source file: mills2.txt Date: Mon, 29 Jul 1996 13:16:22 -0700 Subject: Reply to John From: COUL@ezh.nl (Manuel Op de Coul) > A relation simpler than either Sauveurs or Henflings is the one > Blackwood uses, the relation of the whole tone to the diatonic > semitone. The octave has 5T+2D steps. When d is 0, one gets > 5-tet, when T and D are both 1, 7 steps, when 2:1, 12; 3:2, 19; > 5:3, 31; 3:1, 17; 4:1, 22 4:3, 26; etc. To which might be added that Sauveur's table of 1711 consists of divisions which have the chromatic 12-tone scale embedded in them and hence the diatonic scale too. The connection between Sauveur's and Blackwood's relation is rather simple. The comma plus the chromatic semitone is the diatonic semitone and the chromatic semitone plus the diatonic semitone is the whole tone. So for instance if the ratio comma:chromatic semitone is 2:3 (for 50-tET), then the next is 3:5 and thus D:T is 5:8. > Hypocaffeinemia this AM, alas. With American coffee, that means lots of drinking :-) Manuel Op de Coul coul@ezh.nl Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 30 Jul 1996 07:57 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA13755; Mon, 29 Jul 1996 22:57:51 -0700 Date: Mon, 29 Jul 1996 22:57:51 -0700 Message-Id: <199607300555.WAA04902@dnai.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu