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Message: 4150 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:36:26

Subject: Re: a crackpot idea

From: dkeenanuqnetau

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

> I wrote...
> <...Something agreeing with Dave that musical history is a sort of
> <badness measure (or at least, can be used to check badness 
measures).
> 
> Also, we've been at this a couple of months, long enough that what
> we're talking about has a kind of ecosystem, so what we have names
> for might also be considered here -- what we have names for should
> all be in the 7-limit top 32, I'd wager.  At least, for the 
musicians'
> list.


Not sure about 7-limit yet, but it certainly was striking in my 
spreadsheet that, although Gene provided most of the names, when you 
hit the button to sort it bykeenan badness, practically all the named 
ones went to the top and the unnamed ones to the bottom.

Message: 4151 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 16:24:45

Subject: Re: 32 best 5-limit linear temperaments redux

From: Carl Lumma

>Going by my map:
>
>          max int width  card(map)  me    g
>5-limit   10             2          5     7.257
>11-limit  11             4          2.75  ??
>
>I have no idea how Gene got 7.257, so I can't fill
>g in for the 11-limit.


Dave's getting 7.3 too, with this:

SQRT((E13^2+F13^2+(E13-F13)^2)/3)*1200/L13

Anybody care to explain why this isn't total rubbish?  Putting
both the individual gens per idenitity (E13 and F13) and the
total width of the chain (E13-F13) together into the rms calc???

-Carl

Message: 4152 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:36:47

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
wrote:

> then the maximum interval width (which is also 
> the width of the complete chord - Carl's measure) seems more 
relevant 
> to me than the rms interval width.


and shouldn't it be the maximum or rms *weighted* interval 
width?

Message: 4153 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 06:24:04

Subject: Re: 32 best 5-limit linear temperaments redux

From: dkeenanuqnetau

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
> wrote:

>> then the maximum interval width (which is also 
>> the width of the complete chord - Carl's measure) seems more 
> relevant 

>> to me than the rms interval width.
> 

> and shouldn't it be the maximum or rms *weighted* interval 
> width?


You also asked why max abs? I'll answer that first.

One of the reasons given for using rms was that if there was an 
outlier the LT still got credit for the intervals it did well. But if 
we're looking at say {1,3,5,7} then if _any_ {1,3,5,7} interval is 
very wide, I don't think it is a good {1,3,5,7} temperament. Let it be 
found to be a good {2,5,7} temperament or whatever.

As far as the weighting by odd-limit thing goes. I'm reasonably in 
favour. But it's a very musician-type "subjective" thing to do and not 
at all a mathematician type thing. And I'm not prepared to argue over 
it, mainly because I expect the good temperaments will still make it 
on the list without it. Also, I have no easy way of finding optimum 
generators (which you'd have to do all over again before you can find 
the error). Gene would have to do it.

Message: 4154 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:35:52

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
wrote:

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

>> i thought the paper was going to concern {2,3,5}, {2,3,7}, 
{2,5,7}, 
>> {3,5,7}, and {2,3,5,7}. isn't that right?
> 

> That's ok by me. But if we're listing these separately (which 
>seems 
> the right thing to me),

yes,

> then the maximum interval width (which is also 
> the width of the complete chord - Carl's measure) seems more 
> relevant 
> to me than the rms interval width.


why is that?

Message: 4155 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 06:35:37

Subject: Re: 32 best 5-limit linear temperaments redux

From: dkeenanuqnetau

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
> you lost me.


Never mind. It doesn't matter now.


>> Anyway, if Gene uses the right cutoffs on eror and complexity 
> this is 

>> now a moot point.
> 

> what are the right cutoffs? i favor going well into uninteresting 
> territory on both ends, to demonstrate how the algorithm 
> functions (once it's truly an algorithm -- it seems it may be 
> missing some things currently). best to be explicit about it!


As I posted twice before:

Smith badness < 861
rms complexity < 13.2 gens
rms error < 28.9 cents

You can of course round the numbers up so it doesn't look so 
contrived, provided that doesn't add more than 2 or 3 extra 
temperaments.

Message: 4156 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 16:40:13

Subject: Re: 32 best 5-limit linear temperaments redux

From: Carl Lumma

>carl, if 'identity' is defined as 'consonant interval', then the 
>*only* thing going in here is the individual gens per identity. 
>that's all. E13-F13 is the major sixth or minor third.


Oh.  Well, I'm not sure how that's significant, since in regular
temperaments it will always be the difference of the 3 and 5
mappings.

-Carl

Message: 4157 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:40:47

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
wrote:


> Anyway. I'm willing to accept a list ordered by complexity 
provided 
> smith-badness is not shown anywhere.


phew. a consensus emerges?

Message: 4158 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 06:48:47

Subject: Re: Dave's 18 best 5-limit temperaments

From: dkeenanuqnetau

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

> hmm? i thought dave said 6561:6400 was half-meantone. 


No I called that twin meantone.


> someone needs to write a gentle introduction to contortion, just 
> to list all the issues in one place.


I guess you haven't looked at my spreadsheet yet.
http://uq.net.au/~zzdkeena/Music/5LimitTemp.xls.zip - Type Ok * [with cont.]  (Wayb.)

I named them like this

Comma     Name                 Mapping           Gen   Period
-------------------------------------------------------------
6561/6400 twin meantone	       [0,-1,-4] [2,4,8] 503.8 600
81/80     half meantone-fifth  [0,2,8]   [1,2,4] 348.1 1200
81/80     half meantone-fourth [0,-2,-8] [1,2,4] 251.9 1200

The same pattern repeats for kleismic.

If Gene or anyone already has a different system for naming these, I'd 
like to learn it.

Message: 4159 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:42:04

Subject: Re: 32 best 5-limit linear temperaments redux

From: dkeenanuqnetau

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
> wrote:
> 

>> That's not relevant. My point is that it _does_ hurt someone. It 
> hurts 

>> the person interested in middle-of-the-road temperaments.
>> 

>>> -- and there were 
>>> other reasons for excluding "fourth-thirds", as i recall.
>> 

>> OK. Just substitute "pelogic" for "fourth-thirds" in the above.
> 

> then i'd definitely disagree with you.


Perhaps that got a bit muddled. I mean that using a smith badness 
cutoff without small enough cutoffs on error and complexity, I would 
always find temperaments that any sane musician would consider better 
than either pelogic or 49-gens-to-the-fifth. That would be 
disadvantaging someone.

Anyway, if Gene uses the right cutoffs on eror and complexity this is 
now a moot point.

Message: 4160 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 01:10:32

Subject: Re: Interesting 46-et, 8-tone scale

From: dkeenanuqnetau

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

> Here it is:
> 
> 39375739, plus all its modal forms and their inversions. It has 21 
> 7-limit edges, and 20 7-limit 3-note chords. Its characteristic 

polynomial (the characteristic polynomial of the adjacency matrix, 
which has a 1 if two nodes are connected, and a 0 otherwise) is

> x^8-21*x^6-40*x^5+12*x^4+48*x^3; the -21*x^6 term means it has 21 
> 7-limit intervals, and the -40*x^5 term means it has 20 7-limit 
> three-note chords. The x^2, x, and constant term are all zero which 

means it has multiple zero eigenvalues, but I don't know what *that* 
means, at least as yet.

> 
> The closest competition had only 14 3-note chords!


This does look like a good 8-note 7-limit scale. 

It looks good melodically too (from what little I know about that).  
It is very close to being a subset of Herman Miller's 12-tone Starling 
tuning, from which Herman has used several 7-note subsets. So 
"Starling-8" might be a good name for it.

See miller_12.scl and miller_12a.scl in the Scala archive
Starling temperament is essentially a 7-limit planar temperament where 
the septimal semicomma 125:126 vanishes. Narrowing the octave by about 
1.4 cents improves things. See
Fue Marrgarrel * [with cont.]  (Wayb.)
404 Not Found * [with cont.]  Search for http://uq.net.au/~zzdkeena/Music/DistibutingCommas.htm in Wayback Machine

I'm guessing it should work well in 31-tET too as
2 6 2 5 3 5 2 6

Message: 4161 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:45:27

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
> wrote:

>> then the maximum interval width (which is also 
>> the width of the complete chord - Carl's measure) seems 
more 
> relevant 

>> to me than the rms interval width.
> 

> and shouldn't it be the maximum or rms *weighted* interval 
> width?


by the way, my now-famous heursitic for complexity would sort 
the 5-limit temperaments by the size of the numerators (or 
denominators, or n*d) of the commas. kees van prooijen 
webpages seem to suggest clearly that this should be 
expressible as a distance measure of some kind. no one else 
seems interested in pursuing this obversation, however :(

Message: 4162 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 07:31:06

Subject: Everybody's 26 best 5-limit temperaments?

From: dkeenanuqnetau

See the spreadsheet at
http://uq.net.au/~zzdkeena/Music/5LimitTemp.xls.zip - Type Ok * [with cont.]  (Wayb.)

For those who've already seen it. I've added a button to sort by 
complexity (just plain rms interval-width in gens, not weighted). And 
I've added variable cutoffs on error and complexity for Gene's badness 
measure. You will see that a max rms error of 35 cents and a max rms 
complexity of 15 gens makes Gene's and my lists identical.

However we still need to wait to see what turns up when Gene reruns 
his algorithm with my badness, (and with his own badness and a higher 
badness cutoff). Something went wrong the first time he tried it.

Hey Paul, you've always accepted much larger errors than I ever would. 
Is 35 cents rms extreme enough for you, for something calling itself 
5-limit?

Remember those charts for my chains-of-fifths papers. I allowed up to 
14 gens in an interval. You thought that was way too many to be useful 
and suggested limiting it to 7. So is 15 gens extreme enough for you 
now?

Message: 4163 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 01:44:17

Subject: Dave's 18 best 5-limit temperaments

From: genewardsmith

Here's a list of temperaments with keenan badness less than 15, where
keenan badness is g exp(sqrt(r/7.4)) :

81/80

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

keenan   6.263263749   rms   4.217730124   g   2.943920288

generators   503.8351546   1200



15625/15552

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

keenan   6.601347654   rms   1.029625097   g   4.546060566

generators   317.0796754   1200



128/125

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

keenan   7.686514108   rms   9.677665980   g   2.449489743

generators   491.2018553   400



2048/2025

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

keenan   7.826993942   rms   2.612822498   g   4.320493799

generators   494.5534684   600



32805/32768

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

keenan   8.087460995   rms   .1616904714   g   6.976149846

generators   498.2724869   1200



3125/3072

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

keenan   8.209877206   rms   4.569472316   g   3.741657387

generators   379.9679494   1200



393216/390625

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

keenan   9.019558680   rms   1.071950166   g   6.164414003

generators   387.8196732   1200



78732/78125

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

keenan   9.925545192   rms   1.157498146   g   6.683312553

generators   442.9792974   1200



250/243

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

keenan   10.05091489   rms   7.975800816   g   3.559026083

generators   162.9960265   1200



2109375/2097152

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

keenan   10.08322927   rms   .8004099292   g   7.257180353

generators   271.5895996   1200



25/24

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

keenan   10.18726181   rms   28.85189698   g   1.414213562

generators   350.9775007   1200



648/625

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

keenan   11.09063733   rms   11.06006024   g   3.265986323

generators   505.8656425   300



20000/19683

map   [[0, 4, 9], [1, 1, 1]]

keenan   11.40932735   rms   2.504205191   g   6.377042156

generators   176.2822703   1200



1600000/1594323

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

keenan   11.64300516   rms   .3831037874   g   9.273618495

generators   339.5088258   1200



1990656/1953125

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

keenan   12.03289099   rms   2.983295872   g   6.377042156

generators   77.96498962   1200



16875/16384

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

keenan   12.16857021   rms   5.942562596   g   4.966554810

generators   126.2382718   1200



6561/6400

map   [[0, -1, -4], [2, 4, 8]]

keenan   12.52652750   rms   4.217730124   g   5.887840578

generators   503.8351546   600



135/128

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

keenan   14.05153795   rms   18.07773298   g   2.943920288

generators   522.8623453   1200

Message: 4164 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:47:10

Subject: Re: Dave's 18 best 5-limit temperaments

From: genewardsmith

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:


> Thanks for that Gene. Much appreciated. Why no names?


Because I just gave computer output.


> But I don't understand why we lost the following that _were_ in your 
> list of 32:
> 
> semisuper
> parakleismic
> hemithird


I
suspect it's because the computation broke down in the middle and I
restarted it from where it seemed to have gotten; I'll try again and
see what happens.


> I know why you didn't find the two half-meantones and the two 
> half-kleismics. Because you don't consider them to be 5-limit linear

> temperaments. 


Not this time--I made no attempt to exclude them, but it found 
(81/80)^2 instead of the half-meantones. That's because they all share
the same wedgie.

Message: 4165 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 06:27:41

Subject: Re: Dave's 18 best 5-limit temperaments

From: dkeenanuqnetau

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> 

>> Thanks for that Gene. Much appreciated. Why no names?
> 

> Because I just gave computer output.


Sorry. I thought you had the name lookup automated.


>> But I don't understand why we lost the following that _were_ in 
your 
>> list of 32:
>> 
>> semisuper
>> parakleismic
>> hemithird
> 

> I suspect it's because the computation broke down in the middle and 

I restarted it from where it seemed to have gotten; I'll try again and 
see what happens.

Thanks.

Message: 4166 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 01:42:47

Subject: Re: 32 best 5-limit linear temperaments redux

From: dkeenanuqnetau

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

> dave is trying to make an important subjective decision for 
> musicians. 


This subjective/objective false-dichotomy again? Haven't read enough 
Wilber yet? I'd like us to agree on a badness measure that best 
represents the collective subjective experiences of lots of musicians. 
In the same manner as my favourite definition of "just".


> gene, by insisting on a log-flat measure, best 
> permits the musician to make this decision for him/herself. 
> going too far in both directions doesn't hurt anyone.


How can you say that!? 

I just showed that Gene's list failed to include at least two 
temperaments that are _way_ more interesting and useful than 
"fourth-thirds" and the one with 49 gens to the fifth. Namely 
minimal diesic and the unnamed one with the [-4,3] map and the 126.2 
cent generator. They were discriminated against purely because they 
were middle-of-the-road in error and complexity. 

No matter how far Gene goes with his badness cutoff, I will always be 
able to show that he has left off temperaments which any sane musician 
would find to be much better than some of those he has included, 
unless his error and complexity cutoffs can be adjusted (ad hoc) to 
avoid it.


> gene, you 
> may note, has given his lists in order of complexity (or similar, 
> but it should be in order of complexity), but not as an overall 
> ranking. an overall ranking is pretty meaningless outside of a 
> single musician's desiderata.


Some overall rankings are a lot more meaningful than others. If you're 
going to give a single list and you're going to put the badness 
numbers in there, then why _wouldn't_ readers assume they were 
applicable overall? I don't think that, not putting the list in 
badness order, will be enough.

Message: 4167 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:50:09

Subject: Re: 32 best 5-limit linear temperaments redux

From: genewardsmith

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


> and what if the subset of 'primes' you're thinking about is not 
> really the primes, but is, say, {2, 3, 5/3} or {2, 3, 7/5}?


{2,3,5/3}
defines the same subgroup as {2,3,5}, but {2,3,7/5} is a good example
of a subgroup which doesn't fit the missing prime paradigm. I posted a
list of such subgroups a while back.

Message: 4168 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 05:41:51

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

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

>> orwell with 9 or 13 notes. still 11-limit.
> 

> I show orwell with a 9-tone MOS,


and 13 too . . .

 and this map:

> 
> [0 7 -3 8 2]
> [1 0  0 0 0]
> 
> 'zthat right?  That covers 10 gens in the 5-limit, 11-gens in
> the 7-limit, and 11 gens in the 11-limit.  You're saying...
> 
> [0 -3  2]
> [1  0  0]
> [1  5 11]
> 
> ...only takes 5 notes?


you lost me.


>I know I said "limit", but I meant it
> figuratively, not literally.  It's an abuse of terminology to
> call [1 5 11] the "[1 5 11]-limit", for example, but that's what
> I meant.


is [2 3 7/5] a limit too?


> 
> So if your paper's really going to cover all these (by that I
> mean have a list for each one), I'd suggest ranking by
> complexity, with a sharp cutoff.  Just show the most accurate
> three temperaments for each integer of complexity up to 15 or
> so. 


this is flat badness. i think log-flat is better, and it's what gene's 
using.

Message: 4169 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 00:11:02

Subject: 8-tone Euclidean-reduced scale

From: Carl Lumma

>39375739


Anybody look at the steps in 46?

(0 3 12 15 22 27 34 37 46)

-Carl

Message: 4170 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 01:51:26

Subject: Re: 32 best 5-limit linear temperaments redux

From: dkeenanuqnetau

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

> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 

>> I'd rather they were listed in increasing order of "badness", 
> assuming 

>> "badness" actually means something, like badness. Then if 
> I'm looking 

>> for the best temperament whose error is in a particular range 
> of sizes 

>> I'll just go down the list until I find the first one _in_ that 
range. 
> 

> sounds like a terrible idea.


Would you mind saying why?

I'm just as likely to be looking for the best temperament whose 
generator size is in a particular range or whose period is a 
particular fraction of an octave, or whose rms error is in a 
particular range, as I am to be looking for one whose number of gens 
is in a particular range. Why favour any one of these (and thereby 
make the others much more difficult to find) by sorting the list on 
it?

Message: 4171 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 04:53:18

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
wrote:

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

>> --- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
>> wrote:
>> 

>>> That's not relevant. My point is that it _does_ hurt someone. 
It 
>> hurts 

>>> the person interested in middle-of-the-road temperaments.
>>> 

>>>> -- and there were 
>>>> other reasons for excluding "fourth-thirds", as i recall.
>>> 

>>> OK. Just substitute "pelogic" for "fourth-thirds" in the above.
>> 

>> then i'd definitely disagree with you.
> 

> Perhaps that got a bit muddled. I mean that using a smith 
badness 
> cutoff without small enough cutoffs on error and complexity,


you mean large enough?


> I would 
> always find temperaments


you mean with even larger error and complexity?


> that any sane musician would consider better 
> than either pelogic or 49-gens-to-the-fifth.


you lost me.


> That would be 
> disadvantaging someone.
> 
> Anyway, if Gene uses the right cutoffs on eror and complexity 
this is 
> now a moot point.


what are the right cutoffs? i favor going well into uninteresting 
territory on both ends, to demonstrate how the algorithm 
functions (once it's truly an algorithm -- it seems it may be 
missing some things currently). best to be explicit about it!

Message: 4172 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 00:16:33

Subject: Re: 32 best 5-limit linear temperaments redux

From: Carl Lumma

>> > know I said "limit", but I meant it
>> figuratively, not literally.  It's an abuse of terminology to
>> call [1 5 11] the "[1 5 11]-limit", for example, but that's what
>> I meant.
>

>is [2 3 7/5] a limit too?


In the sense that you can give a list for it or tell the reader
to try Graham's script with input X, so that you don't have to
use rms of the "highest interval width" (Graham's term for the
length of the chain).


>> So if your paper's really going to cover all these (by that I
>> mean have a list for each one), I'd suggest ranking by
>> complexity, with a sharp cutoff.  Just show the most accurate
>> three temperaments for each integer of complexity up to 15 or
>> so. 
>

>this is flat badness.


Which badness formulas produce flat? 


>i think log-flat is better, and it's what
>gene's using.


Ok.  Is steps^n*cents log-flat for any n > 1?

-Carl

Message: 4173 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 02:09:33

Subject: Re: 32 best 5-limit linear temperaments redux

From: paulerlich

--- In tuning-math@y..., "dkeenanuqnetau" <d.keenan@u...> 
wrote:

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

>> dave is trying to make an important subjective decision for 
>> musicians. 
> 

> This subjective/objective false-dichotomy again? Haven't read 
enough 
> Wilber yet? I'd like us to agree on a badness measure that 
best 
> represents the collective subjective experiences of lots of 
musicians. 
> In the same manner as my favourite definition of "just".


ok. let our paper have two sets of lists then.


>> gene, by insisting on a log-flat measure, best 
>> permits the musician to make this decision for him/herself. 
>> going too far in both directions doesn't hurt anyone.
> 

> How can you say that!? 
> 
> I just showed that Gene's list failed to include at least two 
> temperaments that are _way_ more interesting and useful 
than 
> "fourth-thirds" and the one with 49 gens to the fifth.


not in their respective ranges of complexity -- and there were 
other reasons for excluding "fourth-thirds", as i recall.


>> gene, you 
>> may note, has given his lists in order of complexity (or 
similar, 
>> but it should be in order of complexity), but not as an overall 
>> ranking. an overall ranking is pretty meaningless outside of a 
>> single musician's desiderata.
> 

> Some overall rankings are a lot more meaningful than others. 
If you're 
> going to give a single list and you're going to put the badness 
> numbers in there,


*don't* put the badness numbers in there. the important part of 
the paper should be about how temperaments work and why 
they're important, not about how to *rank* them!

Message: 4174 - Contents - Hide Contents

Date: Mon, 11 Mar 2002 00:44:46

Subject: Everybody's 26 best 5-limit temperaments?

From: Carl Lumma

>See the spreadsheet at
>http://uq.net.au/~zzdkeena/Music/5LimitTemp.xls.zip - Type Ok * [with cont.]  (Wayb.)


Great.  This is the best.

I can't figure out how to change ^3 to ^2 for all the "O" rows.  Is
it difficult to add steps^2 badness?


>> Also, we've been at this a couple of months, long enough that what
>> we're talking about has a kind of ecosystem, so what we have names
>> for might also be considered here -- what we have names for should
>> all be in the 7-limit top 32, I'd wager.  At least, for the 
>> musicians' list.
>

>Not sure about 7-limit yet, but it certainly was striking in my 
>spreadsheet that, although Gene provided most of the names, when you 
>hit the button to sort it bykeenan badness, practically all the named 
>ones went to the top and the unnamed ones to the bottom.

Cool.

-Carl

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