source file: mills2.txt Date: Fri, 28 Feb 1997 07:02:03 -0800 Subject: Re: Happy 1000th,Aristoxenos From: UPB_MONIODIS@online.emich.edu On Thu, 27 Feb 1997 15:02:22 -0800 John Chalmers wrote: >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. It had two imperfect fourths of 494 cent as tetrachords, connected by a whole tone of 212 cents. It was not the original intent of the designer, Abp Chrysanthos, for the imperfect fourths, but mistaken calculations (building the tetrachord from the whole tone). As Barbour says regarding Agriola, ("... like many another good man, confused geometrical with arithmetical proportion" p 152). The tetrachord is now set at 4/3 and the morion at the 30th root thereof. Polychronios N. Moniodis Eastern Michigan University Ypsilanti, MI Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 1 Mar 1997 04:03 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01001; Sat, 1 Mar 1997 04:03:08 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA00401 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id TAA16465; Fri, 28 Feb 1997 19:01:12 -0800 Date: Fri, 28 Feb 1997 19:01:12 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu