source file: mills2.txt Date: Tue, 8 Oct 1996 03:30:41 -0700 Subject: Re: Reply to Enrique Moreno, similarity of powers of 3 From: "Enrique Moreno" ---------- > From: PAULE > To: eig@ccrma.Stanford.EDU > Subject: Reply to Enrique Moreno > Date: Monday, October 07, 1996 9:02 AM > > > Enrique- > > While at Yale, I read your book and listened to your tape. I thought it > interesting that you pointed out that you did not yet fully hear the > equivalency that your theory attributes to "morenoctaves." Has your feeling > changed any? Yes. I "got it" one day, when I realized that *similarity* is not octaveness, or "fifthness" or "twelfthness" or any *sensation* associated with a common interval, but some sort of capacity of the mind to to switch inner gears, to see the more abstract level within a pattern already categorized. In other words, it is a cognitive operation, not a psychoacoustical one. For That's why the main goal of the Stanford experiments was to establish if trained musicians can have an *spontaneous* sense of expanded chroma given the appropriate musical context --and if so, to what extent. In this sense, and although I used some (heavily edited) sections of the book as a basis, the final report's (dissertation) emphasis is on *categorical* perception, rather than sensorial or process-oriented perception. It is the context, and only the context (a complete "meaningful" fragment of complying music) what really triggers the possibility of "perceiving, if you will, the hidden geometry which we call similarity, and which is the subtance of --but goes beyond-- octaveness. What is fascinating about the experiments (appart from being my magnus opus, of course, :) )is that "similarity" "equivalence' or the like are never mentioned to the subjects, who had to perform matching tasks without the use, benefit, or help of pre-established verbal categories that could be associated in their minds to an overlearned sensorial category (like "total similarity of tones" to "octaveness"). Of course the twelfth (and multiples) has been an always-present interval in the Western polyphonies, but again, only within the context of our usual 7 diatonic categories --and later chromatic inflexions. That's why the tuning A-12 (12 equal divisions of powers of three) helps the unaware listener to *decontextualize* the learned categorical system, and by strictly avoiding approximations to powers of two the musical context (if effective and complying) compells some sort of information-reduction mechanism to re-categorize and "find" the solution. The moral of the story is that you cannot "find" the solution if you already believe that you know "the" (only) solution. In this latter case, the result is perceived nonsense. Enrique >using square waves helps bring >this out. However, there is no denying that even an out-of-tune octave, even >with square waves, will be heard as more of an equivalence than 3:1. PS Square waves, or any other particular overtone structure, again, were uncorrelated to resuts. Why? Simply remember that the cognitive domain, where the "similarity" operation is accomplished (for both octaves and "morenoctaves" --which are not just simply powers of 3 but psychological categories), must not be confused with the psychoacoustical domain --where squre waves live. This confusion of domains, to which unfortunately most researchers with a physical bacground are prone (including one of my thesis advisers, John Pierce) is the downfall of anyone trying to understand a *musical* phenomenon. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 8 Oct 1996 15:05 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00436; Tue, 8 Oct 1996 14:06:41 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA00434 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA28715; Tue, 8 Oct 1996 06:06:37 -0700 Date: Tue, 8 Oct 1996 06:06:37 -0700 Message-Id: <199610081302.JAA15391@cerberus2.Ensoniq.Com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu