source file: mills3.txt Date: Thu, 20 Nov 1997 20:54:36 +0100 Subject: RE: The severity of scale From: "Paul H. Erlich" > >>>>Does this mean that you're going to go over to squared detuning? >> >>>Go over from where? I used squared error as the loss function to calculate >>>optimal meantone temperaments and the quality of equal-tempered >>>approximations in many posts here. When I said that the maximum error was >>>20 >>>cents, would it have made any difference to say that the maximum squared >>>error is 400 cents squared? No, it would have just made me sound silly. > >>Actually, the difference between squared detuning and regular detuning is >>quite important: > >I agree -- thus my loss function. By absolute detuning, quarter-comma >meantone is optimal. > >>it means that our intervals get worse exponentially. > >You mean quadratically (very different!). > >>The >>regular, "cents detuning" method strongly implies arithmatic worsening. > >Right. The rate of beating is one quantity that does, in fact, increase >linearly with absolute detuning. SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Carl's opinion on FPI tuning PostedDate: 20-11-97 22:22:38 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: 20-11-97 22:21:17-20-11-97 22:21:18,20-11-97 22:21:24-20-11-97 22:21:24 DeliveredDate: 20-11-97 22:21:25 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 C1256555.00754996; Thu, 20 Nov 1997 22:21:05 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04250; Thu, 20 Nov 1997 22:22:38 +0100 Date: Thu, 20 Nov 1997 22:22:38 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA04255 Received: (qmail 18036 invoked from network); 20 Nov 1997 13:22:35 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 20 Nov 1997 13:22:35 -0800 Message-Id: <19971120212418359.AAA291@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu