source file: mills2.txt Date: Mon, 23 Jun 1997 23:01:23 +0200 Subject: Octaves (Paul E) From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: "Paul H. Erlich" The fact that octaves are often not equal to 2, but slightly more than 2, has nothing to do with harmonic series or inharmonic partials. The effect is most pronounced when sine waves are used; I believe a large experiment found that the average subject deemed two sine waves equivalent when they differed by 1209 cents. The typical 2nd harmonic of a piano string is more like 1203 cents. I recently saw an interesting statement on a pretty reputable web page, which I found by following links from John Starrett's page. It claimed that the cochlea winds around once per octave. If this is true, a stimulation at one point in the cochlea may have secondary effects on parallel coils, and octave equivalence becomes a purely psychophysical, not cultural, phenomenon. Those of us who have tried to appeal to the universality of octave equivalence across cultures have been unable convince others among us that octave equivalence is not mere brainwashing. This, if true, may be another quiver in our arrow. We would hope that the true coiling rate, or the interval of gretest cross-stimulation, is 1209 cents rather than 1200 cents, as it would provide a direct explanation for the results of most experiments on the truly "equivalent" octave. Anyone know any physiological evidence for or against this statement? Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 24 Jun 1997 09:05 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA30790; Tue, 24 Jun 1997 09:05:44 +0200 Date: Tue, 24 Jun 1997 09:05:44 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA30789 Received: (qmail 24164 invoked from network); 24 Jun 1997 07:05:35 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Jun 1997 07:05:35 -0000 Message-Id: <33f73cd4.502064089@kcbbs.gen.nz> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu