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Are wedgies real?

🔗Mike Battaglia <battaglia01@...>

9/12/2011 5:47:11 AM

In my last post, I laid out a line of reasoning that attempts to
establish that learned categories don't just consist of harmonic data
(as many JI numerologists think), and that they don't also just
consist of scalar data (as Paul is sometimes fond of saying), but that
on the largest scale, they consist of associations made between scalar
and harmonic data. I used this reasoning to ultimately posit that
Western listeners literally figure out the fundamental pattern of
association between melody and harmony that meantone "is", and hence
internalize its mapping matrix, leading to not only the M3/A4
dichotomy but in general the percept of an interval "function."

If this is true, then something like a wedgie is a "real" thing,
because it's a direct mathematical representation of a particular
pattern of low-level cognitive harmonic-melodic associations. This
line of reasoning suggests that wedgies are real, and that every
temperament could lead to a "functional" experience, once you've
really gotten into the wedgie. (OK, I'll stop).

If it's true that harmonic and melodic associations are in fact
formed, this implies some "cues," much like Rothenberg propriety, that
may make scales easier to learn, all of which I'd like to test:

1) Melodic importance: If a tuning has strong harmonic properties, but
has very weak scalar or melodic properties, it will be more difficult
to learn, because the inability to establish a scalar position will
disrupt the process of expectation-forming.
2) Regularity importance: If a tuning has strong melodic properties,
but has weak harmonic properties such that a particular approximated
harmonic relationship appears twice - say a scale having having both
670 cent and 730 cent intervals at different generic interval classes
- it will be more difficult to learn, being perceived as an
"irregular" circulating temperament until the listener comes to
distinguish the two via intonational information.
3) "Training wheel" tunings: If #1 holds, then harmonically accurate
temperaments with crappy melodic and scalar qualities can be learned
more easily by first exploring a tuning that presents a crystal-clear
rank-order matrix, and then going back to the melodically inferior but
harmonically superior version, so long as the melodically superior but
harmonically inferior version doesn't significantly fall prey to #2
above.

I think that #1 will hold, but actually that #2 might not in all
cases, and that seeing how it fails will yield to some new insights.
#1 and #3 are both things I've experienced personally and heard some
concurrence on from the Mavila crowd, in that many do in fact perceive
25-equal mavila[9] to be more "comprehensible" than 16 or 23-equal.

Lastly, #1, if true, would suggest a new method for tuning
optimization: pick a tuning where the generators can get the heck out
of each other's way. It's really hard to know which position in the
chain you're at if you're in a scale that is stupidly and wildly
improper, and if you can't figure out where in the temperament you
are, it's impossible to imagine any sort of consistent harmonic
context around the interval you're at. Everything I've written above
is an attempt to formalize this one observation.

-Mike