source file: mills3.txt Date: Thu, 29 Jan 1998 18:21:03 +0100 Subject: 60 vs 45 From: Carl Lumma Paul & All, While I agree that equilateral triangles work better than squares for modeling triads, I still feel much better with right angles in 3D (7-Limit). For one thing, while both triangles and squares tile a plane, tetrahedrons aren't space-filling like cubes. For another, one of my favorite 12-tone piano-mappable tunings doesn't work with 60 degree angles... 1/1 21/20 35/32 6/5 5/4 21/16 7/5 3/2 8/5 105/64 7/4 15/8 With squares, this looks like two rectangular prisms, one on top of the other. With tetrahedrons, you wind up with a problem... 5/4-------15/8 / \ . / / . \ / / \ / 1/1-------3/2 ..The dots (7/4 and 21/16) are a 3/2 apart, but are not represented by the same length or direction as the other 3/2's in the diagram. What to do? Carl SMTPOriginator: tuning@eartha.mills.edu From: Paul Hahn Subject: Re: 60 vs 45 PostedDate: 29-01-98 18:30:34 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 29-01-98 18:29:47-29-01-98 18:29:48,29-01-98 18:28:32-29-01-98 18:28:33 DeliveredDate: 29-01-98 18:28:33 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125659B.006017B3; Thu, 29 Jan 1998 18:29:35 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01763; Thu, 29 Jan 1998 18:30:34 +0100 Date: Thu, 29 Jan 1998 18:30:34 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01761 Received: (qmail 21541 invoked from network); 29 Jan 1998 09:29:47 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Jan 1998 09:29:47 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu