Kees-Max and Wedgie Complexity. Twins separated at birth?

I'm working hard to get my Prime Errors and Complexities paper finished by the end of the year. Here's an up to date link:

http://x31eq.com/primerr.pdf

(Yes, I'm on a network that lets me upload to my website!)

I've just added some tables showing lots of different complexities. Two new columns are:

Range -- the true Kees-max error, or the difference between the lowest and highest weighted elements of the generator mapping. Usually I halve this to be comparable to the standard deviation.

Erlich -- This is the wedgie complexity Paul used in The Middle Path. It's the absolute product of the entries of the weighted wedgie.

Now, what's struck me is that these two columns are almost identical in the 5-limit. To a few significant figures for the more accurate temperaments. So why is it? It only works for the 5-limit, in which case the complexity Paul used is equal to the Tenney size of the defining comma. Was anybody expecting that to approximate the Kees-max complexity?

I've also stolen the list of 11-limit temperaments Herman posted on the 8th of January. Here's your chance to object! I'll give credit presently.

Graham

Graham Breed wrote:
> I'm working hard to get my Prime Errors and Complexities > paper finished by the end of the year. Here's an up to date > link:
> > http://x31eq.com/primerr.pdf
> > (Yes, I'm on a network that lets me upload to my website!)

And I've got high-speed internet in my hotel room! I expected to be stuck with dialup, but I guess it's been a while since I've traveled much.

This will give me something to look over the next few days while I've got nothing much else to do. I wonder, though, if there might be other 11-limit temperaments in the same range of error and complexity (probably unnamed ones).

Herman Miller wrote:
> Graham Breed wrote:
>> I'm working hard to get my Prime Errors and Complexities >> paper finished by the end of the year. Here's an up to date >> link:
>>
>> http://x31eq.com/primerr.pdf
>>
>> (Yes, I'm on a network that lets me upload to my website!)
> > And I've got high-speed internet in my hotel room! I expected to be > stuck with dialup, but I guess it's been a while since I've traveled much.

Oh yes, hotel rooms are good places to go online.

> This will give me something to look over the next few days while I've > got nothing much else to do. I wonder, though, if there might be other > 11-limit temperaments in the same range of error and complexity > (probably unnamed ones).

Maybe there are, but I only need a list. It doesn't matter much which list. I note it's missing hemiennealimmal though...

Graham

Graham Breed wrote:
> Herman Miller wrote:
>> Graham Breed wrote:
>>> I'm working hard to get my Prime Errors and Complexities >>> paper finished by the end of the year. Here's an up to date >>> link:
>>>
>>> http://x31eq.com/primerr.pdf
>>>
>>> (Yes, I'm on a network that lets me upload to my website!)
>> And I've got high-speed internet in my hotel room! I expected to be >> stuck with dialup, but I guess it's been a while since I've traveled much.
> > Oh yes, hotel rooms are good places to go online.
> >> This will give me something to look over the next few days while I've >> got nothing much else to do. I wonder, though, if there might be other >> 11-limit temperaments in the same range of error and complexity >> (probably unnamed ones).
> > Maybe there are, but I only need a list. It doesn't matter > much which list. I note it's missing hemiennealimmal though...

I could include higher-complexity temperaments in the list (which I sorted by Paul Erlich's wedgie complexity). Between wizard at 53.169 and hemiennealimmal at 128.040, there are a few other good ones including a variety of garibaldi, compton, hemithird, etc. There are also a bunch of others that look reasonably good but haven't been named yet as far as I can tell.

garibaldi [<1, 2, -1, -3, 13], <0, -1, 8, 14, -23]> 54.678041
compton [<12, 19, 28, 34, 42], <0, 0, -1, -2, -3]> 58.679206
hemithird [<1, 4, 2, 2, 7], <0, -15, 2, 5, -22]> 59.404384
slender [<1, 2, 2, 3, 4], <0, -13, 10, -6, -17]> 59.846329
harry [<2, 4, 7, 7, 9], <0, -6, -17, -10, -15]> 61.656187
unidec [<2, 5, 8, 5, 6], <0, -6, -11, 2, 3]> 62.803801
catakleismic [<1, 0, 1, -3, 9], <0, 6, 5, 22, -21]> 63.163371
hemiw�rschmidt [<1, -1, 2, 2, -3], <0, 16, 2, 5, 40]> 64.721803
trikleismic [<3, 6, 8, 8, 11], <0, -6, -5, 2, -3]> 66.872256
(minorsemi)
vulture [<1, 0, -6, 4, -12], <0, 4, 21, -3, 39]> 67.503588
marvo [<1, -1, -5, -17, -3], <0, 6, 17, 46, 15]> 72.579877
octoid [<8, 13, 19, 23, 28], <0, -3, -4, -5, -3]> 75.192514
guiron [<1, 1, 7, 3, -2], <0, 3, -24, -1, 28]> 78.195049
hendecatonic [<11, 17, 26, 30, 39], <0, 1, -1, 2, -2]> 80.178061
grendel [<1, 9, 2, 7, 17], <0, -23, 1, -13, -42]> 84.070973
(voodoo)
bisupermajor [<2, 1, 6, 1, 8], <0, 8, -5, 17, -4]> 90.473355
kwai [<1, 2, 16, 14, -4], <0, -1, -33, -27, 18]> 96.926689
hemischismic [<2, 3, 6, 9, 12], <0, 1, -8, -20, -30]> 102.916701