source file: mills2.txt Date: Wed, 18 Oct 1995 10:58:57 -0700 Subject: Approximations, Mongolian music From: "John H. Chalmers" Some good sources for historical methods of approximating roots and 12-tet are these, especially the first, for both geometrical and arithmetic techniques. Barbour also suggest choosing a simple ratio for the tempered major third or minor sixth and taking square roots and quotients. Suggested ratios are 100/63, 27/17 and 19/12. Barbour also states that Johann Faulhaber (1630) was the first person to use logs to calculate the 12th roots of 2. The first to publish ET in Europe was Simon Stevin (1586). Barbour, J. Murray. 1951. Tuning and Temperament, Michigan State College Press, East Lansing, reprinted 1953, 1961. Heath, Sir Thomas. 1921. A History of Greek Mathematics, Volumes I and II. Dover Edition, 1981. Dover Publications, Inc. New York. See also Neubauer , Otto (?, Neuberger, etc.) The Exact Sciences in Antiquity. Sorry I don't have a better reference to this book. I may be wrong, but I had thought that the historical Mongolian scale was diatonic and Chinese pentatonic with the pien-tones added later. BTW, Contemporary Mongolian music sounds like C&W (I'm not kidding, a troop visited Berkeley in the late 1980's) and played a mixture of musics, some diatonic, some pentatonic. The vocal style was largely male falsetto with heavy tremolo rather than vibrato. --John Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 19 Oct 1995 10:28 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id BAA20769; Thu, 19 Oct 1995 01:27:53 -0700 Date: Thu, 19 Oct 1995 01:27:53 -0700 Message-Id: <951018222829_127336397@emout04.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu