octave equivalence

Yesterday, when discussing experiments with the Bohlen-
Pierce scale, PAULE wrote: "octave equivalence is a real and
unavoidable phenomenon."

"Octave equivalence" is one of those terms that we all think
we know what it means, but when you get down to actually
trying to define it, it becomes slippery.

An intruiging experiment reported by D. Deutsch in the book
"Psychology of Music" examined octave equivalence from a
melodic, rather than a harmonic perspective. She took a
familiar tune (maybe it was Yankee Doodle, but I'm not sure)
and octave transposed a large number of the tones. When
asked what the melody was, most people could not identify it.
However, if the listeners were prompted (by hearing the
unaltered melody just before) then they could 'hear out' the
melody in the altered version.

One way to interpret this study is that this kind of octave
equivalence is a function of "the brain" rather than of "the
ear" (i.e., is a result of higher level neural processing rather
than lower level sensorial processing). As such, it is likely that
it is highly subject to training, or cultural conditioning.

The Bohlen-Pierce tritave unarguably exhibits one kind of
"tritave equivalence" that is analogous to (one kind of) octave
equivalence. This is: for a harmonic sound with partials at f,
2f, 3f, 4f, 5f, 6f, ... and its octave with partials at 2f, 4f, 6f, 8f,
.. playing the two together adds no new frequency
information. Similarly, when a sound with only odd partials f,
3f, 5f, 7f, 9f, ... and its tritave with partials at 3f, 9f, 12f, ...
playing the two together adds no new frequency information.
In fact, if you program up the scale, you can hear this kind of
equivalence.

So, here are two kinds of "octave equivalence", neither of
which is the kind meant by PAULE.

Nonetheless, I know what PAULE means when he says "I
found that 33 steps above the bass sounded like a resolution
while 39 steps above the bass did not." Perhaps this is a
result of our 12-tet octavocentric brainwashing (i.e., cultural
conditioning).

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