source file: mills3.txt Date: Fri, 19 Dec 1997 19:10:08 +0100 Subject: Limit From: "Paul H. Erlich" >}>In each series below, each term represents the number of notes in the >}>simplest equal temperament that improves upon the accuracy of the >}>previous one. Tunings in parentheses are the second-best for up to that >}>many notes. I don't go beyond 200TET. Accuracy is defined with respect >}>to JI in the indicated odd limit; equal temperaments not consistent >}>within the given limit are excluded. > >}This chart ROCKS! Could you tell us more about how you define "limit"? > >Limit can refer either to a standard of consonance or the design of a just >tuning system. In the latter usage, a prime number characterizes the largest >prime number occuring as a factor in any of the just ratios. When referring >to a standard of consonance, it usually refers to the largest ODD factor in >all the ratios considered consonant. Partch usually used it in this way, as >he subscribed to a fairly strong form of octave equivalence. As it happens, >Partch's music can be called 11-limit using both definitions. I was using the >standard of consonance definition in this chart. I have already posted on >consistency, otonal limit, utonal limit, and saturated chords; unfortunately >I don't think an archive exists for the last two years of the digest. SMTPOriginator: tuning@eartha.mills.edu From: Johnny Reinhard Subject: Re: My Friends the Aliens PostedDate: 19-12-97 19:12:31 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: 19-12-97 19:10:23-19-12-97 19:10:23,19-12-97 19:09:59-19-12-97 19:10:00 DeliveredDate: 19-12-97 19:10:00 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 C1256572.0063D22B; Fri, 19 Dec 1997 19:12:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19893; Fri, 19 Dec 1997 19:12:31 +0100 Date: Fri, 19 Dec 1997 19:12:31 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA19849 Received: (qmail 12624 invoked from network); 19 Dec 1997 09:54:02 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 19 Dec 1997 09:54:02 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu