source file: mills3.txt Date: Sun, 24 Aug 1997 17:23:31 +0200 Subject: Doubly Positive systems From: John Chalmers "Doubly Positive," is a term from Bosanquet's General Theory of the Octave and refers to regular cyclic systems whose fifths are sharper than 12-tone equal temperament and of which the difference between 12 fifths and 7 octaves (B#-C) is 2 degrees. Another way of expressing this is that the difference between the 5-fifths semitone (B-C) and the 7-fifths semitone (C-C#) is 2 degrees. The doubly positive systems are 10, 22, 34, 46, 58, 70.....10+M*12 where M-2 is the number of degrees between C and C#. For, 22-tet M is 3 degrees and 22-tet is described by Wilson as a doubly-positive, ternary system. Other ternary systems are 29, 36, 43 and 50-tets. --John SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net Subject: Re: syntonic and skhismatic notation PostedDate: 24-08-97 17:16:58 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 28-08-97 09:57:42-28-08-97 09:57:43,28-08-97 09:55:16-28-08-97 09:55:17 DeliveredDate: 28-08-97 09:55:17 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564FD.0053F089; Sun, 24 Aug 1997 17:16:50 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA20453; Sun, 24 Aug 1997 17:16:58 +0200 Date: Sun, 24 Aug 1997 17:16:58 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA20447 Received: (qmail 26792 invoked from network); 24 Aug 1997 15:16:54 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Aug 1997 15:16:54 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu