source file: mills2.txt Date: Sat, 30 Nov 1996 08:36:55 -0800 Subject: Error in Tuning and Temperament From: John Chalmers I've found another error in J. Murray Barbour's "Tuning and Temperament." Table 3 on page 16 is labelled "Eratosthenes' Enharmonic," though the ratios are those of Ptolemy's enharmonic genus (in the Dorian mode). I have just noticed that the decimal-fraction sexagesimal string lengths in the first line are also wrong. They are, in fact, those of Didymos's enharmonic, 1/1 32/31 16/15 4/3 3/2 48/31 8/5 2/1, though it is stated on page 21 that "Didymus' enharmonic is not included in the above tables." As Barbour states on p.21 elsewhere that the pyknon of Didymos's tuning was "resulting from an arithmetical division of the 16:15 semitone," this would seem to be a production error. The correct decimal-fraction sexagesimal string lengths for Ptolemy's enharmonic, 1/1 46/45 16/15 4/3 3/2 23/15 8/5 2/1, are 120.00 117.39 112.50 90.00 80.00 78.26 75.00 60.00 to two decimal places. There is another error on p.21, Table 21 where the name of Ptolemy's Diatonic Homalon is given as Hemiolion. BTW, the text Harry Partch used was Barbour's dissertation upon which this book is based. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 30 Nov 1996 17:47 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12633; Sat, 30 Nov 1996 17:49:06 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA12844 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA20615; Sat, 30 Nov 1996 08:49:03 -0800 Date: Sat, 30 Nov 1996 08:49:03 -0800 Message-Id: <961130114634_1784789785@emout17.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