source file: mills3.txt Date: Mon, 3 Nov 1997 20:28:27 +0100 Subject: RE: TUNING digest 1225 From: "Paul H. Erlich" Paul Fly wrote, >Also, I'm interested in learning more, but need a primer on the >mathematical aspects (ie, what is "5-limit" exactly, etc), any >suggestions? I think it is fair to say that Harry Partch's _Genesis of a Music_, for all its inconsistencies, forms a common grounding for a great many of us on this list in our discussions. By the way, I intend to model Partch's "one-footed bride" with a sort of octave-equivalent harmonic entropy function; that is, rather than using a Farey series (or a series such as used by Mann where the sum of numerator and denominator does not exceed a certain limit), using instead the ratios up to a given Partch limit ("odd limit", that is, the largest odd factor of either the numerator or denominator does not exceed a certain limit). Instead of letting the order of the Farey series approach infinity, I will let the odd limit approach infinity, and I expect that for some realistic assumption about pitch resolution, the one-footed bride will emerge. SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: RE: Erlich's Theory PostedDate: 03-11-97 20:43:54 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: 03-11-97 20:42:54-03-11-97 20:42:55,03-11-97 19:43:20-03-11-97 19:43:20 DeliveredDate: 03-11-97 19:43:20 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 C1256544.006C482D; Mon, 3 Nov 1997 20:42:43 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01539; Mon, 3 Nov 1997 20:43:54 +0100 Date: Mon, 3 Nov 1997 20:43:54 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01537 Received: (qmail 230 invoked from network); 3 Nov 1997 11:43:48 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 3 Nov 1997 11:43:48 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu