Here are the 11 and 13 limit MT reduced bases for the 58 et; perhaps some 58-et scale possibilities can be explored with their help.

11-limit: <126/125, 176/175, 243/242, 896/891>

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

--- 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>

--- 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?

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

> --- 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?

Here's another possibility, which I obtained by trying to minimize

Tenney height:

[1, 56/55, 36/35, 26/25, 22/21, 16/15, 14/13, 12/11, 11/10, 10/9,

9/8, 8/7, 15/13, 7/6, 13/11, 6/5, 40/33, 11/9, 26/21, 5/4, 14/11, 9/7, 13/10, 21/16, 4/3, 27/20, 15/11, 11/8, 7/5, 45/32, 10/7, 13/9, 22/15, 40/27, 3/2, 32/21, 20/13, 14/9, 11/7, 8/5, 21/13, 13/8, 33/20, 5/3, 22/13, 12/7, 26/15, 7/4, 16/9, 9/5, 20/11, 11/6, 13/7, 15/8, 21/11, 25/13, 35/18, 55/28]

The smallest interval here is between 7/5 and 45/32; this could no doubt be smoothed out more than this, but it seems clear that we can get something decent in 58 tones, 13-limit JI which is epimorphic.