165.542 218.726 274.905 328.089 384.268 437.452 493.631 546.815 600.000 656.178 709.363 765.542 818.726 874.905 928.089 984.268 1037.452 1093.631 1146.815 1200.000 Are there any plans to add this functionality to Scala? You should be able to generate the scales easily enough from knowing the period and generator. Graham
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