source file: m1588.txt Date: Fri, 20 Nov 1998 15:48:32 -0500 Subject: RE: Triads, tuners, tonality From: "Paul H. Erlich" Hello Daniel Wolf and thank you for your intelligent comments. I will reply to them below and hope that you will consider my replies with an open mind. I see no need for the hostile tone that our arguments often take on and I apologize if I have contributed to that tone in the past. >I have witnessed both Balzano and Babbitt demonstrate virtuoso >aural command over the tonal materials in their respective systems (Balza= >no >in 20tet, Babbitt in 12tet), demonstrating convincingly that 'set and >group' properties are not just abstract constructions but real resources >for organizing musical works. I don't doubt it -- but it must have taken them some compositional ingenuity to avoid the tonal implications of simple intervals in order to make these other features reign. Where can I get Balzano's music to listen to? >Hearing highly structured, non-tonal music = Balzano's system is supposed to be as "tonal" as traditional diatonic music, according to his theory. He explicitly rejects the important of simple ratios, except (implicitly) powers of two, in the development of Western tonality and tuning. That is the point where I exclaim, "bunk!" Similarly for Clough&Douthett with respect to Indian music. . . >in >these temperaments may not reflect the modes of audition closest to the >biases of the physiological system, but it does remind one that the physi= >cs >of musical intervals has no such bias and that musical cognition, with >training, can be a far richer resource than the ear alone. (In different >domains, the works of Alvin Lucier are constantly demonstrating that the >frequencies in the margins between rhythm and pitch or pitch and timbre a= >re >both perceivable and musical rich.) I prefer to build cognition upon, rather than reject, the biases of the psychological system. Music that is "out," i.e., far from tonal, can fascinate me for long periods of time, but once in a while I break down and want to hear something that pleases me on a visceral, almost precognitive level. >If Mr. Erlich has a formula for determining the relative strength of an >"organizing force in music", I would certainly like to know it. Naturally= >, >this should be independent of any local cultural biases. = Clearly this is absurd, perhaps some kind of mockery of my quantitative bent. I did say "the music I enjoy". Therefore I can't declare myself independent of local cultural biases (but then again neither can anyone else). >I can't help but note that I find it surpring that Mr. Erlich is framing >his argument in this way. His own work in 22tet is within a systwm whose >set and group properties are certainly more useful than the quality of it= >s >representation of ratios of small whole numbers. = Please elaborate. If you mean the properties I describe in my paper, note that virtually all these properties presuppose representations of ratios of small whole numbers. If you don't mean those, then which ones do you mean? Also note that 22tET's representation of 7-limit ratios is about as good as 12tET's representation of 5-limit ratios, and that 12tET evolved in, and largely superceded the authentic tunings of, a musical style where 5-limit ratios were of primary importance (it could do so because the quality of its approximations was sufficient). I do examine non-ET 7-limit tunings which contain the scales in my paper, but find that they are optimally tuned very close to 22tET. The impetus for choosing an ET rather than an open, meantone-type system is certainly a "group" property, that of infinite transposability with a finite number of notes. I would be more than happy to advocate a non-ET, open 7-limit tuning if it had any significant acoustical advantages over 22tET. It doesn't. On the other hand, meantone is audibly superior to 12tET for 5-limit diatonic music, and the important group property of transposability can be recovered for meantone in 19 or 31tET. Musicians chose 12tET over 19 or 31tET only for convenience. Therefore, for Balzano or Clough to ascribe features of tonal practice (ones that date back to the meantone era) to properties of 12 which are not shared by 31, amounts to a sort of revisionism that I object to.