source file: mills2.txt Date: Fri, 19 Jul 1996 14:11:03 -0700 Subject: RE: Digest 600, XH16 article, Brian From: PAULE I have seen neither TD 600 nor XH16, but I thought I'd throw in my 21.5 cents: Paul Rapoport wrote: >10. <22-tET has nothing in common with traditional tunings.> Does anyone >agree with this? Well, in Paul Rapoport's point of view, 22 would fall into the same category as 27, 41, 46, and 53, where syntotic comma (81:80) displacements are necessary to get good thirds, and if 27, 41, 46, or 53 is traditional, then so is 22. Paul Rapoport's notation probably deals with 15 and 34 in the same way. Is this correct? However, I'm not aware of much of a "tradition" of notating comma displacements in actual musical practice, so I'd have to say the only traditional tunings are 12, 19, 31, 43, 50, 55, etc. I have a feeling I would have a bigger problem with Paul Rapoport's system, since it seems the minor third and its purity are being ignored. It's that consistency issue again. If the best approximation of the perfect fifth minus the best approximation of the major third is not the best approximation of the minor third, a notation based on just 5-limit intervals is not appropriate for the tuning. In 20tet, for example, the perfect fifth is 12 steps, and the closest approximation to the major third is 6 steps, so should the minor third be 6 steps too? No, 5 steps is a far better minor third. This seems to be a fatal blow to notating 20tet with Pythagorean scales and syntotic commas. However, I should shut up now because I haven't read Rapoport's article. Getting back to 22tet, I've written a paper on it, which includes a very convenient method of notating 22tet based on 7-limit harmony. While traditional notation and musical practice benefit from the vanishing of the syntotic comma in traditional tunings, 7-limit notation and practice will benefit from the vanishing of the septimal comma (64:63) in 22tet. This paper is in the process of being rethunk for the purposes of publication, but I've been e-mailing around a summary of my current ideas to a few tuning list members in exchange for additions to my music collection. Any more takers? Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 19 Jul 1996 23:48 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA12785; Fri, 19 Jul 1996 14:47:09 -0700 Date: Fri, 19 Jul 1996 14:47:09 -0700 Message-Id: <62960719214326/0005695065PK3EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu