source file: mills3.txt Date: Mon, 3 Nov 1997 19:27:34 +0100 Subject: RE: Erlich's Theory From: "Paul H. Erlich" >>So correct me if I'm wrong, but doesn't this tend to support that measuring >>the cent detuning of Just intervals does not messure change in dissonance? > >The harmonic entropy curve, like the Plomp-Levelt roughness curve for tones >with harmonic partials, has local minima at small-integer ratios. It is >standard in physics (and justified by calculus) to approximate any local >minimum with a parabola. Therefore, near a just ratio, the change in >dissonance is proportional to the squared detuning. > >>Wouldn't it also tend to support that a 2 cent detuning of the 19/16 could >>produce "a first-order qualitative difference"? > >No, because there is rarely, if ever, a local minimum at 19/16. However, in a >tuning based on the 16th-32nd harmonics, there will be a massive accumulation >of combination tones reinforcing the sense of the missing fundamental, so >detuning any note will be quite noticeable. SMTPOriginator: tuning@eartha.mills.edu From: "Paul H. Erlich" Subject: RE: TUNING digest 1225 PostedDate: 03-11-97 20:28:27 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 20:27:24-03-11-97 20:27:25,03-11-97 19:27:50-03-11-97 19:27:50 DeliveredDate: 03-11-97 19:27:50 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 C1256544.006ADE33; Mon, 3 Nov 1997 20:27:17 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01534; Mon, 3 Nov 1997 20:28:27 +0100 Date: Mon, 3 Nov 1997 20:28:27 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01532 Received: (qmail 28877 invoked from network); 3 Nov 1997 11:28:21 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 3 Nov 1997 11:28:22 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu