source file: mills3.txt Date: Tue, 4 Nov 1997 18:10:32 +0100 Subject: Dare to Square From: Carl Lumma >>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. Does this mean that you're going to go over to squared detuning? Are you sure we should be squaring logorithmic measures of detuning? Parabolas aside, my original warning regarding cent-detuning was that you can bump into other low-number ratios without knowing it. We got into this 19/16 thing because I said that 16 cents flat of a 6/5 we have old 300, and 18 cents flat we have 19/16. By cents-detuning, the 19/16 is worse than the 300 cent interval. By cents detuning squared it'd still be worse. Even if you don't agree there's a difference between 300 and 19/16, it doesn't make the 19/16 worse than the 300. But there must be more-better examples. Maybe: the 12TET minor 7th is 18 cents flat of a 9/5, and 22 cents south of the 9/5 we have 16/9. |-----------------------------------------| | Carl Lumma | | http://users.nni.com/source_of_goodness | |-----------------------------------------| SMTPOriginator: tuning@eartha.mills.edu From: Carl Lumma Subject: Misc 2 PostedDate: 04-11-97 18:16:48 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: 04-11-97 18:15:43-04-11-97 18:15:44,04-11-97 17:16:07-04-11-97 17:16:08 DeliveredDate: 04-11-97 17:16:08 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 C1256545.005ED042; Tue, 4 Nov 1997 18:15:37 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02374; Tue, 4 Nov 1997 18:16:48 +0100 Date: Tue, 4 Nov 1997 18:16:48 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA02372 Received: (qmail 2033 invoked from network); 4 Nov 1997 09:16:44 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 4 Nov 1997 09:16:44 -0800 Message-Id: <19971104171940500.AAA335@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu