source file: m1586.txt Date: Wed, 18 Nov 1998 18:38:54 -0500 Subject: reply to Stephen Soderberg From: "Paul H. Erlich" I haven't been taking about triads too much -- mostly "consonant" tetrads and pentads -- but suffice it to say that I feel the Balzano/Clough/Douthett approach to scales is bunk. The acoustical nature of simple intervals is a much stronger organizing force in music (at least the music I enjoy) than abstract set and group constructs. Harry Partch devoted his life to exploring microtonality and the results he puts forward are not to be taken lightly. For the most part, he is in agreement with a millenia-old tradition of musician/mathematicians for whom the acoustical "pull" of simple ratios is undeniable. At present, at least three distinct psychoacoustical phenomena have been identified which contribute to this impression, and octave equivalence is a fourth factor which Balzano happily accepts while rejecting the others. Partch has shown that music with a simple-ratio basis need not be backward-looking, but can be as exciting and unexpected as any 20th century music. It is heartening that most on this list seem to understand that there is a relationship between frequency ratios and consonance and are not content to choose frequencies just because their logarithms make pretty necklace-like patterns (although that can be important too).