source file: mills3.txt Date: Sat, 20 Dec 1997 07:14:24 +0100 Subject: Mckyyy's LCMs From: Gregg Gibson Mckyyy said: > There are many ways to arrive at the "most consonant" just > intervals. The following is the output of a program that > approaches that subject from the perspective of least common > multiple. As most of you must know by now, I favor this as a > measure because it correlates with a physical property of the > composite sound, i. e. the length of the pattern. Also, the > concept is independent of "limits" as in 5-limit, 7-limit, etc. I vaguely recall something in Mersenne to this effect, back in the 17th century; Euler used this principle also, I think, but maybe in a different context. It certainly is one of the traditional methods of evaluating consonance. It definitely has problems though, but perhaps not insuperable problems. For example, 9:2 is certainly not consonant, even though the product of its ratio members is less than that of 5:4 for example. But probably my comments are nothing new to you. I tried to use this once, but could never reconcile my ears with the resulting numbers. But there may be a way. SMTPOriginator: tuning@eartha.mills.edu From: Aline Surman Subject: personal insights PostedDate: 20-12-97 09:56:08 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: 20-12-97 09:54:00-20-12-97 09:54:01,20-12-97 09:53:35-20-12-97 09:53:36 DeliveredDate: 20-12-97 09:53:36 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 C1256573.0030E1C3; Sat, 20 Dec 1997 09:55:51 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA22539; Sat, 20 Dec 1997 09:56:08 +0100 Date: Sat, 20 Dec 1997 09:56:08 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA22576 Received: (qmail 17481 invoked from network); 20 Dec 1997 00:56:05 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 20 Dec 1997 00:56:05 -0800 Message-Id: <349B90AB.2971@dnvr.uswest.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu