RE: Reply to Paul Hahn

>(a) I wish to go beyond basic (level 1) consistency because it is
>possible for an ET to be level 1 consistent and still err from a given
>just ratio by nearly half the stepsize of the ET. An extreme example:
>18TET is consistent to the 7-limit, but its 11-step "fifth" is only
>barely better as an approximation to the 3/2 than its 10-step interval.
>One is over 31 cents high, the other more than 35 cents low; the
>difference between the two errors is less than four cents!

That's a good reason, but it would seem highly unlikely that the most
appropriate consistency level for this purpose would turn out to be an
integer, unless you had particular composite ratios in mind that you
care about representing consistently. It was the ratios of large
composite numbers I was objecting to, since treating them more carefully
than ratios of numbers with larger prime factors, even if the latter
numbers are smaller than the former ones, is something that those who
believe in prime characteristics will advocate, but I find no
justification for.