(21/20)(15/14)(8/7)^2 (7/6)^2

I may have done this already, but now I know it's really interesting,
so it's worth doing it again, even so. I get 30 of these; calculating
the 7-limit characteristic polynomial, the champ is

1-15/14-5/4-10/7-3/2-12/7

characteristic polynomial: x^6 - 12x^4 - 16x^3

The two runners up are

1-8/7-6/5-7/5-8/5-12/7
x^6 - 11x^4 - 14x^3 + 4x^2 + 8x

1-7/6-5/4-10/7-5/3-7/4
x^6 - 11x^4 - 14x^3 + 4x^3 + 8x

From the characteristic polynomial, the champ has 12 7-limit consonant
intervals and 8 7-limit triads; this becomes less amazing when we
realize it is the hexany. For our consonance circle scales, we would
want to take one of these scales--and the hexany seems like the one to
pick on--and split each of its steps into a product of two consonance
circle intervals, down an octave. Each of the six steps can be so
split in two ways, so once again we have something we can readily
analyze. On to the next stage!

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Each of the six steps can be so
> split in two ways, so once again we have something we can readily
> analyze. On to the next stage!

Unfortunately the next stage doesn't work, because splitting the
intervals by anthing on our consonance circle list does not lead out
of the hexany. Of course there are scales with two hexanies in them. :(