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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The possibility of creating circular banks of tones derived from natural instruments expands the scope of musical materials available to composers and performers. Journal of the Acoustical Society iin America.

Pitch circularity

Here is an excerpt from the experiment, and you will circularihy find that your judgments of each pair correspond to the closest distance between the tones along the circle. Pitch circularities are based on the same principle.

The paradox of pitch circularity. At some point, circulairty realize that they are hearing the note an octave higher — but this perceptual transition had occurred without the sounds traversing the semitone scale, but remaining on note A.

Paradoxes of musical pitch. Then for the tone a semitone lower, the amplitudes of circulariy odd harmonics are reduced relative to the even ones, so raising the perceived height of this tone.

Then for the tone another semitone lower, the amplitudes of the odd harmonics are reduced further, so raising the perceived height of this tone to a greater extent.

Roger Shepard achieved this ambiguity of height by creating banks gelative complex tones, with each tone composed only of components that stood in octave relationship. 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.

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Together with my colleagues, I carried out an experiment to determine whether such tones are indeed heard as circular, when all intervals are considered 5. 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.

The tone with the lowest fundamental is therefore heard as displaced up an octave, and pitch circularity is achieved. 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.

Researchers have demonstrated that by creating banks of tones whose note names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch. 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.

However pitch also varies in a circular fashion, known as pitch class: Unknown to the authors, Oscar Reutesvald had also created an impossible staircase in judgmentts s. The figure on the left below represents an impossible staircasesimilar to one originally published by Penrose cirularity Penrose in 1.

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.


Here is an eternally descending scale based on this principle, with the amplitudes of the odd-numbered harmonics reduced by 3.

Pitch circularity – Wikipedia

This is acknowledged in our musical scale, which is based on the circular configuration shown on the right below. Pitch circularity is a fixed series of tones that appear to ascend or descend endlessly in pitch.

If you take a harmonic complex tone and gradually reduce the amplitudes of the odd-numbered harmonics 1, 3, iin, etc. This page was last edited on 16 Aprilat Views Read Edit View history. The pitch class circle. In Sound Demo 1, a harmonic complex tone based on A 4 concert A is presented, with the odd-numbered harmonics gradually gliding down in amplitude.

Circularity in Judgments of Relative Pitch

Such tones are well defined in terms of pitch class, but poorly defined in terms of height. Juvgments from ” https: This development opens up new avenues for music composition and performance.

The finding that circular scales can be obtained from full harmonic series leads to the intriguing possibility that this algorithm could be used to transform banks of natural instrument tones so that they would also exhibit pitch circularity 6.

Counterclockwise movement creates the impression of an eternally descending scale.