Circularity in Judgments of Relative Pitch. Authors: Shepard, Roger N. Publication: The Journal of the Acoustical Society of America, vol. 36, issue 12, p. The Shepard illusion, in which the presentation of a cyclically repetitive sequence of complex tones composed of partials separated by octave intervals (Shepard. Circularity in relative pitch judgments for inharmonic complex tones: The Shepard demonstration revisited, again. EDWARD M. BURNS. Department ofAudiology.

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This is acknowledged in our musical scale, which is based on the circular configuration shown on the right below. However pitch also varies in a circular fashion, known as pitch class: William Brent, then a graduate student at UCSD, has achieved considerable success using bassoon samples, and also some success with oboe, flute, and violin samples, and has shown that the effect is not destroyed by vibrato.

We begin with a bank of twelve harmonic complex tones, whose fundamental frequencies range over an octave in semitone steps. Here is an excerpt from the experiment, and you iudgments probably find that your judgments of each pair correspond to the closest distance between the tones along the circle. Such tones are well defined in terms of pitch class, but poorly defined in terms of height.

In Sound Demo 1, a harmonic complex tone based on A 4 concert A is presented, with the odd-numbered harmonics gradually gliding ot in amplitude. Retrieved from ” https: This page was last edited on 16 Aprilat Shepard 2 reasoned that by creating banks of tones whose note names pitch classes are clearly defined but whose perceived heights are ambiguous, the helix could be collapsed into a circle, so enabling the creation of scales that ascend or descend endlessly in pitch.


Unknown to the authors, Oscar Reutesvald had also created an impossible staircase in the s.

Journal of the Acoustical Society of America, I further reasoned that we should be able to produce pitch circularities on kudgments principle. Views Read Edit View history. The tone with the lowest fundamental is therefore heard as displaced up an octave, and pitch circularity is achieved. Researchers have demonstrated that by creating banks of tones whose relarive names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch.

A different algorithm that creates ambiguities of pitch height by manipulating the relative amplitudes of the odd and even harmonics, was developed by Diana Deutsch and colleagues.

The paradox of pitch circularity. Since each stair that is one step clockwise from its neighbor relatibe also one step downward, the staircase appears to be eternally descending.

When such tones are played traversing the pitch class circle in clockwise direction, one obtains the impression of an eternally ascending scale— C is heard as higher than C; D as higher than C ; D as higher than D. See the review by Deutsch 4 for details.

Jean-Claude Risset achieved the same effect using gliding tones instead, so that a single tone appeared to glide up or down endlessly in pitch. The pitch class circle. Then for the tone a semitone lower, the amplitudes of the odd harmonics are reduced relative to the even ones, so raising the perceived height of this tone.

Paradoxes of musical pitch. Here is an eternally descending scale based on this principle, with the amplitudes of the odd-numbered harmonics reduced by 3. The possibility of creating circular banks of tones derived from natural instruments expands the scope of musical materials available to composers and performers. This development has led to the intriguing possibility that, using this new algorithm, one might transform banks of natural instrument samples so as to produce tones that sound like those of natural instruments but still have the property of circularity.


Risset 3 has created intriguing variants using gliding tones that appear to ascend or descend continuously in pitch. For the tone with the highest fundamental, the odd and even harmonics are equal in amplitude.

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Pitch circularity

To accommodate both the linear and circular dimensions, music theorists have suggested that pitch should be represented as a helix having one complete turn per octave, so that tones that are separated by octaves are also close on this representation, as shown below. Later, I reasoned that it should be possible to create circular scales from sequences of single tones, with each tone comprising a full harmonic series.

Pitch circularities are based on the same principle. The figure on the left below represents an impossible staircasesimilar to one originally published by Penrose and Penrose in 1.

Diana Deutsch – Pitch Circularity

Journal of the Acoustical Society of America. As we ascend this scale in semitone steps, we repeatedly traverse the pitch class circle in clockwise direction, so that we play C, CD, and so on all around the circle, until we reach A, AB – and then we proceed to C, CD again, and so on.

At some point, listeners realize that they are hearing the note an octave higher — but this perceptual judgmdnts had occurred without the sounds traversing the semitone scale, but remaining on note A.