source file: mills3.txt Date: Fri, 12 Dec 1997 14:44:44 +0100 Subject: RE: Oops... back to school for me From: "Paul H. Erlich" >I've obvioulsly got my hands full with 22, but I noticed the other day >that (more or less) the 3/2 +/- 7 cents gives 19 & 22, +/- 5 cents >gives 31 & 34 -- two meantone and two commaful temperaments, and that >19 + 22 gives 41 and 31 + 34 gives 65, both with a 3/2 less than 0.5 >cents off just. What I've heard of 31 never "did" it for me, and I'll >have to wait to get Neils new CD to hear 34. Did you notice this: The 3/2 in 22TET is off by .1308 degrees. The 3/2 in 19TET is off by -.1143 degrees. The 3/2 in 41TET (= 19+22) is off by .0165 (= .1308 - .1143) degrees. I noticed this in 1991. More examples: The 3/2 in 7TET is off by -.0947 degrees. The 3/2 in 5TET is off by .0752 degrees. The 3/2 in 12TET (= 5+7) is off by -.0196 (= -.0947 + .0752) degrees. In 27TET, the 3/2 is off by .2060 degrees, and the 5/4 is off by .3079 degrees. In 26TET, the 3/2 is off by -.2090 degrees and the 5/4 is off by -.3701 degrees. In 53TET (= 26+27), the 3/2 is off by -.0030 (= .2060 - .2090) degrees, and the 5/4 is off by -.0622 (= .3079 - .3701) degrees. 53 is also 31+22, 34+19, and 41+12, which shows that the errors in these pairs of tunings are nearly equal and opposite when measured in degrees of the tuning. SMTPOriginator: tuning@eartha.mills.edu From: alves@orion.ac.hmc.edu (Bill Alves) Subject: Re: 22-tone equal, reply to Ehrlich PostedDate: 12-12-97 19:56:33 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: 12-12-97 19:54:37-12-12-97 19:54:38,12-12-97 19:54:21-12-12-97 19:54:21 DeliveredDate: 12-12-97 19:54:21 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 C125656B.0067DDBB; Fri, 12 Dec 1997 19:56:26 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14029; Fri, 12 Dec 1997 19:56:33 +0100 Date: Fri, 12 Dec 1997 19:56:33 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA13430 Received: (qmail 4000 invoked from network); 12 Dec 1997 10:56:29 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 12 Dec 1997 10:56:29 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu