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 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.
We begin with a bank of twelve harmonic complex tones, whose fundamental frequencies relayive over an octave in semitone steps. Together with my colleagues, I carried juddgments an experiment to determine whether such tones are indeed heard as circular, when all intervals are considered 5.
From Wikipedia, the free encyclopedia. Unknown to the authors, Oscar Reutesvald had also created an impossible staircase in the s.
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. Journal of the Acoustical Society of America.
Here is an excerpt from the experiment, and you will probably find that your judgments of each pair correspond to the closest distance between the tones along the circle. Retrieved from ” https: This development opens up new avenues for music composition and performance. 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.
Here is an eternally descending scale based on this principle, with the amplitudes of the odd-numbered harmonics reduced by 3. Subjects judged for each pair whether it ascended or descended in pitch.
Since each stair that is one step clockwise from its neighbor is also one step downward, the staircase appears to be eternally descending. Such tones are well defined in terms of pitch class, but poorly defined in terms of height. 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.
Circularity in Judgments of Relative Pitch
See the review by Deutsch 4 for details. This page was last edited on 16 Aprilat Paradoxes of musical pitch.
The possibility of creating circular banks of tones derived from natural instruments expands the scope of musical materials available to composers and performers. Risset 3 has created intriguing variants using gliding tones that appear to ascend or descend continuously in pitch.
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. The figure on the left below represents an impossible staircasesimilar to one originally published by Penrose and Penrose in 1.
He achieved this ambiguity by creating banks of complex tones, with each tone consisting only of components that were separated by octaves, and whose amplitudes were scaled by a fixed bell-shaped spectral envelope. 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. This is acknowledged in our musical scale, which is based on the circular configuration shown on the right below.
The pitch class circle.
Pitch circularity is a fixed series of tones that appear to ascend or descend endlessly in pitch. 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.
Shepard 2 reasoned that by creating banks of tones whose note names pitch classes are putch 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 o in pitch.
Journal of the Acoustical Society of America, Views Read Edit View history. However pitch also varies in a circular fashion, known as pitch class: