source file: mills2.txt Date: Thu, 29 Aug 1996 15:03:08 -0700 Subject: Byzantine tuning, Kami reply From: John Chalmers RE Byzantine 68-tet: I don't think the Greek Orthodox Church really considered playing in 68-tet, but rather thought of constructing the tetrachords of its liturgical music in 28 parts rather like the Aristoxenian 30 parts of classical Greek theory. I found a number of such tetrachords in a book by Octavio Tiby, "La Musica Byzantina," Fratelli Bocia, Milan, 1938. The tetrachords are 12 +13+ 3; 12 + 5 + 11;. 12 + 9 + 7; and 9 + 12 + 7. In this system, the whole tone has 12 parts (212 cents), and the octave consists of two such tetrachords and 12 parts for the disjunctive tone. Hence the formula is 28 + 12 + 28 = 68 parts for the octave. 12 + 5 + 11 is a pretty fair "Phrygian" tetrachord, but 3 parts is roughly a 1/4-tone and 9 parts 3/4 of a tone. Other writers on Byzantine music, including Xenakis in "Musiques Formelles," give quite different tunings in the 30 parts-to-the-4th system. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 30 Aug 1996 00:17 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA06836; Fri, 30 Aug 1996 00:18:12 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA06694 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA16826; Thu, 29 Aug 1996 15:18:11 -0700 Date: Thu, 29 Aug 1996 15:18:11 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu