source file: m1421.txt Date: Tue, 19 May 1998 10:59:22 -0400 Subject: equal steps for melody From: "Paul H. Erlich" The 5-limit diatonic scale has two step sizes -- or is it three? In just intonation, it's three: 9/8 10/9 16/15 9/8 10/9 9/8 16/15 and Bill Alves might argue that this is just how the diatonic scale should be, melodically or otherwise. However, compare the 5-limit diatonic scale in 12-equal: 2 2 1 2 2 2 1 (2 step sizes) with that in 22-equal 4 3 2 4 3 4 2 (3 step sizes). The 12-equal version sounds better melodically, even though 22-equal has consonant intervals closer to those of JI. I think this is because having three different step sizes is awkward melodically (in this case), and in JI the 9/8 and 10/9 are, as Ben Johnston would say, close enough to sound like melodically equal steps. Note that while the 5-limit led Ben Johnston to a 53-near-equal JI scale, the 7-limit led him to a 22-near-equal JI scale (which I read about in Perspectives of New Music). Anyone familiar with other near-equal scales Johnston used? Bill Alves' was my favorite piece on the tape swap, and I think its strengths are rhythm and harmony. The harmonic basis for the melody was strong enough that even the few awkward melodic passages can sound somehow "right," though in a very exotic sort of way.