norman@sdics.ucsd.EDU (Donald A. Norman) (12/05/87)
Shepard's tones: the description of the illusion was correct. The
name comes from Roger Shepard, now a professor of psychology at
Stanford University who invented them.
The perception of a cintunally rising pitch comes about because the
psychological space for pitch is a three-dimensional spiral.
Basically, think of pitch being represented by points located around a
horizontal circle, moving, say, from c1 to c1# to d1 to ... g1, to
g1#, and back to c again, except as c2 (one octave up). Except that
as you move along the circle, also rise a little bit on the z axis,
moving up. So when you get back to C, as C2, one octave up, you are directly
above C1 one octave below. So you can now see that C1 is closer to
C2 than it is to, say F1 or G1.
Roger Shepard developed the major techniique of multidimensional
scaling in use today. He showed that multidimensional scaling
produces this three dimensional spiral of the pitch space. And then
he developed a computer-synthesized demonstration of the ever-rising
pitch, both as a pleasant demonstration, and as proof that the theory
that he had developed could predict this most unusual and heretofore
unknown illusion. (All this in the days when computer sythesis of
sound was quite difficult, taking big computers and lots of equipment:
he did the sound at Bell Labs working with Max matthews, I believe.)
Don Norman
Donald A. Norman
Institute for Cognitive Science C-015
University of California, San Diego
La Jolla, California 92093
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