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Cangwu badness and Keenan's lists

🔗genewardsmith <genewardsmith@...>

12/30/2011 5:22:11 PM

Looking at Keenan's new temperament lists on the Xenwiki reminds me of why I hated Paul's procedure for constructing his lists. I took the top two listed temperaments, and equated their Cangwu polynomials, solving for the positive root. But in each case, it turned out they didn't have a positive root! The lists are so badly skewed in favor of low complexity that using simple badness as a metric would actually favor error over complexity *more*. Maybe Keenan should give simple badness a try.

🔗genewardsmith <genewardsmith@...>

12/30/2011 6:04:13 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> But in each case, it turned out they didn't have a positive root!

Sorry, ignore this; the complaint doesn't really make sense since it is about the comparison of the two temperaments in question, and simple badness weighs error highly (the other name for it being "relative error".) Maybe I should equate the top and bottom of the lists.

🔗genewardsmith <genewardsmith@...>

12/30/2011 6:59:11 PM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> Maybe I should equate the top and bottom of the lists.

I followed through on this suggestion, which makes more sense as a way of getting a listing corresponding to the Keenan list, and applied it to a list of 11-limit temperaments I have around. The result, in order, of the start of that list is augene, pajara, meantone, porcupine, meanenneadecal, orwell, injera, valentine, triforce, keemun, magic, pajarous, meanpop, myna, garibaldi, progress, miracle/duodecim tie...