Re: Absolute frequency / Absolute color

[Christian Kaernbach <chris@xxxxxxxxxxxxxxxxxxxxxxxxxx>]

Martin Braun wrote:
> Small children, up to 5-7 years of age, only have to learn the 12
> tones of ONE octave. We don't have more than these 12 tone names,
> by the way. When talking about different octaves we have to add an
> octave name to one of the 12 tone names (A3, A4, A5, etc.)...
> In tests, absolute-pitch possessors often commit octave errors...

Diana Deutsch wrote:
> Actually you only need 12 categories for AP -at least for Western
> tonal music - because of  octave equivalence. Perception of
> differences in height between notes of the same pitch class are not
> related to AP.

Sure, there is no such thing like octave equivalence in color
perception. There are specialties in color perception (see below) that
are not present in pitch perception, and vice versa. It was not my idea
to compare color and pitch perception. But if it is done, it should be
done in a fair and unbiased way.

"An AP possessor has more than 12 categories." That's all I want to say.
Due to a specialty in pitch perception that may not be cultural but of a
more general nature - octave equivalence - the AP possessor organizes
these categories along 12 tone names. But it would be not correct to
assume that the number of available categories is just 12.

I was informed that octave errors are committed (although to my
knowledge they would occur rarely with professional musicians; is that
true, Martin?), and I have heard that also hemitonic errors are
sometimes committed. This shows that the categories are not perfect. A
non-musician AP possessor might commit more octave errors, and if we
would carefully avoid to teach octave names at all, we would get perfect
octave confusion. That would not constitute a fair test of the maximum
number of pitch categories in an AP possessor.

If an AP possessor is making octave errors that does not mean that the
octave response is randomized. There is additional information
available. The actual number of categories might be less than 80, but
surely more than 12.

This is not to say that these more-than-12 categories are linearly
arranged "in our head". Colors are also not arranged linearly but
circularly (more precisely: closed paraboloid), and pitch representation
has often been described by a helix.

> Color circles of 12 colors are quite common and can be learned
> in a few minutes.

This is not so obvious. Elena Heider (later work published after
marriage under the name of Rosch) has done quite a lot of work on color
naming, see e.g.
        Heider, E. (1972). Universals of color naming and memory.
        Journal of Experimental Psychology, 93, 10-20.
where she shows that the focal colors - there are 11 of them, black,
white, red, green, yellow, blue, brown, lilac, pink, orange, gray - do
not depend on learning of category names. The Dani know only two words
for colors, but in behavioral tests they favor these 11 colors much in
the same way as the English. Color naming follows perceptual universals
- for yellow there has been quite a body of research, studying the
"Urgelb" (is it "prime yellow"?) which can be reproduced by every
subject with an ultimate reliability. The exact equivalent of Urgelb
varies slightly across subjects, but each subject is very precise about
his/her Urgelb. This seems to originate from counter-balancing red-green
opponent channels in our visual system. Other physiological laws may be
at the origin of the other focal colors.

As long as a color naming system is oriented on these physiologically
favored focal colors it can be learned in a few minutes. Actually, it
needs not even be learned because it already is. We would have to go to
the Dani to see whether it can be learned. Helena Rosch has done it, but
I don't have the paper at hand. It seems that the Dani learn fantasy
names quite easily for focal colors, but not for other colors.

Taking these focal colors as corner stones the number of learnable color
categories is probably quite a bit higher. But this would refer to
variations in three dimensions (hue, saturation, brightness). If we
reduce it to one dimension (hue) it could well be that we end up with 12
learnable categories. I don't remember a study that has done it.

O.k., back to the auditory list... There are no such things like focal
pitches (physiologically preferred frequencies) in audition. Some bats
have, but we don't. So we would have more problems to learn a 12-names
system (I am not speaking of tone names within an octave, but for
pitches of the entire available range). But I remember it has been done,
not with 12, but with 7 (the notorious 7+-2 type of study). Does
somebody of the list remember this study? And as far as I remember it
worked...

Summary: I was probably wrong with 12: A learnable absolute memory for
pitches (50-5000Hz) for non-AP subjects might attain a number of 7
categories. Absolute memory for color hue could span 12 categories. The
major reason for this distinction is probably due to the different
physiological basis of pitch and color perception, with physiologically
preferred corner-stone focal colors in color perception. An
AP-possessor, however, has much more than 12 categories.

- Christian