Page 14 - Summer 2010

For example, what happens when the pattern C-F# is pre- sented? Or the pattern A#-E? Since proximity cannot then be invoked, will such judgments be ambiguous, or will some- thing else occur?
I conjectured that for such patterns, the auditory system would not settle for ambiguity, but would instead make refer- ence to the absolute positions of the tones along the pitch class circle, so that tones in one region of the circle would be heard as higher and tones in the opposite region as lower. This conjecture was confirmed in a series of experiments employing Shepard tones consisting of six octave-related components, with tones within a pair generated under the
respond with a show of hands whether each tone pair ascend- ed or descended in pitch. This demonstration is particularly striking when played to a group of professional musicians, who are quite certain of their own judgments and yet recognize that others are obtaining entirely different percepts.
In other experiments, R. Richard Moore, Mark Dolson and I studied two-part melodic patterns composed of the same octave-related complexes, and found that judgments here also depended on the positions of the tones along the
25,26
same spectral envelope.
20
The experimental design controlled
pitch class circle.
sions, one dimension can influence the other.
for sources of artifact—for example tones were generated
under envelopes that were placed in different positions along
along the pitch class circle.
Another and entirely unexpected finding also emerged
from these studies—the orientation of the pitch class circle with respect to height varied strikingly across listeners. For example, some subjects would hear the tone pair D-G# (and C#-G, and D#-A) as ascending, whereas others would hear the same patterns as descending. Then the first set of subjects would hear the tone pair G#-D (and G-C#, and A-D#) as descending while the second set of subjects would hear these patterns as ascending. Such individual differences can be easi- ly demonstrated by presenting the four tritone pairs in Sound Demonstration 10 to a group of listeners, and asking them to
Summary and conclusions
The phenomenon of pitch circularity has implications for our understanding of pitch perception, as well as for musical composition and performance. It is likely to intrigue acousticians, mathematicians, and musicians for many years to come. The experiments and sound demonstrations described here indicate that the classical definition of pitch as “that attribute of auditory sensation in terms of which sounds may be ordered on a scale extending from high to low” 27 should be amended to include the circular dimension also. The experimental decoupling of the linear and circular com- ponents of pitch provides a useful tool for the further inves- tigation of the neural underpinnings of these two compo- nents, which are presumably processed separately at some stage in the auditory system. For musicians the development
the spectrum.
21,22, 23,24
Judgments of relative pitch were found to depend in an orderly fashion on the positions of the tones
In general, the tritone paradox and relat- ed paradoxes formed of two-part patterns show that while pitch height and pitch class are in principle separate dimen-
Pitch Circularity 13