ASA's Auditory Demonstrations
Circularity in Pitch Judgment
One of the most widely used auditory illusions is Shepard's (1964)
demonstration of pitch circularity, which has come to be known as the
"Shepard Scale" demonstration.
The demonstration uses a cyclic set of complex tones, each composed
of 10 partials separated by octave intervals. THe tones are
cosinusoidally filtered to produce the sound level distribution
shown below, and the frequencies of the partials are shifted upward
in steps corresponding to a musical semitone (= ~ 6 %).
The result is an "ever-ascending" scale, which is a sort of auditory analog to the ever-ascending staircase visual illusion.
Several variations of the original demonstration have been described.
J-C. Risset created a continuous version. Other variations are described by
Burns (1981), Teranishi (1986), and Schroeder (1986).
- "Two examples of scales that illustrate circularity in pitch judgment are presented.
The first is a discrete scale of Roger N. Shepard, the second is a continuous scale of
- R. N. Shepard (1964), "Circularity in judgments of
relative pitch," J. Acoust. Soc. Am. 36, 2346-2353.
- I. Pollack (1977), "Continuation of auditory frequency gradients
across temporal breaks," Perception and Psycophys. 21, 563-568.
- E. M. Burns (1981), "Circularity in relative pitch
judgments: the Shepard demonstration revisited, again," Perception and Psychophys. 30, 467-472.
- R. Teranishi (1986), "Endlessly rising or falling chordal tones which
can be played on the piano; another variation of the Shepard demonstration,"
Paper K2-3, 12th Int. Congress on Acoustics, Toronto.
- M. R. Schroeder (1986), "Auditory paradox based on fractal waveform,"
J. Acoust. Soc. Am. 79, 186-189.
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