Reply to Enrique Moreno, similarity of powers of 3

----------
> 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.


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>up and halves with each octave transpose down. The tuning maps into an
>exponential table, which is stored as 128 steps per semitone or 1536 steps
>per semitone.

Whoops, that's 1536 steps per OCTAVE.

Steve Curtin
Ensoniq Corp


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