source file: m1406.txt Date: Tue, 5 May 1998 14:10:51 -0400 Subject: RE: Reply to Paul Hahn From: "Paul H. Erlich" >(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.