source file: mills2.txt Date: Thu, 21 Nov 1996 13:06:42 -0800 Subject: Re: Discussion on "Reply to Gary Morriso From: PAULE Hello, Heinz! Unfortunately I don't know German, but I would like to share with you the article by Pierce, Roberts, and Matthews in _Harmony and Tonality_ (proceedings of the Royal Swedish Academy of Music, edited by J. Sundberg). Other articles in the book mention your scale. Randy Winchester has done a good job composing/improvising in it. I don't think he uses square waves, but Enrique Moreno and I agree that this doesn't matter as much as Pierce first thought it would. (Did you discuss overtone structure in your original article?) Manfred Schroeder describes "Pierce's scale" alongside "Bach's well-tempered scale" in his truly wonderful book, _Fractals, Chaos, Power Laws_, and the footnote is to the article "Theoretical and experimental explorations of the Bohlen-Pierce scale." J. Acoust. Soc. Am. 84, 1214-1222. Before I knew of these scales, I had recognized 7-limit chords such as 3:5:7 as consonant and found a scale (based on normal octaves) from which they could be derived. This is described in a paper I am currently completing and which will appear in Xenharmonikon 17. I don't believe that major or minor thirds were heard, even unconsciously, as anything other than the dissonant intervals they were in the early and middle Middle Ages. I do believe, however, that triadic harmony makes the diatonic scale easier to use and understand, since three (not necessarily all major) complete consonant triads do give you the whole scale. My scales have this property as well, using complete consonant tetrads . . . Heinz, what subset of the 13 notes do you feel is the best analogy to the major scale? Pierce, et al describe the mode 0 1 3 4 6 7 9 10 12 (13). Did you come up with this? -Paul Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 21 Nov 1996 23:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02963; Thu, 21 Nov 1996 23:04:37 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA02962 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA03715; Thu, 21 Nov 1996 14:04:34 -0800 Date: Thu, 21 Nov 1996 14:04:34 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu