source file: mills3.txt Date: Thu, 29 Jan 1998 21:41:27 +0100 Subject: Re: TUNING digest 1312 From: Carl Lumma (Graham Breed) >I've worked out that Paul Erlich's Pentachordal modes can be >written as 10 JI notes plus three commas of 50/49. You wouldn't mind posting them? (Paul Hahn) >You don't need the tetrahedra to fill space. The lattice fills space >perfectly fine (if you look at the Voronoi cells of the vertices, >they're rhombic dodecahedra, which _do_ fill space); but instead of >dividing space up into cubes you get alternating tetrahedra and >octahedra. > >In crystallography this relationship is called "face-centered cubic >close-packing" and is quite common. > >I believe this structure was actually patented by Buckminster Fuller >under the name "Octotruss". The tetrahedra and octahedra space-filling combo is called the face-centered cubic. Fuller called it both the 'isotropic vector matrix' (in general) and the 'octet truss' (for architecture). I don't know what a Voronoi cell is, but if you center a unit sphere on each point in the face-centered cubic, then each sphere will touch all 12 faces of a rhombic dodecahedron right in the middle, and the rhombic dodecahedra will fill the space. But the face-centered cubic isn't regular, and the rhombic dodecahedron has too many verticies. >This isn't right--21/16 should be plotted, not where you have it, but >like this: > > 5/4-------15/8 > / \ / > / . \ / . > / \ / > 1/1-------3/2 > >in which case the spatial/visual relationship between pitches 3/2 apart >is preserved. Ah... I've got a tensegritoy model right here. The tops don't look like this to me. Carl SMTPOriginator: tuning@eartha.mills.edu From: Paul Hahn Subject: 60 vs 45 (90, really) PostedDate: 29-01-98 22:21:40 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 22:20:47-29-01-98 22:20:48,29-01-98 22:19:32-29-01-98 22:19:32 DeliveredDate: 29-01-98 22:19:32 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.00753FD8; Thu, 29 Jan 1998 22:20:40 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01931; Thu, 29 Jan 1998 22:21:40 +0100 Date: Thu, 29 Jan 1998 22:21:40 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01929 Received: (qmail 28170 invoked from network); 29 Jan 1998 13:20:51 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Jan 1998 13:20:51 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu