>>>> 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.
>
> since you're interested in 217, 494 and the like, be sure to use the
> mouse-over zoom feature.
Awesome!
Except I found I wanted a 333&1/3 zoom so I could see 217 and 494 (and
possibly 612) on the same plot. Some people are never satisfied. ;-)
I couldn't find any explanation of why some numbers are in various
hues of red, orange and magenta. Only some stuff about red lines not
drawn.
Message: 6429 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 22:32:21
Subject: poking monz (was: Re: naming temperaments(
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:
> unfortunately haven't yet invested the time in
> cleaning up the table
monz, the table you have there now was simply pasted in from a link i
gave you -- except that you fixed some of the scientifically notated
ratios so that they didn't look like unisons.
the table at the original url now includes the ratios in full decimal
representation, as well as important info like the generator of each.
so it would seem that you simply need to do the pasting again -- does
it take a lot of time? my impression was that it was an instantaneous
operation -- please correct me if i'm wrong.
sorry for poking,
paul
Message: 6430 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 17:23:30
Subject: Re: A common notation for JI and ETs
From: David C Keenan
At 07:05 AM 11/02/2003 +0000, George Secor wrote:
>>> ... unless there is something between 13.47 and 14.37
>cents
>>> that we need to have in the comma category.
>>
>> I believe there is. Namely the 7:125-comma and the 43-comma.
>>
>> N From C with cents Popularity Ocurrence
>> ranking
>> ------------------------------------------------
>> 7:125 Ebb-9.67 D+13.79 35 0.21%
>> 43 E#+9.99 F-13.473 58 0.10%
>> 143 Ebb-11.40 D+12.06 66 0.09%
>> 17:19 D+11.35 Ebb-12.11 72 0.08%
>>
>> The 143 (=11*13) and 17:19 cases above are not a problem because
>we'd be
>> forced to notate them all as ~)| anyway.
>>
>> The question really becomes: How far either side of the half
>Pythagorean
>> comma would a pair of "commas" have to be before we'd notate them
>using two
>> different symbols?
>>
>> In size order we have
>> ~)|
>> .~|(
>> '~)|
>> ~|(
>>
>> The 5:17-kleisma of 12.78 cents is notated exactly as .~|( and it
>needs to
>> be called a kleisma because there is also a 5:17-comma at 36.24
>cents
>> (unless we were going to pull the comma-carcinoma boundary down
>below
>> 36.24, which I don't recommend).
>>
>> I propose that if it's notated as ~)| or .~|( then it's a kleisma
>and if
>> its notated as ~|( or '~)| it's a comma.
>>
>> So in size order we have:
>> ~)| primarily the 17:19-kleisma 11.35 c
>> (but the 143-kleisma 12.06 c is more popular)
>> .~|( primarily the 5:17-kleisma 12.78 c
>> '~)| 43-comma 13.473 c
>> or possibly 7:125 comma 13.79 c
>> ~|( primarily the 17-comma 14.73 c
>>
>> The boundary then is most tightly defined between .~|( and '~)|. We
>already
>> have the 5:17-kleisma at 12.78 cents for .~|(. The most popular
>thing I can
>> find that _might_ be notated as '~)| is the 7:125-comma of 13.79
>cents. It
>> would otherwise be notated as ~|( so it would still be called a
>comma.
>> However the most popular that _needs_ to be notated as '~)| is the
>43-comma
>> of 13.473 cents.
>>
>> Similarly the comma-carcinoma boundary should be between
>> ~|) primarily the 5:17-comma 36.24 c
>> /|~ primarily the 5:23-carcinoma 38.05 c
>>
>> These are less than a 5-schisma apart and so there are no
>combinations with
>> the 5-schisma flag to confuse the issue. Halfway is at 37.14 cents.
>>
>> Many commas come in pairs that differ by a Pythagorean comma, so it
>would
>> be an advantage to have the distance from the kleisma-comma
>boundary to the
>> comma-carcinoma boundary being exactly a Pythagorean comma. That
>way we are
>> guaranteed never to find such a pair falling into the comma
>category.
>>
>> A Pythag comma up from 13.47 is 36.93 cents, which will do nicely.
>>
>> To summarise:
>> 0
>> schismina
>> 0.98
>> schisma
>> 4.50
>> kleisma
>> 13.47
>> comma
>> 36.93
>> carcinoma
>> 45.11
>> diesis
>> 56.84
>> ediasis
>> 68.57
>
>The way you have it, the kleisma-comma boundary is right at the 43
>comma.
Just below it.
> If we put the kleisma-comma boundary at ~13.125c, or halfway
>between the 5:17 kleisma (~12.777c) and the 43 comma (~13.473c), then
>a Pythagorean comma up from this would be ~36.585c. But if we put
>the comma-diesis boundary at ~37.144c, or halfway between the 5:17
>comma (~36.237c) and the 5:23 comma (~38.051c), then a Pythagorean
>comma down from this would be ~13.684c. Why not split the difference
>and make the boundaries ~13.404c and ~36.864c?
This would seem to make sense, but there's always a fly in the ointment.
You may have missed where I later wrote:
>> Here's another data point relevant to the comma-name boundaries
>> discussion.
>>
>> 49:125 E-13.469 Fb-36.929
>>
>> 36.929 c must be notated as ~|) which should make it a comma.
>> Therefore 13.469 c ought to be a kleisma, as it would be with a 13.47
>> c boundary.
What it amounts to is that it is impossible to have the boundaries based on
the change of symbols and at the same time satisfy the no-two-anomalies in
the same category (for a given ratio) requirement. Although we can make it
work for a fair way down the popularity list. Which is more important:
no-two-anomalies in the same category, or categories correspond to sets of
symbols?
-- Dave Keenan
Brisbane, Australia
Dave Keenan's Home Page * [with cont.] (Wayb.)
Message: 6431 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 22:33:58
Subject: Re: naming temperaments
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Graham Breed <graham@m...> wrote:
> Carl Lumma wrote:
>> 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?
when i wrote blocks in the sentence above, i meant *finite* scales.
Message: 6432 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 00:18:41
Subject: Re: naming temperaments
From: Carl Lumma
>{{As it stands, there's no good way to talk about the *blocks*
>behind popular temperaments.}}
>
>Why do you say blocks are behind temperaments?
What do you call meantone without the 81:80 tempered out? Paul
tried to deny the existence of such beasts, but this hardly
seems possible in light of adaptive JI.
-Carl
Message: 6433 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 22:39:34
Subject: Re: naming temperaments
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>>> 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
if you use strict JI but treat 81:80 as a unison, you're still in the
realm of the diatonic system as explained in my paper "the forms of
tonality" -- and very far from any kind of dicot system.
Message: 6434 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 00:32:21
Subject: Re: poking monz (was: Re: naming temperaments(
From: monz
hi Dave,
> From: <d.keenan@xx.xxx.xx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Monday, February 10, 2003 10:29 PM
> Subject: [tuning-math] poking monz (was: Re: naming temperaments(
>
>
re:
Definitions of tuning terms: equal temperament... * [with cont.] (Wayb.)
> I couldn't find any explanation of why some numbers
> are in various hues of red, orange and magenta. Only
> some stuff about red lines not drawn.
Message: 6435 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 15:10:42
Subject: Re: naming temperaments
From: Carl Lumma
>> >hat do you call meantone without the 81:80 tempered out?
>
>i would *not* call it "untempered dicot"!
Oh, neither would I. I switched the example.
>> Paul tried to deny the existence of such beasts,
>
>i did?
Well, you asked "dicot is a temperament, generated by neutral
thirds. in what sense does it make sense to speak of an untempered
temperament?
>> but this hardly seems possible in light of adaptive JI.
>
>please fill in the blanks for us, carl.
Do you not argue in the Forms of Tonality that PBs are fundamental
musical structures?
Is there a difference between music written for meantone and
music written for 5-limit JI? Does that difference go away
when the former is rendered in adaptive JI?
-Carl
Message: 6436 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 11:27:05
Subject: Re: naming temperaments
From: Graham Breed
Carl Lumma wrote:
> 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?
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. The problem with that is that it becomes multidimensional.
Planar temperaments combine with equal temperaments to give linear
temperaments, but planar temperaments combining with other planar
temperaments won't work in general.
>>> An alternative would be to name the important commas, and then
>>> name blocks and temperaments by concatenating the names of the
>>> commas involved, with prefixes to indicate vanishing.
>>
>> already there's the problem that the pythagorean comma doesn't vanish
>> in pythagorean tuning. but i like the idea . . . nevertheless, what
>> basis do you use? the TM basis for the 7-limit miracle kernel is
>> {225:224, 1029:1024}, yet the breedsma does vanish too, which this
>> wouldn't tell you by names alone . . .
>
> Good point. Maybe we need to name wedgies... does that solve the
> problem?
Wedgies or mappings will tell you if a given comma vanishes in a given
temperament. You can start with a list of known commas and keep all
those that vanish in each temperament -- no need to restrict yourself to
the TM basis. What do you want them for?
Graham
Message: 6437 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 23:23:28
Subject: Re: naming temperaments
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>>> What do you call meantone without the 81:80 tempered out?
>>
>> i would *not* call it "untempered dicot"!
>
> Oh, neither would I. I switched the example.
ok, so what are we talking about exactly?
>>> Paul tried to deny the existence of such beasts,
>>
>> i did?
>
> Well, you asked "dicot is a temperament, generated by neutral
> thirds. in what sense does it make sense to speak of an untempered
> temperament?
now we *are* talking about "untempered dicot" again? make up your
mind!
>>> but this hardly seems possible in light of adaptive JI.
>>
>> please fill in the blanks for us, carl.
>
> Do you not argue in the Forms of Tonality that PBs are fundamental
> musical structures?
yes . . . ?
> Is there a difference between music written for meantone and
> music written for 5-limit JI?
there can be . . . but most western music is simply written for 7
nominals, sharps, and flats . . .
> Does that difference go away
> when the former is rendered in adaptive JI?
it might not, depending on the music and how it's notated. the forms
of tonality argues that the diatonic model holds up quite well in all
these alternatives (i think i list 5).
Message: 6438 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 15:38:48
Subject: Re: naming temperaments
From: Carl Lumma
>ok, so what are we talking about exactly?
What terminology should be used when discussing
untempered PBs.
You said many different PBs might represent a
single untempered temperament.* Would they all
still share some essential feature?
* I assumed this happens like: given a bunch of
commas, one can swap factors around between them
and come up with a different bunch of commas,
that generate a different block, but the temperament
would map both blocks to the same pitches.
>>>> Paul tried to deny the existence of such beasts,
>>>
>>> i did?
>>
>> Well, you asked "dicot is a temperament, generated by neutral
>> thirds. in what sense does it make sense to speak of an untempered
>> temperament?"
>
>now we *are* talking about "untempered dicot" again? make up your
>mind!
It was the "in what sense..." part that I was referring to.
>> Is there a difference between music written for meantone and
>> music written for 5-limit JI?
>
>there can be . . .
Ok, that's an answer. Forget Western music. I've always
believed in an affirmative answer here, too, though I realize
I'm at a loss as to how I'd test for it. So I asked.
>> Does that difference go away
>> when the former is rendered in adaptive JI?
>
>it might not, depending on the music and how it's notated. the forms
>of tonality argues that the diatonic model holds up quite well in all
>these alternatives (i think i list 5).
Ok, so it does make sense to talk about an untempered temperament.
What's the appropriate way to talk about it?
-Carl
Message: 6440 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 23:45:22
Subject: Re: naming temperaments
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>> ok, so what are we talking about exactly?
>
> What terminology should be used when discussing
> untempered PBs.
well, there are fokker periodicity blocks, other things
like "semiblocks" that gene's defined . . . and of course you might
have commatic unison vectors even in the untempered case . . .
> You said many different PBs might represent a
> single untempered temperament.* Would they all
> still share some essential feature?
>
> * I assumed this happens like: given a bunch of
> commas, one can swap factors around between them
> and come up with a different bunch of commas,
> that generate a different block, but the temperament
> would map both blocks to the same pitches.
not if one or more the the "commas generating the block", or unison
vectors, is chromatic. then you might end up with a chromatically
altered block.
>>>>> Paul tried to deny the existence of such beasts,
>>>>
>>>> i did?
>>>
>>> Well, you asked "dicot is a temperament, generated by neutral
>>> thirds. in what sense does it make sense to speak of an untempered
>>> temperament?"
>>
>> now we *are* talking about "untempered dicot" again? make up your
>> mind!
>
> It was the "in what sense..." part that I was referring to.
ok, so in a sense, my paper discusses, as one
possibility, "untempered meantone". in which comma drift can occur.
how are we doing?
Message: 6441 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 00:04:23
Subject: Re: Janata paper
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>> 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.
no, i don't see why you're thinking that. where do neutral thirds
come in??
Message: 6442 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 15:52:19
Subject: Re: naming temperaments
From: Carl Lumma
>> >hat terminology should be used when discussing
>> untempered PBs.
>
>well, there are fokker periodicity blocks, other things
>like "semiblocks" that gene's defined . . . and of course you might
>have commatic unison vectors even in the untempered case . . .
//
>ok, so in a sense, my paper discusses, as one
>possibility, "untempered meantone". in which comma drift can occur.
>
>how are we doing?
Good! So how can one quickly refer to blocks that correspond
to temperaments? Do I have to say "the 7-tone PB which has
commatic uv x and chromatic uv y"? Does it make sense to say
"untempered [temperament-x]"? etc.
-Carl
Message: 6443 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 00:08:55
Subject: Re: a tuning-math question
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx "daniel_anthony_stearns
<daniel_anthony_stearns@y...>" <daniel_anthony_stearns@y...> wrote:
> Hi Paul,
>
> Unfortunately I really can't be back, but I have had enough free
time
> lately so that I can at least visit a bit.
>
> This problem seems so simple, but it is one that has vexed me for
> years. What I'm looking for is another way to approach the aspect
of
> scale generalization that has to do with how one orders scale
steps.
> So by "line segment" I really mean period,
circle?
> and what I'm trying to
> answer is something like this:
>
> If you have a line segment and you want to divide it into 9 pieces
of
> 3 different sizes where 5 are smallest, 3 are largest, and 1 is
> larger than the smallest and smaller than the largest, what are
some
> general methods for organizing the 9 pieces within the segment?
general methods? so you'd like a method that produces every possible
ordering? counts them? produces them more cleverly than brute force?
> Obviously what I'm looking for is a mathematical generalization
that
> agrees well enough with existing theory
existing combinatorics? i suspect it all exists already, and gene
knows it . . .
> so that it might be a useful
> blueprint when applied to scales that we know nothing about. Surely
> the math is very simple and it's simply a matter of finding a
method
> that works. So that's what I'm looking for some help with... and if
I
> get a flood of suggestions I'm sure I'll find it (and then I can
> sleep at night too).
in the past you've asked something similar, but it sure looks like
this is a distinct question. so i guess you just need to clarify it.
can you go further with the example? maybe a much simpler example, so
we can lay out all the possibilities, if need be?
sorry for being such a dunce,
paul
Message: 6444 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 23:54:20
Subject: Re: naming temperaments
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> Good! So how can one quickly refer to blocks that correspond
> to temperaments? Do I have to say "the 7-tone PB which has
> commatic uv x and chromatic uv y"?
it helps . . .
> Does it make sense to say
> "untempered [temperament-x]"? etc.
>
> -Carl
untempered meantone would not be enough to tell you how many notes
are in the block, just that you won't have any 81:80 pairs in it.
Message: 6445 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 00:29:57
Subject: Re: Janata paper
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>>> 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
dicot is a temperament, generated by neutral thirds. in what sense
does it make sense to speak of an untempered temperament?
no, janata's torus has 12 keys, i don't see why you need 7 except to
get the conventional letter-naming -- and *that* derives from the
chromatic unison vector being 25:24, 135:128, or etc.
Message: 6446 - Contents - Hide Contents
Date: Tue, 11 Feb 2003 22:17:08
Subject: Re: poking monz (was: Re: naming temperaments(
From: monz
hi paul,
> From: <wallyesterpaulrus@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Tuesday, February 11, 2003 2:32 PM
> Subject: [tuning-math] poking monz (was: Re: naming temperaments(
>
>
> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:
>
>> unfortunately haven't yet invested the time in
>> cleaning up the table
>
> monz, the table you have there now was simply pasted in from a link i
> gave you -- except that you fixed some of the scientifically notated
> ratios so that they didn't look like unisons.
>
> the table at the original url now includes the ratios in full decimal
> representation, as well as important info like the generator of each.
> so it would seem that you simply need to do the pasting again -- does
> it take a lot of time? my impression was that it was an instantaneous
> operation -- please correct me if i'm wrong.
>
> sorry for poking,
> paul
no need to apologize -- i try to stay on top of my webpages
to make sure they're correct and as up-to-date as i can make
them, and i know that you've sent me (several times) some
stuff that i still need to incorporate. i've just been real
busy lately ... sorry.
can you please post the link to the table again?
i'll try to get right on it.
-monz
Message: 6447 - Contents - Hide Contents
Date: Wed, 12 Feb 2003 10:18:56
Subject: New from Springer
From: Gene W Smith
The Springer 2003 ad arrived a few days back, and had the following two
new books in it:
(1) Mathematics and Music, edited by Assayag, Feichtinger and Rodrigues
(2) Foundations of Diatonic Theory *A Mathematically Based Approach to
Music Fundamentals*,
by T.A. Johnson, Ithaca College.
I'm having modem problems, so I can't respond yet to some things I read,
but Paul might like to know that my announcement of the Baton Rouge
meeting was a consequence of his email, which I did not mention because I
was not sure if it was to be kept private.
Message: 6448 - Contents - Hide Contents
Date: Wed, 12 Feb 2003 19:47:23
Subject: Re: a tuning-math question
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx "daniel_anthony_stearns
<daniel_anthony_stearns@y...>" <daniel_anthony_stearns@y...> wrote:
> Yes, the "line segment" that I'm using as an example could just as
> easily be a circle or a square or a space (or whatever) so long as
it
> can be reduced to a linear sequence in the end.
>
> The obvious method that comes to mind is something like ME, with
its
> tendency to adhere to palindromic symmetry.
ME is defined on a circle, and if you break the circle into a line,
you'll only get a palindrome occasionally -- usually you won't.
> The problem is that while
> a:
>
> *---*---*---1/1---*---*---*
>
> and its LsLLLsL agrees with existing theory well enough, a:
>
> (*)--*
> / \ / \
> *---*--1/1--*---*
> \ / \ /
> *--(*)
>
> and its LsMLMsL does not.
is this a 5-limit lattice? what are the notes in parentheses? what do
you mean by "agrees with existing theory"??
> It's certainly possible that no math model will ever fully satisfy
> the rather opposing demands of this sort of a generalization--one
> that's attempting to make an end-run around just intonation--
look, dan, if you can pin down for us just what your generalization
entails, i'm sure it can be "mathematized" -- but, as usual, i have
extreme difficulty comprehending your ideas. that won't stop me from
continuing to try with all my might!
Message: 6449 - Contents - Hide Contents
Date: Wed, 12 Feb 2003 19:54:38
Subject: thanks monz (was: Re: naming temperaments)
From: wallyesterpaulrus
--- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:
>
> hi paul,
>
>
>> From: <wallyesterpaulrus@y...>
>> To: <tuning-math@xxxxxxxxxxx.xxx>
>> Sent: Tuesday, February 11, 2003 2:32 PM
>> Subject: [tuning-math] poking monz (was: Re: naming temperaments(
>>
>>
>> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:
>>
>>> unfortunately haven't yet invested the time in
>>> cleaning up the table
>>
>> monz, the table you have there now was simply pasted in from a
link i
>> gave you -- except that you fixed some of the scientifically
notated
>> ratios so that they didn't look like unisons.
>>
>> the table at the original url now includes the ratios in full
decimal
>> representation, as well as important info like the generator of
each.
>> so it would seem that you simply need to do the pasting again --
does
>> it take a lot of time? my impression was that it was an
instantaneous
>> operation -- please correct me if i'm wrong.
>>
>> sorry for poking,
>> paul
>
>
>
> no need to apologize -- i try to stay on top of my webpages
> to make sure they're correct and as up-to-date as i can make
> them, and i know that you've sent me (several times) some
> stuff that i still need to incorporate. i've just been real
> busy lately ... sorry.
>
> can you please post the link to the table again?
> i'll try to get right on it.
>
>
> -monz
the table can be sorted any way you please, but i think most helpful
for the user would be alphabetically by temperament name, so that one
can see a green line on the graph and immediately find the relevant
info:
Yahoo groups: /tuning/database? * [with cont.]
method=reportRows&tbl=10&sortBy=6
my second choice would be sorting by the "odd limit" of the vanishing
comma's ratio:
Yahoo groups: /tuning/database? * [with cont.]
method=reportRows&tbl=10&sortBy=4
feel free to replace the 60+-digit numerators and denominators with
the scientific notation on your current table, if you wish.
thanks again and let me know when you have time again to revisit your
wonderful Dictionary, so that i may help improve it.
-paul
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