source file: m1405.txt Date: Mon, 4 May 1998 16:08:37 -0400 Subject: Reply to Paul Hahn From: "Paul H. Erlich" >'Scuse me for butting in, but it was an open letter. I certainly agree. >I'm not sure what I can contribute to such an effort, but I'm on your >side at least. Well, I'm not sure what this effort will be or how best to focus it; the misunderstanding that needs to be combatted here is diffuse and widespread. I almost wanted to include you, but your concept of higher-level consistency seems to support the other side. For example, insisting that the approximations to 3-limit intervals be level-2 consistent means that you care about approximating certain 9-limit intervals. But I claim that in order for any 9-limit intervals become relevant (that is, for any just 9-limit ratios become relevant in describing the effect/affect of any tempered intervals), all 7-limit ratios would already be considered consonant (by an acoustical, not cultural, evaluation), and therefore should be consistently expressed. So insisting on full 9-limit consistency in this case would be more appropriate. Of course, you may simply want to exclude the number 7 from the harmonies and include the number 9. I can understand if there is a particular odd number that one wishes to exclude from the harmony and therefore one does not need consistency for. Well, aside from my usual consistency definition, which means all odd numbers up to the limit can be included in ratios that are all consistent with one another, one can concoct a more general definition based on any set of odd numbers. For example, 22tET is consistent over the set of odd numbers {3,5,7,9,11,15,17} -- 17-limit consistent if 13 is excluded.