source file: mills2.txt Date: Thu, 27 Feb 1997 15:02:07 -0800 Subject: Happy 1000th,Aristoxenos From: John Chalmers I'd like to second Adam's comments and express my appreciation to David Madole (and Greg Higgs) for starting and administering the Tuning List for the past three years. The accumulated digests, Bibliography, and other FTP files, etc. are a unique resource containing information accessible only with difficulty elsewhere, if at all. Some comments on recent digests: Plomp and Levelt's model is simpler to program and computes faster than Kameoka and Kuriyagawa's. I'm told they give essentially the same results as far as predicting the relative dissonance of intervals in specific timbres. As for the use of 5/4. Eratosthenes, who may be responsible for the linear misinterpretation of Aristoxenos's parts, used 19/15 as his enharmonic ditone. By Ptolemy's time, the enharmonic was no longer used in popular music except as a semitonal pentatonic produced by gapping the diatonic sequence (Winnington-Ingram, Mesomedes hymns, etc.) Frankly, I'm somewhat suspicious of Ptolemy's enharmonic and chromatic genera as they have a rough 1:2 division of the pyknon (Barbera), even if it meant that he had to reorder the intervals resulting from "katapyknosis" to obtain usable superparticular ratios. But, I do agree that the kithara and lyra tunings probably represent practice. I also find his Equable Diatonic interesting as it resembles extant 3/4-tone Islamic diatonic tunings. Aristoxenos's (or Cleonides's) parts are still used by the Eastern Orthodox Churches to describe their tetrachords, though at one time another system of 68 parts to the octave, 28 to the fourth was in use. (Savas, Xenakis, Athanasopoulos, Tiby, etc.). I do not know the origin of this system, however. I would agree with Dan that Aristo was a cognitive (proto)scientist more concerned with perception rather than mathematical niceties. Whatever he might have met, his scales are certainly worth hearing and using, even if we tune them to some 0 mod 12 ET or even try to interpret them as Ptolemy and Eratosthenes did as linear division. I think he may also be a witness for his own contemporary practice as he gives scales plausibly interpretable as Archytas's and the old Pythagorean forms. He may also have been documenting the various tuning of the relatively new chromatic genus. Kathleen Schlesinger also understood Aristoxenos to mean the 9/8 tone, but she then fantasically interpreted his genera in terms of a part of 17+ cents and a fourth of 510+ cents to try to make it agree with theories. Has anyone actually tried repeating his experiment on a replica kithara without tuning machines? I suspect it wouldn't be hard to loose the comma in the chain of intervals. I don't have copies of Barker's books handy and I would appreciate it very much if someone could send me (or post) the "planetary scales" in the several genera. I would like to check them against a list of correspondences with KS's harmoniai as used by the Anthroposophists, including Elsie Hamilton. Winnington-Ingram states that Censorinus and Pliny list planetary scales which resemble the Dorian and Phrygian of Aristides Q. with chromatic, rather than enharmonic, intervals. It would be interesting to see if Steiner's correspondences are the same as the Greek theorists and writers, but I am unable to get either the classical or Steiner's texts at the moment. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 28 Feb 1997 00:05 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA32458; Fri, 28 Feb 1997 00:05:12 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA32445 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id PAA11539; Thu, 27 Feb 1997 15:03:01 -0800 Date: Thu, 27 Feb 1997 15:03:01 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu