source file: m1534.txt Date: Thu, 24 Sep 1998 15:45:40 -0400 Subject: Re: scale derived by intersection of sets From: "Paul H. Erlich" I wrote, >> I once tried tuning several guitar strings to such a >> drone and found that I could generally tune a remaining string to any >> pitch that formed a 7-limit consonance with either 1/1 or 3/2, or an >> 11-limit consonance with both 1/1 and 3/2. (This is sort of mentioned in >> my 22-tET paper.) The resulting scale: >> >> 1/1 21/20 15/14 12/11 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3 11/8 7/5 10/7 >> 3/2 8/5 5/3 12/7 7/4 9/5 15/8 (2/1) >> >> Coincidentally, this scale has 22 notes while Robin Perry's has 12. Paul Hahn wrote, >Umm, do you not consider 11/9 an 11-limit consonance? (I know we have >periodic wars on this subject on the list, at least when Brian is >contributing.) If you do, then 11/6 and 18/11 also fit your criteria, >which makes it a 24-note scale instead of 22. Paul, you're right, and my paper is wrong. I guess 11/9 is often harder to hear than some other ratios of 11, and I was too eager to provide a simple mathematical description of what I heard. I should trash all of page 20 (in the .pdf version) of my paper, as well as two columns of table 5. Although it's too late for Xenharmonikon, perhaps if Carl Lumma reppears we can revise the .pdf version accordingly. Aaargh!!! Do you mean Brian McLaren? I don't remember those days too well.