source file: mills2.txt Date: Wed, 17 Jul 1996 09:51:55 -0700 Subject: from McLaren From: John Chalmers From: mclaren Subject: Paul Turner's ideas on xenharmonic theory & Geralrd G. Balzano's group theoretic micrtonal ideas --- The talented Australian composer Paul Turner recently wrote me a letter in which he described some provocative ideas about microtonality. Paul's ideas were based on group theory. Because different equal temperaments exhibit different cyclic rotational properties, Paul pointed out that a number of different tunings which appear outwardly dissimilar share underlying structural properties. This idea is particularly interesting because Paul appears to have arrived at it independently. Gerald G. Balzano also came up with similar ideas about 15 years ago. His best-known paper is his Computer Music Journal article "The Group Theoretic Structure of 12-fold and Microtonal Tunings." Balzano's CMJ paper is interesting insofar as it distills a number of properties which Balzano sees as definitive of the major mode in Western music. He then goes on to show that tunings of the form (N)*(N+1) satisfy this criterion. Thus for N = 3 Balzano's theory gives a 12-TET scale; for N = 4 Balzano's theory gives a 20-TET scale; and for N = 5 Balzano derives a 30-TET scale. He was able to show that all three scales exhibit similar melodic properties. This is an interesting idea because it proceeds solely from a consideration of the melodic properties of the scales in question. To my knowledge, the only only microtonal theorists who have put forth theories of microtona scales based solely on the melodic properties of the tunings in question are R. Vermeulen, Max Meyer and Boomsliter & Creel. The advantage of such a theory is that it reveals similarities between tunings which would otherwise appear to have nothing in common. The disadvantage of such a theory is that--because it's solely concerned with the melodic properties of scales--the harmonic properties of the scales thus generated tend to be unpredictable. In the case of the 20-TET and 30-TET scales, neither one has fifths particularly close to the value of the third member of the harmonic series. This is neither "good" nor "bad," of course, but it is certainly *different* from 12-TET...which has a perfect fifth which falls within 1/600 of an octave of the third member of the harmonic series. Thus, while the 20- and 30-TET systems will likely sound similar melodically to 12, they will sound harmonically very different. Paul Turner also recently sent me a number of piano pieces in 5, 7, 8 and 9 tones per octave. Why is it that the most interesting music being done today always seems to arrive in the mail on someone's cassette? Maybe someone can explain this to me. Whenever I buy a CD of the "latest" so-called "serious" contemporary music done in New York or Boston or some other high-powered place, the music usually sounds okay--it's generally performed with verve and gusto, and the acoustics are very nice. But the *really* interesting new music seems to come out of nowhere, from people I've scarcely heard of, on cassettes. There must be a good reason for this. Perhaps gobs of hard cash can't substitute for musical talent...? Nahhhhhh! This America. Gobs of hard cash can substitute for *anything.* As Bill Wesley remarked when I asked why the French and Germans and Japanese had bullet trains when we in the U.S.A. didn't: "This is America. We've got bullets, we don't need trains." --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 17 Jul 1996 20:42 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA10266; Wed, 17 Jul 1996 11:42:05 -0700 Date: Wed, 17 Jul 1996 11:42:05 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu