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Message: 10000

Date: Tue, 10 Feb 2004 07:51:47

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> >We're trying to come up with some reasonable way to decide on which
> >temperaments of each type to include in a paper on temperaments, given
> >that space is always limited. We want to include those few (maybe only
> >about 20 of each type)
> >Our starting point (but _only_ a starting point) is the knowledge
> >we've built up, over many years spent on the tuning list, regarding
> >what people find musically useful, with 5-limit ETs having had the
> >greatest coverage.
> 
> You're gravely mistaken about the pertinence of this 'data source'.
> Even worse than culling intervals from the Scala archive.

How do you know this?

> >So we add complexity and error cutoffs which
> >utterly violate log-flat badness in their region of application (so
> >why  violate log-flat badness elsewhere and make the transition to
> >non-violatedness as smooth as possible.

That was meant to be "(so why not violate log-flat badness elsewhere ..."

> Okay, now I have a definition of moat.  How do they compare to Gene's
> "acceptance regions"?

As I understand it, a moat is intended to surround an acceptance
region and quarantine it to some small degree from the kind of
objections I mentioned.


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Message: 10001

Date: Tue, 10 Feb 2004 16:56:32

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Carl Lumma

>> Could you do me a favor and attempt to speak to me as a human being, 
>> and not deal with me like a chess opponent, trying to look several 
>> moves ahead so that you can defeat me?
>
>I washed out of the first round of the US correspondence championship.
>It's my brother who is the grandmaster.

Is he really a grandmaster?

-Carl


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Message: 10002

Date: Tue, 10 Feb 2004 20:02:31

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> >We're trying to come up with some reasonable way to decide on which
> >temperaments of each type to include in a paper on temperaments, 
given
> >that space is always limited. We want to include those few (maybe 
only
> >about 20 of each type)
> 
> For musicians, I'd make the list 5 for each limit; 10 tops.

If that's the case, and if we're also going to use log-flat, then my 
name is probably off the paper. It'll offer far too little of use for 
ordinary musicians.

> >which we feel are most likely to actually be
> >found useful by musicians, and we want to be able to answer 
questions
> >of the kind: "since you included this and this, then why didn't you
> >included this". So Gene may have a point when he talks about 
cluster
> >analysis, I just don't find his applications of it so far to be
> >producing useful results.
> 
> I haven't seen any cluster analysis yet!

It was principal components analysis, but the reasoning behind the 
implementation was obscure.

> >Our starting point (but _only_ a starting point) is the knowledge
> >we've built up, over many years spent on the tuning list, regarding
> >what people find musically useful, with 5-limit ETs having had the
> >greatest coverage.
> 
> You're gravely mistaken about the pertinence of this 'data source'.
> Even worse than culling intervals from the Scala archive.

OK, Carl, so everyone's been sorely underestimating the true 
usefulness of 665-equal and 612-equal, yes?

> >It may be an objective mathematical fact that log-flat badness 
gives
> >uniform distribution, but you don't need a multiple-choice survey 
to
> >know it is a psychological fact that musicians aren't terribly
> >interested in availing themselves of the full resources of 4276-ET
> >()or whatever it was.
> 
> So far this can be addressed with a complexity bound.

Which contradicts the notion of 'badness'.

> >So we add complexity and error cutoffs which
> >utterly violate log-flat badness in their region of application (so
> >why  violate log-flat badness elsewhere and make the transition to
> >non-violatedness as smooth as possible.
> 
> ?

Dave's exactly right. If we're violating it suddenly at the cutoffs 
but nowhere else, we're clearly not conforming to any kind of 
psychological badness criterion.


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Message: 10003

Date: Tue, 10 Feb 2004 21:10:18

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 
> > It was principal components analysis, but the reasoning behind 
the 
> > implementation was obscure.
> 
> The reasoning was to draw an elliptical moat.

OK, I'd be happy to revisit that, then.

> > OK, Carl, so everyone's been sorely underestimating the true 
> > usefulness of 665-equal and 612-equal, yes?
> 
> Sounds like you are. Not everyone plays live music and has that as
> their focus, like you.

But are you using these to approximate JI or truly for their inherent 
properties?

> > Dave's exactly right. If we're violating it suddenly at the 
cutoffs 
> > but nowhere else, we're clearly not conforming to any kind of 
> > psychological badness criterion.
> 
> And if you are simply drawing squiggly lines on a graph, you are?

What squiggly lines? Your lines, with their two "corners", are a lot 
squigglier than ours.


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Message: 10004

Date: Tue, 10 Feb 2004 22:16:50

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 
> > Years ago, when you first made be aware of this fact, I was 
seduced 
> > by it, to Dave's dismay. Did you forget? Now, I'm thinking about 
it 
> > from a musician's point of view. Simply put, music based on 
> > constructs requiring large numbers of pitches doesn't seem to be 
able 
> > to cohere in the way almost all the world's music does. 
> 
> You've gotten all the way up to 22 notes to the octave.

False, and I don't appreciate the sarcastic tone of this either.


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Message: 10005

Date: Tue, 10 Feb 2004 01:16:32

Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears)

From: Carl Lumma

>>Related how? Via log-flat badness? Meanwhile, error and complexity 
>>are related?
>
>If C is the complexity and E is the error for a 7-limit linear 
>temperament which belongs to an infinite list of best examples,
>then E ~ k C^2.

Whoa dude, howdoyoufigure?

-Carl


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Message: 10006

Date: Tue, 10 Feb 2004 08:09:47

Subject: Re: loglog!

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> Yahoo groups: /tuning-math/files/Paul/et5loglog.gif *
> 
> Ok, easy!  No moat needed, at least for ETs.  Just draw a
> circle around the origin and grow the radius until it would
> include something that exceeds a single bound -- a "TOP
> notes per 1200 cents" bound.  For ETs at least.  Choose a
> bound according to sensibilities in the 5-limit, round it
> to the nearest ten, and use it for all limits.
> 
> -Carl

Something like that may be worth looking at, except for the fact that
the origin (as in the point 0,0) does not appear anywhere on a log log
graph, as Paul has been at pains to point out several times over the
past few days.

But I agree that one could use a circle to take the bite out of the
side that I talked about elsewhere. At least we agree on that general
shape! 

One can freely choose not only the radius, but also the center point.
And it would still be wise to try to fit it into a moat, for reasons
already given.

Whether the same circle can be generalised in such a simple way to
other limits remains to be seen, but seems unlikely.

And it still seems simpler to me to draw a straight line on a linear
plot than a circle on a log plot. And the linear axes themselves are
closer to representing "pain" than log ones.


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Message: 10007

Date: Tue, 10 Feb 2004 17:13:55

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Carl Lumma

>> >> >> ...still trying to understand why the rectangle doesn't enclose
>> >> >> a finite number of temperaments...
>> >> >
>> >> >Which rectangle?
>> >> 
>> >> The rectangle enclosed by error and complexity bounds.
>> >
>> >Yes, that would enclose a finite number of temperaments.
>> 
>> Then why the hell do we need a badness bound?
>
>To keep the utter crap at bay, and allow us not to try to publish a
>list of 1000000 "temperaments". Did you see the vast clouds of
>darkness on Paul's plots?

I'm looking at...

Yahoo groups: /tuning-math/files/Paul/et5loglog.gif *

...is a badness bound here shown by a line, say, through 12 and 171,
as on Dave's mock-up ASCI plot?  Oh, so you want to keep the likes
of 3 and 2513 off the list?  If so, a circle would do this, or an
error-comp. rectangle with a diagonal at about 45deg. to either
axis.

-Carl


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Message: 10009

Date: Tue, 10 Feb 2004 21:11:01

Subject: Re: !

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 
> > Did either of you guys look at the loglog version of the moat-of-
23 7-
> > limit linear temperaments?
> 
> I have a plot with unlabled axes and a curved red line on it.
> Obviously, since I don't know what is being plotted, I draw no 
>conclusion.

I've already clarified this for you!!


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Message: 10010

Date: Tue, 10 Feb 2004 22:20:03

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 
> > > > OK, Carl, so everyone's been sorely underestimating the true 
> > > > usefulness of 665-equal and 612-equal, yes?
> > > 
> > > Sounds like you are. Not everyone plays live music and has that 
as
> > > their focus, like you.
> > 
> > But are you using these to approximate JI or truly for their 
inherent 
> > properties?
> 
> I'm in the middle of working on an ennealimmal piece now. Inherent
> properties are a major aspect for this kind of thing.

You're using a full basis for the kernel? And it's audible? (Real 
questions, not rhetorical or riddles.)

> 612 is a fine
> way to tune ennealimmal, though I plan on using TOP for this one. 
This
> stuff really is practical if you care to practice it. 
> 
> In terms of commas, we have a sort of complexity of the harmonic
> relationships they imply--distance measured in terms of the
> symmetrical lattice norm possibly being more relevant here than
> Tenney.

How so? You really think a progression by perfect fifths is as 
complex as a progression by ratios of 7?

> Past a certain point the equivalencies aren't going to make
> any differences to you, and there is another sort of complexity 
bound
> to think about.

I thought this was the only kind. Can you elaborate?


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Message: 10011

Date: Tue, 10 Feb 2004 00:16:34

Subject: Re: loglog!

From: Carl Lumma

>One can freely choose not only the radius, but also the center point.
>And it would still be wise to try to fit it into a moat, for reasons
>already given.
>
>Whether the same circle can be generalised in such a simple way to
>other limits remains to be seen, but seems unlikely.

Why do you say that?

>And it still seems simpler to me to draw a straight line on a linear
>plot than a circle on a log plot. And the linear axes themselves are
>closer to representing "pain" than log ones.

Didn't Gen ask for a linear plot?

-Carl



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Message: 10014

Date: Tue, 10 Feb 2004 21:12:34

Subject: Re: The same page

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
> 
> > > Forgot 'em, but you seem to have them figured out. Modulo some 
> > slight 
> > > fiddling if you must fiddle,
> > 
> > I'd like to understand this slight fiddling, and apply this 
> > understanding to the 7-limit linear case (and elsewhere).
> 
> You can take the val and simply choose the first number in it, the
> number of steps in an octave. Or, you can normalize it by
> 1/log2(prime), and take the maximum. Or, you can TOP tune it,
> normalize that, and take the maximum.

Or you can take the sum. What I'm trying to get at is what these 
*mean*, beginning with the 3-limit cases in the "Attn: Gene 2" post.


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Message: 10015

Date: Tue, 10 Feb 2004 22:24:39

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:

> > > It's possible we could come to some kind of consensus
> > > if you would attempt to treat people with something better than 
the
> > > contempt you have shown lately.
> > 
> > I can take your attitude in no other way, unless you either 
ignored 
> > completely or have an abominably low level of respect for the 
> > discussions Dave and I posted on the topic.
> 
> Dave has been treating the rest of us with respect and discussing
> things. I'd like the same from you.

Then let's start over, and out with the sarcasm!

> > Let's start over. If I'm willing to tolerate a certain level of 
> > error, and a certain level of complexity, why wouldn't I be 
willing 
> > to tolerate both together?
> 
> From some points of view complexity doesn't even matter,

?

> so the whole
> premise we've all been operating under can be questioned by someone
> who is interested in the character of the commas in the kernel, not
> what complexity they give.

Please elaborate on this point of view -- I'm not seeing it.

> As for your question, are you arguing *for*
> straight line error and complexity bounds, because I don't see where
> else you can possibly go with it?

Could you do me a favor and attempt to speak to me as a human being, 
and not deal with me like a chess opponent, trying to look several 
moves ahead so that you can defeat me?

> Tolerating both together is exactly
> what Dave doesn't tolerate, and I thought you agreed with that.

I'll let Dave speak for himself, but I was hoping we would be 
starting over, rather than arguing about what was said before.


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Message: 10018

Date: Tue, 10 Feb 2004 20:05:57

Subject: Re: !

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> 
wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> > wrote:
> > > Why should we want to multiply instead of add?
> > 
> > Oh, for God's sake Paul-have you looked at your own plots? Did 
you 
> > notice how straight the thing looks in loglog coordinates? Your 
plots 
> > make it clear that loglog is the right approach. Look at them!
> 
> I don't much care how it's plotted, so long as we zoom in on the
> interesting bit. So, on these plots, what shape would you make a
> smooth curve that encloses only (or mostly) those ETs that musicians
> have actually found useful (or that you think are likely to be found
> useful) for approximating JI to the relevant limit? Having regard 
for
> the difficulty caused by complexity as well as error.

Did either of you guys look at the loglog version of the moat-of-23 7-
limit linear temperaments?

> I wonder if, when you say that there is no particular problem with
> complexity you are thinking of cases where you may use a subset of 
an
> ET, in the way that Joseph Pehrson is using a 21 note subset of 72-
ET.
> In that case you are really using a linear temperament, not the ET
> itself. I think the complexity of an ET should be considered as if 
you
> planned to use _all_ its notes.

I'd say that if you planned to use any set of commas that generate 
the ET's kernel (for chord-pump progressions, say), we're justified 
to consider that you're planning to use the ET itself.


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Message: 10019

Date: Tue, 10 Feb 2004 21:13:56

Subject: Re: 23 "pro-moated" 7-limit linear temps

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> > >Thus it's great for a paper for mathematicians. Not for musicians.
> > 
> > The *contents* of the list is what's great for musicians, not
> > how it was generated.
> 
> No; I agree with Graham that we should "teach a man to fish".

I disagree. It's just too hard for non-mathematicians. Unless by
"fish" you mean "go to Graham's web site and use the temperament
finder there" in which case I'm all for it! And this would let us not
worry too much that we may have left some temperament out of the paper
that someone someday may find useful.


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Message: 10022

Date: Tue, 10 Feb 2004 20:07:38

Subject: Re: loglog!

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> Yahoo groups: /tuning-math/files/Paul/et5loglog.gif *
> 
> Ok, easy!  No moat needed, at least for ETs.  Just draw a
> circle around the origin

Where's the origin, Carl? I don't see it.

> and grow the radius until it would
> include something that exceeds a single bound -- a "TOP
> notes per 1200 cents" bound.

I'm not following.

> For ETs at least.  Choose a
> bound according to sensibilities in the 5-limit, round it
> to the nearest ten, and use it for all limits.

The complexity measures cannot be compared across different 
dimensionalities, any more than lengths can be compared with areas 
can be compared with volumes.


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