source file: m1417.txt Date: Fri, 15 May 1998 17:06:00 -0400 Subject: Two schools of ET From: "Paul H. Erlich" >>I'll grant that equal temperaments are easy to hear in melodic terms Carl Lumma wrote, >Whoa! Wait a minute? Where did this come from? I don't know where it came from, but it's true. Even Mathieu admits that a 12-tone chromatic scale is melodically smoother in 12tET than in an unequal tuning. >This brings up the subject of the two schools of Equal Temperament. On the >left we have those who want to approximate Just Intonation. Erlich and >Hahn are of this school. They want a tuning be consistent and fairly >accurate at a given limit before considering it usable at any higher limit. Note that in my paper, as clarified by you (Carl Lumma), I do not care about the 5-limit accuracy of 22tET, only that its 7-limit accuracy be at least as great as the 5-limit accuracy of 12tET. Also, I am interested in scales that fulfill some but not all of the properties of diatonicity as outlined in my paper, such as Blackwood's 10-note scale in 15tET and a couple of 14-note scales in 26tET. >On the right we have those who insist that any ET is usable and "good". >Students of this school include Ivor Darreg and Easley Blackwood. Actually, Easley Blackwood thinks that 12tET is much more usable and "good" than any other tuning. See the interview in PNM. The funny thing is that Blackwood's microtonal music is generally much better than Darreg's. >the best 11/9 will be off by the absolute value of the sums of >the errors of the 11/8 and 9/8, consistency or no If you mean the best 11/8 and the best 9/8, then that might not be true, although consistency will guarantee that it's true. If you don't mean the best 11/8 and the best 9/8, then what do you mean? >On the other hand, 25 >isn't consistent past the five limit, and it has horrible fifths, but its >strong 3's and 7's make it great for the 7-limit, as Paul Rapaport proved >in his "Study in Fives". Did you mean horrible thirds or strong 5s?