Tuning-Math Digests messages 6400 - 6424

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Message: 6400

Date: Mon, 10 Feb 2003 15:37:03

Subject: Re: naming temperaments

From: Carl Lumma

>naming wedgies is the same thing as naming temperaments, isn't it?

Yeah, probably.  Looks like there's no good shorthand for talking
about this stuff.  If there was, Dave would probably have already
found it!  :)

-Carl


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Message: 6401

Date: Mon, 10 Feb 2003 17:26:24

Subject: Re: A common notation for JI and ETs

From: David C Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx George Secor wrote:

>I have given a lot of thought to those who may come after me,
>particularly the novice.  I want the first step in learning the
>single-symbol version of the notation to be *conceptually* as simple as
>possible.  The notation for 24-ET (considered either alone or as a
>subset of 72-ET) or 31-ET is so simple that even a child would be able
>to understand and remember the symbols with minimal effort.  Unless I
>see some *compelling* reason that one to three shafts and X, along with
>an up or down arrowhead, is too difficult to *read* or *distinguish*,
>then I must reject any departure from this as an unnecessary
>*complication* that would make the notation more *difficult to learn*.
>I want someone's reaction to the first lesson in microtonal notation to
>be, "Hey, this is a lot easier than I expected!"  We should remember
>that first impressions are very important.  Therein lies the "sacred
>cow" that you're up against.
...
>A major
>advantage of the vertical lines (and even the X) is that they don't
>interfere with or otherwise detract from the perception or
>identification of the flags, because they look completely different.
>
>I hope I've adequately (and rationally) addressed the issues you
>raised.  If you still want to make some sort of symbol proposal based
>on what you sketched above -- some actual symbols in a graphic, then
>I'd be happy to look at them.  Otherwise, I can't imagine how something
>like that could be an improvement.

I guess you're saying "Put up or shut up". Fair enough.

You've made some good points about ease of learning and first impressions. 
But I don't understand why you would fail to imagine that there might be a 
way to retain those benefits while eliminating the two problems I have 
described regarding the X shafts.

I played around with various ideas by modifying a copy of your 
Symbols6.gif. The first thing I decided was to retain the triple shafts 
since I found I could not adequately distinguish wide and narrow V shafts. 
So I looked at just changing the X shafts, and in the end decided, surprise 
surprise, that X's are best!

What I've come up with is simply a different X. Its two shafts cross at a 
point that aligns with the note being modified, instead of the one below. 
Of course when it is used with two concave or wavy flags it does look like 
a V, but I think this is fine. Its shafts are slightly closer to vertical 
than those of the previous X's, so there is no danger of confusing them 
with straight flags, particularly since they (like all the shafts) are 
longer and thinner than straight flags.

I've also modified a few of the two and three shaft symbols with two flags 
to a side, to eliminate the cases where a shaft passed through the middle 
of a flag. Previously this was done in some cases but not in others. And 
I've added a conventional joined-double-flat symbol.

By the way, I like all the flag-combinations the way you've done them. In 
particular I prefer your ~)| to mine.

See
Yahoo groups: /tuning-math/files/Dave/Symbols6c.GIF *

-- Dave Keenan
Brisbane, Australia
Dave Keenan's Home Page *


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Message: 6402

Date: Mon, 10 Feb 2003 15:02:04

Subject: Re: Janata paper

From: Carl Lumma

>not at all. if a key is identified with its relative minor, that
>might mean that 81:80 is vanishing, but it sure doesn't mean 25:24
>is vanishing!

But to get the "keys", don't we need dicot?

-C.


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Message: 6403

Date: Mon, 10 Feb 2003 16:28:07

Subject: Re: Janata paper

From: Carl Lumma

>> But to get the "keys", don't we need dicot?
>> 
>> -C.
>
>no, i don't see why you're thinking that. where do neutral thirds 
>come in??

They're not actually neutral, because it's "untempered dicot", but
isn't it where from we get the 7-tone system, as you yourself said?
I thought we agreed we needed 7-in-12 to get Janata's torus.

-Carl


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Message: 6404

Date: Mon, 10 Feb 2003 16:11:19

Subject: Re: naming temperaments

From: Carl Lumma

{{Good point. Maybe we need to name wedgies... does that solve the
problem?}}

Naming wedgies is the same as naming temperaments, which is what we've
been doing.


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Message: 6405

Date: Mon, 10 Feb 2003 16:02:10

Subject: Re: naming temperaments

From: Gene W Smith

Carl Lumma <ekin@xxxxx.xxx> writes:

{{Rather than naming every linear temperament of interest (and
presumably, every planar one also), why not name blocks of
interest, and use a prefix to denote which comma(s) vanish?}}

It seems to me that which commas vanish pretty well tells you what you
need to know right there. I also don't see why blocks in general warrant
names, though some clearly do.

{{As it stands, there's no good way to talk about the *blocks*
behind popular temperaments.}}

Why do you say blocks are behind temperaments?


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Message: 6406

Date: Tue, 11 Feb 2003 08:34:09

Subject: Re: naming temperaments

From: Gene W Smith

Carl Lumma <ekin@xxxxx.xxx> writes:

>What do you call meantone without the 81:80 tempered out?
>tried to deny the existence of such beasts, but this hardly
>seems possible in light of adaptive JI.

Paul is right. Adaptive JI either removes the 81/80 or it doesn't; if it
doesn't, it isn't meantone.


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Message: 6407

Date: Tue, 11 Feb 2003 10:45:25

Subject: Re: naming temperaments

From: Carl Lumma

>> i've been dreaming of a huge website where scales are organized by 
>> blocks and one can click on which unison vectors to 
>> temper/detemper . . .
>> 
>> That would be truly awesome.  The culmination of years of work.
>
>Then the sooner we start, the sooner it'll be ready.
>
>What do you mean by "blocks"?  Planar temperaments?

Periodicity blocks.  No temperament.

>I can see how it would be nice to have a dynamic version of Monz's 
>diagram, where you could click on equal temeperaments or pairs of equal 
>temperaments to get linear temperaments.  But what you want seems to be 
>the other way round -- starting with commas rather than equal 
>temperaments.

Right.

Paul's database and zoom-graphs already go a long way...

-Carl


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Message: 6410

Date: Tue, 11 Feb 2003 01:46:37

Subject: Re: naming temperaments

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> All;
> 
> Rather than naming every linear temperament of interest (and
> presumably, every planar one also), why not name blocks of
> interest, and use a prefix to denote which comma(s) vanish?

But Carl,

I believe that musicians, as opposed to mathematicians, think of
strange temperaments more in terms of what the generator(s) and period
are, rather than what commas vanish.


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Message: 6411

Date: Tue, 11 Feb 2003 10:53:56

Subject: Re: naming temperaments

From: Carl Lumma

>>What do you call meantone without the 81:80 tempered out?
>>tried to deny the existence of such beasts, but this hardly
>>seems possible in light of adaptive JI.
>
>Paul is right. Adaptive JI either removes the 81/80 or it doesn't;
>if it doesn't, it isn't meantone.

It wouldn't be JI if it removed it.  But it's more than random
JI, it's JI treating the 81:80 as a unison.  What do you call
that?

-Carl


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Message: 6413

Date: Tue, 11 Feb 2003 11:06:41

Subject: Re: naming temperaments

From: Gene W Smith

Carl Lumma <ekin@xxxxx.xxx> writes:

>It wouldn't be JI if it removed it. But it's more than random
>JI, it's JI treating the 81:80 as a unison. What do you call
>that?

Comma drift.


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Message: 6416

Date: Tue, 11 Feb 2003 02:35:54

Subject: Re: S/K notational specificity

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:
> Question for anyone who can point me to an archive or offer a quick
answer: What is the smallest acceptable notational - intonational
error in the proposed Secor / Keenan notation system, and on what
grounds has this smallest margin of error been agreed upon?
> 

Hi Aaron,

Thanks for your interest. I expect you meant what is the _largest_
acceptable error, but were at the same time thinking what is the
smallest pitch change that can be notated, or how small is the largest
error. 

We have not allowed
any approximation greater than a cent, and many are less than half a
cent. And in fact there is no approximation at all until one goes
beyond 11-odd-limit in the single-symbol and double-symbol forms of
the notation, or beyond the 31-prime-limit in the multi-symbol form.

It is exact in all equal and linear temperaments. This is possible
because the symbols are not defined as referring to specific numbers
of cents but as giving the best approximation of various ratios
relative to a chain of fifths. The size of those fifths is a variable
that must be specified by the composer. If it's in an ET then it is
usually enough to say which ET.

These notational fifths are always between 3/5 and 4/7 octave but are
usually much closer to just. Non-octave scales can probably also be
accomodated by specifying a stretched or compressed "octave", the
limits of which have not been decided but will need to be close to 1:2.

On what grounds has the half-schisma/one-cent maximum error been
agreed on?

At first it was simply political. If there were to be no errors ever,
you would need an infinite number of symbols, or potentially infinite
strings of a finite number of symbols. So there had to be _some_
approximations. And while we personally could tolerate errors of two
to three cents, we wanted the notation to be acceptable to strict
just-intonationists, so we decided to try to match or better the
accuracy of the notation promoted by Johnny Reinhard of the AFMM,
which uses integers representing cents.

Much later we found we wanted to introduce symbols for the 5-schisma
anyway. As the smallest ratio to be notated, our maximum error becomes
half of this. But as I said, in most cases we can be exact, because we
are not constrained to notating relative to 12-ET or 24-ET.


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Message: 6417

Date: Tue, 11 Feb 2003 13:00:41

Subject: Ets for Ennealimmal and Hemiennealimmal

From: Gene W Smith

This is connected to the question of using nine-nominal notation for EJI.
My choice remains 612, which is a great utility et for notation anyway.

Here is the 3500 row of the Farey sequence, pruned by requiring that the
lcm of the denominator with 18 be less than 3500:

11/270 < ... < 2/49 < 133/3258 < 97/2376 < 61/1494 < 43/1053 < 37/906 <
68/1665 < 25/612 <
139/3402 < 19/465 < 89/2178 < 32/783 < 103/2520 < 71/1737 < 13/318 < ...
< 7/171

Here are the corresponding ets for Ennealimmal:

270 ... 441, 3258, 2376, 1494, 1053, 2718, 1665, 612, 3402, 1395, 2178,
783, 2520, 1737, 954 ... 171

And for Hemiennealimmal:

270 ... 882, 3258, 2376, 1494, 2106, 2718, 3330, 612, 3402, 2790, 2178,
1566, 2520, 3474, 954 ... 342

We have 68/1665, hardly distinguishable from 25/612, as poptimal in the
5-limit. In the 7-limit,
43/1053 and 61/1494, in the range between 441 and 612, are poptimal,
whereas in the 11-limit we go over to the other side, with 23/1566 (1566
= 2*783) a Hemiennealimmal poptimal generator. The 612 et is a good
all-around choice, and it has a nice list of divisors, including 12: [2,
3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612]. We
might compare this to 270: [2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54,
90, 135, 270] which has a 6 but no 12, or
342: [2, 3, 6, 9, 18, 19, 38, 57, 114, 171] for fans of 19, or 
882: [2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441]


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Message: 6418

Date: Tue, 11 Feb 2003 02:47:56

Subject: poking monz (was: Re: naming temperaments(

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" 
> <d.keenan@u...> wrote:
> 
> > I believe that musicians, as opposed to mathematicians, think of
> > strange temperaments more in terms of what the generator(s) and 
> period
> > are, rather than what commas vanish.
> 
> all the more reason monz should update the table of commas and 
> temperaments here:
> 
> Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *

This is an extraordinarily beautiful and informative graphic.

I assume you mean he should add generator and period to the table of
commas and temperaments. Absolutely!


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Message: 6419

Date: Tue, 11 Feb 2003 13:37:53

Subject: Baton Rouge AMS Southeastern Section Meeting

From: Gene W Smith

According to January's AMS Notices, this meeting, held March 14-16 at
Louisiana State University, will have a Special Session organized by
Judith Baxter of the University of Illinois at Chicago and Robert Peck of
Louisiana State called "Mathematical Techniques in Musical Analysis". I'm
sorry I didn't mention this before but I didn't look at the Baton Rouge
program until just now. It would be interesting to know if this is going
to be written up as proceedings.

Sorry, but the deadline for contributed papers has passed. :)


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Message: 6421

Date: Tue, 11 Feb 2003 21:55:08

Subject: Re: naming temperaments

From: Carl Lumma

>>It wouldn't be JI if it removed it. But it's more than random
>>JI, it's JI treating the 81:80 as a unison. What do you call
>>that?
>
>Comma drift.

???

What do you call _the scale_?

Did you read _The Forms of Tonality_?

-Carl


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Message: 6422

Date: Tue, 11 Feb 2003 02:55:41

Subject: Re: A common notation for JI and ETs

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>"
<gdsecor@y...> wrote:
> > See
> > Yahoo groups: /tuning-math/files/Dave/Symbols6c.GIF *
> 
> Okay, then, let's run with it!

Yikes! OK! :-)


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Message: 6424

Date: Tue, 11 Feb 2003 03:15:38

Subject: poking monz (was: Re: naming temperaments(

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" 
> <d.keenan@u...> wrote:
> > > Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *
> > 
> > This is an extraordinarily beautiful and informative graphic.
> 
> thanks -- i can't believe this is your first time seeing it.

I think I saw a very early version and hadn't looked at it since.


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