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Message: 4025 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 18:09:12

Subject: Re: some output from Graham's cgi

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

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.

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.

Manuel

Message: 4026 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 09:45:41

Subject: Re: gene's lists, monzo's lines

From: Carl Lumma

>> >ot on monz's chart.  What's "g"?
>

>An average number of generator steps to get to the consonances.


Aha!  The most important measure of all!  Is this the mean?

-Carl

Message: 4027 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 14:13:39

Subject: omigawd

From: Carl Lumma

There is sooo much stuff in the idea pool here... will we
drown?  I hope somebody is on top of it all.

Capstone temperaments... there is only one per limit, right?

5 = meantone
7 = ennealimmal
11 = ?
13 = ?

Gene, I have your top 20 for steps^3, but not steps^2 (you
once said you had a list of 505 here...).

-Carl

Message: 4028 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 00:52:37

Subject: Re: Some 58-et reduced bases

From: paulerlich

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

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

>> 13-limit: <126/125, 144/143, 176/175, 196/195, 354/363>
> 

> <126/125, 144/143, 176/175, 196/195, 364/363>


i tried the fokker pb of these and it has five exceedingly small 
steps -- 1375:1372s and 3025:3024s. so a reduction to 53 is implied 
(as in cassandra, etc.). is there a better basis for holding up 58 in 
this regard?

Message: 4029 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 10:01:58

Subject: Re: listing linear temperaments

From: Carl Lumma

>> >) 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.


It's the answers to the questions I've been asking.  So people can
use it without... having to ask the questions I'm asking.  That falls
under "the program", I guess.


>> () 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.


I just want to enter identities 7 9 11.  If I want 11-limit, make me
enter 1 3 5 7 9 11.


>> () 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.


It could.  One gripe I have with the catalog is that it gives different
names for the same temperament at different limits.  IIRC Cassandra
1 and 2 are two different extensions of schismic, one of which should
be schismic, and the other Cassandra x, if its complexity (or g) is low
enough to warrant a place in the catalog (which I don't think it is,
but I could see including it for historical reasons).


>> () return all fields for each temperament (ie "not unique" or "unique")
>

>You think that's important?  It won't be difficult to change.


It makes the output of the one that lists multiple temperaments easier
to parse.  Ideal would be uniqueness level.


>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.


Required fields should be marked with a star, or something.


>There are already lists on the site, but I'm not planning to update them 
>now the CGI's there.


That's fine by me.  One man can't do everything.


>> () 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.


What's Gene's measure called there?  Is it steps^3 or steps^2?

I was able to get 20 results.


>> () 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?


2nd order = triads, 1st order = dyads?  That would be splendid.
Up to hexads would be nice.  Don't let anybody tell you they need
more than that.


>> 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.


If you're looking at it that way, then good!  


>Still, you're welcome to generate your own lists and put them on your own 
>site.


I was referring to the paper.  No cgi support there yet. :)


>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.


Sounds like a good idea to me.


>> 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.

Cool.

>It can't enforce uniqueness either, or know about the simplest MOS, so
>it doesn't duplicate my static lists.

That's fine.

-Carl

Message: 4030 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 00:50:13

Subject: Re: error-free badness

From: paulerlich

--- In tuning-math@y..., graham@m... wrote:


> 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.


don't forget mohajira!


> 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 agree (i think).

Message: 4031 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 10:06:12

Subject: Re: some output from Graham's cgi

From: Carl Lumma

>>>>> >0.25, 1.57192809489)
>>>> 

>>>> Never heard of it.
>>> 

>>> Then you've learnt something!
>> 
>> Unfortunately not.
>

>This is the [4,4,4,-2,5,-3] system which came in #10 when I was using
>the funky badness measure with steps^3. It's a Paul favorite, since it
>is associated to the octatonic scale of jazz and Stravinsky. We could
>call it igor, I suppose. :)


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.

-Carl

Message: 4032 - Contents - Hide Contents

Date: Wed, 6 Mar 2002 00:17:07

Subject: Re: a real powerful 11-limit comma

From: monz

> From: paulerlich <paul@xxxxxxxxxxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Tuesday, March 05, 2002 3:16 PM
> Subject: [tuning-math] a real powerful 11-limit comma
>
>
> 151250:151263
> 
> anyone seen this before?




for those who might like to know the prime-factorization:

   prime-factors        exponents

[2  3  5  7  11] ** [ 1 -2  4 -5  2]



-monz


 



_________________________________________________________

Do You Yahoo!?

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

Message: 4033 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 07:33:42

Subject: Re: listing linear temperaments

From: genewardsmith

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


> 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.


I gave a top 20, which might do. How many do you want for "the" list?

Message: 4034 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 12:46:47

Subject: Re: listing linear temperaments

From: Carl Lumma

>> >ell, 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.
>

>I gave a top 20, which might do. How many do you want for "the" list?


I think around 20 is good... however many it is, and whatever badness
measure is used, we just have to be sure to get augmented, diminished,
schismic, and meantone.  That will impress the ivory tower types.

-Carl

Message: 4035 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 21:40:02

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.
> 

> Wait- is this complexity or badness? 

badness. sorry.

Message: 4036 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 21:50:53

Subject: Re: gene's lists, monzo's lines

From: paulerlich

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

>>> Not on monz's chart.  What's "g"?
>> 

>> An average number of generator steps to get to the consonances.
> 

> Aha!  The most important measure of all!  Is this the mean?


gene was using rms, i believe.

Message: 4037 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 22:00:21

Subject: Re: listing linear temperaments

From: genewardsmith

--- In tuning-math@y..., graham@m... wrote:


> 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.  


An algorithm which will find some of them, consistent or not, is to wedge with commas until you get an et.

Message: 4038 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 08:53:09

Subject: Re: a real powerful 11-limit comma

From: genewardsmith

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

> 151250:151263
> 
> anyone seen this before?


No, but I would have if I had wedged miracle with hemiennealimmal,
since
one take on it is that it is miracle^hemiennealimmal. Besides that, it
seems to be associated with a whole boatload of high quality
microtemperaments which have 1/6 octave as a period, and I wonder why
that is? 

If you like 7/5, 11/7, and 10/9 a whole lot, there's the one with map

[[0,17,35,36,37],[6,-6,-18,-16,-13]]

which I think is downright cute.

Message: 4039 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 22:32:26

Subject: Re: listing linear temperaments

From: genewardsmith

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


> I think around 20 is good... however many it is, and whatever badness
> measure is used, we just have to be sure to get augmented, diminished,
> schismic, and meantone.  That will impress the ivory tower types.


Do you mean by augmented and diminished 5-limit temperaments? 
I get a badness of 142 for 128/125 and of 385 for 648/625. They both made my list of 32 (not 20) best, and are discussed on

Yahoo groups: /tuning-math/message/1997 * [with cont.] 

Paul followed up and suggested "octo-diminished" for the 648/625 system, but "diminished" should be fine. The "octo" part
came, I think, since I pointed out how well 64-et could do this
system.

Message: 4040 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 01:13:08

Subject: gene's lists, monzo's lines

From: Carl Lumma

5-limit


>135/128
>
>Map:
>
>[ 0 1]
>[-1 2]
>[ 3 1]
>
>Generators: a = 10.0215/23; b = 1
>
>badness: 46.1
>rms: 18.1
>g: 2.94
>errors: [-24.8, -17.7, 7.1]


Not on monz's chart.  What's "g"?


>648/625
>
>Map:
>
>[ 0 4]
>[ 1 5]
>[ 1 8]
>
>Generators: a = 21.0205/64; b = 1/4
>
>badness: 385
>rms: 11.06
>g: 3.266
>errors: [-7.82, 7.82, 15.64]
>
>64-et, anyone? It could also be used to temper the 12-et.

diminished.

>250/243
>
>Map:
>
>[ 0 1]
>[-3 2]
>[-5 3]
>
>Generators: a = 2.9883/22; b = 1
>
>badness: 360
>rms: 7.98
>g: 3.559
>errors: [9.06, -1.29, -10.35]
>
>One way to cure those 22-et major thirds of what ails them.

porcupine.

>128/125
>
>Map: 
>
>[ 0 3]
>[-1 6]
>[ 0 7]
>
>Generators: a = 11.052/27 (~4/3); b = 1/3
>
>badness: 142
>rms: 9.68
>g: 2.449
>errors: [6.84, 13.69, 6.84]

augmented

>3125/3072
>
>Map:
>
>[ 0 1]
>[ 5 0]
>[ 1 2]
>
>Generators: a = 12.9822/41 (=6.016/19); b = 1
>
>badness: 239
>rms: 4.57
>g: 3.74
>errors: [-2.115, -6.346, -4.231]
>
>Graham has named this one: Magic.

>81/80
>
>Map:
>
>[ 0 1]
>[-1 2]
>[-4 4]
>
>Generators: a = 20.9931/50; b = 1
>
>badness: 108
>rms: 4.22
>g: 2.944
>errors: [-5.79, -1.65, 4.14]
>
>Nothing left to say about this one. :)

>2048/2025
>
>Map:
>
>[ 0 2]
>[-1 4]
>[ 2 3]
>
>Generators: 14.0123/34 (~4/3); b = 1/2
>
>badness: 211
>rms: 2.613
>g: 4.32
>errors: [3.49, 2.79, -.70]
>
>A good way to take advantage of the 34-ets excellent 5-limit
>harmonies is two gothish 17-et chains of fifths a sqrt(2)
>apart.

diaschismic

>78732/78125 = 2^2 3^9 5^-7
>
>Map:
>
>[ 0 1]
>[ 7 -1]
>[ 9 -1]
>
>Generators: 23.9947/65 (~9/7); b = 1
>
>badness: 346
>rms: 1.157
>g: 6.68
>errors: [-1.1, 0.5, 1.6]


un-named on monz's chart!


>393216/390625 = 2^17 3 5^-8
>
>Map:
>
>[ 0 1]
>[ 8 -1]
>[ 1 2]
>
>Generators: a = 31.9951/99 (~5/4); b = 1
>Works with 31,34,65,99,164
>
>badness: 251
>rms: 1.072
>g: 6.16
>error: [.602, 1.506, .904]

wuerschmidt

>2109375/2097152 = 2^-21 3^3 5^7 Orwell
>
>Map:
>
>[ 0 1]
>[ 7 0]
>[-3 3]
>
>Generators: a = 19.01127197/84; b = 1
>
>badness: 305.93
>rms: .8004
>g: 7.257
>errors: [-.828, -1.082, -.255]
>
>ets: 22,31,53,84

>15625/15552 = 2^-6 36-5 5^6 Kleismic
>
>Map:
>
>[ 0 1]
>[ 6 0]
>[ 5 1]
>
>Generators: a = 14.00435233/53 (~6/5); b = 1
>
>badness: 97
>rms: 1.030
>g: 4.546
>errors: [.523, -.915, -1.438]
>
>ets: 19,34,53,68,72,87,140

>1600000/1594323 = 2^9 3^-13 5^-2 Acute Minor Third system
>
>Map:
>
>[ 0 1]
>[-5 3]
>[-13 6]
>
>Generators: a = 28.00947813/99 (~243/200); b = 1
>
>badness: 305.53
>rms: .3831
>g: 9.273
>error: [-.5009, .0716, -.4293]


not on monz's chart.


>6115295232/6103515625 = 2^23 3^6 5^-15 Semisuper
>
>Map:
>
>[ 0 2]
>[ 7 -3]
>[ 3 2]
>
>Generators: a = 52.00397043/118 (~3125/2304); b = 1/2
/.../
>badness: 190
>rms: .1940
>g: 9.933
>errors: [.0226, .2081, .2255]


not on monz's chart.


>32805/32768 Shismic
>
>Map:
>
>[ 0 1]
>[-1 2]
>[ 8 1]
>
>Generators: a = 120.000624/289 (~4/3); b = 1
>
>badness: 55
>rms: .1617
>g: 6.976
>errors: [-.2275, -.1338, .0937]

7-limit

//augmented

>When extended to the 7-limit, this becomes the 
>
>[ 0 3]
>[-1 6]
>[ 0 7]
>[ 2 6]
>
>system I've already mentioned in several contexts, such as
>the 15+12 system of the 27-et. Both as a 5-limit and a
>7-limit system, it is good enough to deserve a name of its
>own.


Jeez- I just realized that the wholetone scale contains
4:5:7 chords.  Here's the 4:5:6:7 in augmented in 27-et:

27 1200
0 0
9 400
16 711
22 978

This nonatonic looks interesting: 0 2 4 9 11 13 18 20 22 (27)


>(1) [6,10,10,-5,1,2] ets: 22
>
>[0 2]
>[3 1]
>[5 1]
>[5 2]
>
>a = 7.98567775 / 22 (~9/7) ; b = 1/2
>measure 3165


What is this?  What's "measure"?


>(4) [10,14,14,-7,6,-1] ets: 26
>
>[0 2]
>[5 2]
>[7 3]
>[7 4]
>
>a = 3.026421762 / 26; b = 1/2
>measure 8510


This and the above look suspiciously like
the decatonic and double-diatonic systems.
But they're not, are they?

-Carl

Message: 4041 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 22:43:07

Subject: Re: listing linear temperaments

From: paulerlich

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


> Paul followed up and suggested "octo-diminished" for the 648/625 
>system,


only when it occurs in 64-equal.


>but "diminished" should be fine.


i hope monz will catch on. also, on his et page, it seems he forgot 
that "<" meant "less than" and he appended ">" to each entry that 
referred to a mention *before* a certain date. but i should wait for 
him to catch up on all the other stuff first . . .


>The "octo" part came, I think, >since I pointed out how well 64-et 
>could do this system.


right -- i think i was making a rough analogy to the hepta-diminished 
system of 28-equal. i guess 32-equal is actually octo-diminished . . .

Message: 4042 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 09:34:59

Subject: Re: gene's lists, monzo's lines

From: genewardsmith

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


> Not on monz's chart.  What's "g"?


An average number of generator steps to get to the consonances.




>> (1) [6,10,10,-5,1,2] ets: 22
>> 
>> [0 2]
>> [3 1]
>> [5 1]
>> [5 2]
>> 
>> a = 7.98567775 / 22 (~9/7) ; b = 1/2
>> measure 3165
> 

> What is this?  What's "measure"?


This
I think is the steps^3 thing some people wanted in order to weight
thelow-rent temperaments more strongly. I like log-flat measures
myself, I'veconcluded.


>> (4) [10,14,14,-7,6,-1] ets: 26
>> 
>> [0 2]
>> [5 2]
>> [7 3]
>> [7 4]
>> 
>> a = 3.026421762 / 26; b = 1/2
>> measure 8510
> 

> This and the above look suspiciously like
> the decatonic and double-diatonic systems.
> But they're not, are they?


One is the 9/7 generator thing of 22-et, and the other doesn't look
diatonic to me. Aside from 26-et, it could be tried on h34+v7.

Message: 4043 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 09:53:44

Subject: Re: some output from Graham's cgi

From: genewardsmith

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

>>>> basis:
>>>> (0.25, 1.57192809489)
>>> 

>>> Never heard of it.
>> 

>> Then you've learnt something!
> 
> Unfortunately not.


This
is the [4,4,4,-2,5,-3] system which came in #10 when I was using the
funky badness measure with steps^3. It's a Paul favorite, since it is
associated to the octatonic scale of jazz and Stravinsky. We could
call it igor, I suppose. :)

Message: 4044 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 16:36:55

Subject: errgggh...

From: Carl Lumma

Well, wonderful.  The continuity of messages I forwarded here
between Dave and I was annihilated.

-Carl

Message: 4045 - Contents - Hide Contents

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

Subject: Re: error-free badness

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <200203060123.g261NaN04450@xxxxx.xxxxxx.xxx>
Carl Lumma wrote:


> 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.


If an LT's being used for melody, our idea of what makes it good can't be 
so well formed after all.  Isn't it something we should be thinking about?


               Graham

Message: 4046 - Contents - Hide Contents

Date: Wed, 06 Mar 2002 19:30:59

Subject: Re: error-free badness

From: Carl Lumma

>> > 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.
>

>If an LT's being used for melody, our idea of what makes it good can't
>be so well formed after all.  Isn't it something we should be thinking
>about?


Paul likes tetrachordality, I like propriety, and there are reasons to
talk about MOS.  Let's show these properties, but not rank by them:

() There's a singular mathematical beauty about complexity vs. good
approximations that we want to expose, and which is completely
independent of anything melodic.

() Some of the melodic properties mentioned above are not invariants
of a map.  Propriety can change depending on the number of tones, and
as Dave has pointed out, it can change wildly with changes to the
generator size.

-Carl

Message: 4047 - Contents - Hide Contents

Date: Thu, 07 Mar 2002 05:21:40

Subject: 32 best 5-limit linear temperaments redux

From: genewardsmith

27/25 limmal

map   [[0, -2, -3], [1, 2, 3]]

generators   268.0564391   1200

badness   358.9821660   rms   35.60923982   g   2.160246899

ets
4
5
9
14


16/15 fourth-thirds

map   [[0, -1, 1], [1, 2, 2]]

generators   442.1793558   1200

badness   129.0161774   rms   45.61410700   g   1.414213562

ets
1
2
3
5
6
8


135/128 pelogic

map   [[0, -1, 3], [1, 2, 1]]

generators   522.8623453   1200

badness   461.2348421   rms   18.07773298   g   2.943920288

ets
2
7
9
11
16
23


25/24 neutral thirds

map   [[0, 2, 1], [1, 1, 2]]

generators   350.9775007   1200

badness   81.60548797   rms   28.85189698   g   1.414213562

ets
3
4
6
7
10
13
17
20


648/625 diminished

map   [[0, -1, -1], [4, 8, 11]]

generators   505.8656425   300

badness   385.3013916   rms   11.06006024   g   3.265986323

ets
4
8
12
16
24
28
36
40
52
64


250/243 porcupine

map   [[0, -3, -5], [1, 2, 3]]

generators   162.9960265   1200

badness   359.5570529   rms   7.975800816   g   3.559026083

ets
7
8
15
22
29
30
37
44
51
59
66


128/125 augmented

map   [[0, -1, 0], [3, 6, 7]]

generators   491.2018553   400

badness   142.2320613   rms   9.677665980   g   2.449489743

ets
3
6
9
12
15
18
21
24
27
30
33
36
39
42


3125/3072 small diesic

map   [[0, 5, 1], [1, 0, 2]]

generators   379.9679494   1200

badness   239.3635979   rms   4.569472316   g   3.741657387

ets
3
6
16
19
22
25
35
38
41
44
57
60
63
66
76
79
82
85
104
107


81/80 meantone

map   [[0, -1, -4], [1, 2, 4]]

generators   503.8351546   1200

badness   107.6110644   rms   4.217730124   g   2.943920288

ets
5
7
12
19
24
26
31
36
38
43
45
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55
57
62
67
69
74
76
81
86
88
93
98
100
105
117
129


2048/2025 diaschismic

map   [[0, -1, 2], [2, 4, 3]]

generators   494.5534684   600

badness   210.7220901   rms   2.612822498   g   4.320493799

ets
2
10
12
14
20
22
24
32
34
36
44
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54
56
58
66
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92
102
112
114
124
126
136
148
160


78732/78125 tiny diesic

map   [[0, 7, 9], [1, -1, -1]]

generators   442.9792974   1200

badness   345.5378445   rms   1.157498146   g   6.683312553

ets
8
19
27
38
46
57
65
73
76
84
92
103
111
122
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149
157
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306
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363
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390
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539
558
623


393216/390625 wuerschmidt

map   [[0, 8, 1], [1, -1, 2]]

generators   387.8196732   1200

badness   251.1018953   rms   1.071950166   g   6.164414003

ets
3
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28
31
34
37
62
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68
71
93
96
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127
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133
136
158
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365
387
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2109375/2097152 orwell

map   [[0, 7, -3], [1, 0, 3]]

generators   271.5895996   1200

badness   305.9258786   rms   .8004099292   g   7.257180353

ets
9
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181
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203
212
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234
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265
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305
309
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327
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349
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402
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433
455
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486
517
570


15625/15552 kleismic

map   [[0, 6, 5], [1, 0, 1]]

generators   317.0796754   1200

badness   96.73525308   rms   1.029625097   g   4.546060566

ets
4
15
19
23
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38
49
53
57
68
72
76
83
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102
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367
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386
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405
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507
526
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560
579
613
632
666
719


1600000/1594323 amt

map   [[0, -5, -13], [1, 3, 6]]

generators   339.5088258   1200

badness   305.5372197   rms   .3831037874   g   9.273618495

ets
7
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113
145
152
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244
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304
311
318
350
357
364
371
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502
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516
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569
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622
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781
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827
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919
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972
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986


1224440064/1220703125 parakleismic

map   [[0, -13, -14], [1, 5, 6]]

generators   315.2509133   1200

badness   372.7314879   rms   .2766026501   g   11.04536102

ets
19
38
42
57
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76
80
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118
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156
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217
236
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434
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571
590
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628
647
651
670
689
708
727
746
765
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807
826
845
864
887
906
925
944
963
982


6115295232/6103515625 semisuper

map   [[0, 7, 3], [2, -3, 2]]

generators   528.8539366   600

badness   190.1507467   rms   .1940181460   g   9.933109620

ets
16
18
34
50
68
84
100
102
118
134
136
152
168
186
202
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236
252
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286
304
320
338
354
370
372
388
404
422
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472
488
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506
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590
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658
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692
708
726
742
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810
826
844
860
876
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894
910
928
944
962
978
994
996


19073486328125/19042491875328 enneadecal

map   [[0, -1, -1], [19, 38, 52]]

generators   497.9709056   1200/19

badness   391.2170134   rms   .1047837215   g   15.51343504

ets
19
38
57
76
95
114
133
152
171
190
209
228
266
285
304
323
342
361
380
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418
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494
513
532
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570
589
608
627
646
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703
722
760
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817
836
855
874
893
931
950
969
988


32805/32768 shismic

map   [[0, -1, 8], [1, 2, -1]]

generators   498.2724869   1200

badness   54.89487859   rms   .1616904714   g   6.976149846

ets
12
17
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29
36
41
53
65
77
82
89
94
101
106
118
130
135
142
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566
578
590
602
607
614
619
626
631
643
655
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667
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679
684
696
708
720
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732
737
744
749
761
773
778
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797
802
814
826
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850
855
862
867
879
891
896
903
908
915
920
932
944
956
961
968
973
985
997


582076609134674072265625/581595589965365114830848  heptadecal

map   [[0, 2, 1], [17, 16, 34]]

generators   386.2716180   1200/17

badness   477.6214948   rms   .3437099513e-1   g   24.04163055

ets
34
68
102
136
153
187
221
255
289
323
357
391
425
476
510
544
578
612
646
680
714
748
765
799
833
867
901
935
969


274877906944/274658203125 hemithird

map   [[0, -15, 2], [1, 4, 2]]

generators   193.1996149   1200

badness   137.9992271   rms   .6082244804e-1   g   13.14026890

ets
25
31
56
62
87
93
112
118
143
149
174
180
205
211
230
236
261
267
292
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323
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348
354
379
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410
416
441
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497
503
528
534
559
584
590
615
621
646
652
671
677
702
708
733
739
764
770
789
795
820
826
851
857
882
888
907
913
938
944
969
975
1000


50031545098999707/50000000000000000

map   [[0, 17, 35], [1, -1, -3]]

generators   182.4660890   1200

badness   386.2264718   rms   .2546863438e-1   g   24.75210428

ets
46
79
92
125
171
217
250
263
296
342
388
434
467
480
513
559
605
638
651
684
730
776
809
822
855
901
947
980
993


7629394531250/7625597484987

map   [[0, -2, -3], [9, 19, 28]]

generators   315.6754868   400/3

badness   188.0842271   rms   .2559261582e-1   g   19.44222209

ets
27
45
72
99
126
144
171
198
243
270
297
315
342
369
414
441
468
486
513
540
567
585
612
639
684
711
738
756
783
810
855
882
909
927
954
981


2475880078570760549798248448/2474715001881122589111328125

map   [[0, -31, 12], [1, 5, 1]]

generators   132.1945105   1200

badness   463.2524095   rms   .1499283745e-1   g   31.37939876

ets
9
109
118
127
218
227
236
245
336
345
354
363
454
463
472
481
572
581
590
599
690
699
708
717
808
817
826
835
926
935
944
953


9010162353515625/9007199254740992

map   [[0, -8, 5], [2, 9, 1]]

generators   437.2581077   600

badness   113.0912513   rms   .1772520822e-1   g   18.54723699

ets
22
44
52
66
74
96
118
140
162
170
184
192
206
214
236
258
280
288
302
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324
332
354
376
398
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472
494
516
538
546
560
568
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634
656
664
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686
708
730
752
774
782
796
804
826
848
870
892
900
914
922
936
944
966
988


116450459770592056836096/116415321826934814453125

map   [[0, -33, -25], [1, 17, 14]]

generators   560.5469696   1200

badness   178.7704200   rms   .1239024539e-1   g   24.34474618

ets
15
30
122
137
152
167
274
289
304
319
411
426
441
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471
563
578
593
608
700
715
730
745
760
852
867
882
897


444089209850062616169452667236328125/444002166576103304796646509039845376

map   [[0, -51, -52], [1, 15, 16]]

generators   315.6478750   1200

badness   346.6194848   rms   .4659979284e-2   g   42.05551886

ets
19
38
57
76
365
384
403
422
441
460
479
498
517
825
844
863
882
901
920
939
958


450359962737049600/450283905890997363

map   [[0, -2, -37], [1, 2, 10]]

generators   249.0184480   1200

badness   146.1980313   rms   .5736733648e-2   g   29.42787794

ets
53
106
159
188
212
241
265
294
318
347
371
400
424
453
506
559
612
665
718
771
800
824
853
877
906
930
959
983


162285243890121480027996826171875/162259276829213363391578010288128

map   [[0, 14, -47], [1, -1, 11]]

generators   221.5678655   1200

badness   326.5508398   rms   .3538891098e-2   g   45.18849411

ets
65
130
195
222
260
287
325
352
390
417
482
547
612
677
742
807
834
872
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937
964


22300745198530623141535718272648361505980416/
22297583945629639856633730232715606689453125

map   [[0, 47, -22], [1, -2, 4]]

generators   91.53102125   1200

badness   352.1515837   rms   .2843331166e-2   g   49.84643083

ets
13
105
118
131
223
236
249
341
354
367
459
472
485
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603
708
721
826
839
944
957


381520424476945831628649898809/381469726562500000000000000000

map   [[0, -35, -62], [1, 11, 19]]

generators   322.8013866   1200

badness   256.7937928   rms   .3022380142e-2   g   43.96210490

ets
26
145
171
197
316
342
368
487
513
658
684
803
829
855
974
1000


17763568394002504646778106689453125/17763086495282268024161967871623168

map   [[0, 49, 15], [1, -6, 0]]

generators   185.7541789   1200

badness   34.16161967   rms   .7631994496e-3   g   35.50586806

ets
71
84
155
168
239
252
323
407
478
491
562
575
646
659
730
801
814
885
898
969
982

Message: 4048 - Contents - Hide Contents

Date: Thu, 7 Mar 2002 14:41 +00

Subject: Re: listing linear temperaments

From: graham@xxxxxxxxxx.xx.xx

In-Reply-To: <200203061801.g26I1Mt30684@xxxxx.xxxxxx.xxx>
Carl Lumma wrote:


> I just want to enter identities 7 9 11.  If I want 11-limit, make me
> enter 1 3 5 7 9 11.


Well, you're in luck!  That's the other thing I added on Monday night.
 

>> 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.
> 
> It could.  One gripe I have with the catalog is that it gives different
> names for the same temperament at different limits.  IIRC Cassandra
> 1 and 2 are two different extensions of schismic, one of which should
> be schismic, and the other Cassandra x, if its complexity (or g) is low
> enough to warrant a place in the catalog (which I don't think it is,
> but I could see including it for historical reasons).


The problem of integration is that the catalog's in static HTML, whereas 
the script would have to get the names from a database or a global 
dictionary somewhere.  The catalog could be made dynamic, but it'd mean 
the comments would also have to go in a database and some provision made 
for the inharmonic one.  It's easier not to bother, and have two different 
lists, that are bound to get out of sync...

The intention of the catalog is to record temperaments that have been 
singled out.  There's no value judgement on my part as to what goes in 
there.  The Cassandras could go under schismic, and Shrutar could go under 
diaschismic.  Currently Paultone/Twintone/Pajara is under diaschismic.


>>> () return all fields for each temperament (ie "not unique" or 
>> "unique")
>> 

>> You think that's important?  It won't be difficult to change.
> 

> It makes the output of the one that lists multiple temperaments easier
> to parse.  Ideal would be uniqueness level.


If some of the temperaments don't have "unique" at the bottom, you can get 
more on the screen at once to compare them.


>> 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.
> 
> Required fields should be marked with a star, or something.


But as I supply defaults for most (which I think makes it easier to see 
what they're intended for) it wouldn't make any difference to normal 
operation if they were option.  A separation between "important" and 
"geeky" might be better.


>>> () Uniqueness level.
>> 

>> Ooh!  I can only do this up to 2nd order so far.  Would that be okay?
> 

> 2nd order = triads, 1st order = dyads?  That would be splendid.
> Up to hexads would be nice.  Don't let anybody tell you they need
> more than that.


It'd be "all second order intervals are unique" because I've got a routine 
for generating the second order intervals.  That could easily be adapted 
for fourth order but not, as it stands, third order.


>> Still, you're welcome to generate your own lists and put them on your 
> own >site.
> 

> I was referring to the paper.  No cgi support there yet. :)


Oh.  Well, my paper will include examples I found promising after trying 
them on my ZTar (which I'll hopefully be getting soon).  Also, a link to 
the CGIs and the source code for anybody who wants to duplicate it all.  
That's going to take a while to finish, so until then I'm trying to make 
what's on the web as accessible as possible.


              Graham

Message: 4049 - Contents - Hide Contents

Date: Thu, 07 Mar 2002 14:13:24

Subject: Re: omigawd

From: paulerlich

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


> There is sooo much stuff in the idea pool here... will we
> drown?  I hope somebody is on top of it all.


bless you carl for taking an interest. i mean that with all sincerity!

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