Paul has taken up the challenge of finding the exact value of the

Osmium Meantone, which is the limit of the sequence 4/7, 7/12, 7/12,

11/19, 14/24, 18/31, 25/43, 32/55 ..., and is about 1/5-comma

meantone. If he solves that, this should be easy:

3/8, 4/11, 7/19, 7/19, 11/30, 14/38, 18/49, 25/68, 32/87, 43/117,

57/155... . If you multiply the denominators by 9, you get 72, 99,

171, 171, 270, 342, 441, 612, 783, 1053, 1395 ..., so this is the

Osmium version of a generator which doesn't yet have a name, so far

as I know, but which has been discussed several times.

(Why Osmium? I'll explain that after Paul either solves the problem

or asks for my solution.)

I'd also like to know what to do with the sequence 9, 10, 12, 19, 22,

31, 41, 53, 72, 94, ... It doesn't seem like Miracle, or Orwell

either, but the ets make sense, at any rate, even if the resultant

commas don't. Apparently this Osmium business doesn't always give you

a generator that makes much sense.