Wuerschmidt/Wurschmidt/Worschmidt question

I was going through some of the rank-2 temperaments at the xenharmonic
wiki, and came across the wuerschmidt page here:
http://xenharmonic.wikispaces.com/Wuerschmidt+family

>> Wurschmidt
>
> Wurschmidt, aside from the commas listed above, also tempers out 225/224. 31edo or 127edo can be used as tunings. Wurschmidt has <<8 1 18 -17 6 39|| for a wedgie.
>
>
>> Worschmidt
>
> Worschmidt tempers out 126/125 rather than 225/224, and can use 31edo, 34edo, or 127edo as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt. The wedgie now is <<8 1 -13 -17 -43 -33|. In practice, of course, both mappings could be used ambiguously, which might be an interesting avenue for someone to explore.

Note that for Wurschmidt, possible tunings are 31-edo and 127-edo, and
for Worschmidt, possible tunings are... 31-edo and 127-edo. How is
this possible? So what's the 31 and 127 tuning... Wurschmidt or
Worschmidt?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I was going through some of the rank-2 temperaments at the xenharmonic

Check out the new page on Starling temperaments.

> Note that for Wurschmidt, possible tunings are 31-edo and 127-edo, and
> for Worschmidt, possible tunings are... 31-edo and 127-edo. How is
> this possible? So what's the 31 and 127 tuning... Wurschmidt or
> Worschmidt?

Wurschmidt and Worschmidt are identical in 31, and use a different mapping in 127. "Worschmidt tempers out 126/125 rather than 225/224, and can use 31edo, 34edo, or 127edo as a tuning. If 127 is used, note that the val is <127 201 295 356| and not <127 201 295 357| as with wurschmidt."