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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Pitch circularity from tones comprising full harmonic series. 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.
This is acknowledged in our musical scale, which is based on the circular configuration shown on the right below. At some point, relatkve realize that they are hearing the note an octave higher — but this judgmentx transition had occurred without the sounds traversing the semitone scale, but remaining on note A.
I further reasoned that we should be able to produce pitch circularities on this principle. If you take a harmonic complex tone and gradually reduce the amplitudes of the odd-numbered harmonics 1, 3, 5, etc. The pitch class circle. For the tone with the highest fundamental, the odd and even harmonics are equal in amplitude. Retrieved from ” https: The finding that circular ciecularity can be obtained from full harmonic series leads to the intriguing possibility that this algorithm judhments be used to transform banks of natural instrument tones so that they would also exhibit pitch circularity 6.
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. The paradox of pitch circularity.
Pitch circularity is a fixed series of tones that appear to 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. 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.
Together with my colleagues, I carried out an experiment to determine pirch such tones are indeed heard as circular, when all ij are considered 5. The possibility of creating circular banks of tones derived from natural instruments expands the scope of musical materials judgment to composers and performers.
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. 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 relaive.
See the review by Deutsch 4 for details. Here is an eternally descending scale based on this principle, with the amplitudes of the odd-numbered harmonics reduced by 3.
We created a bank of twelve tones, and from this bank we paired each tone sequentially with every other tone e. Risset 3 has created intriguing variants using gliding tones that appear to ascend or descend continuously in pitch.
Journal of the Acoustical Society of America, 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.
This development opens up new avenues for music composition and performance. Unknown to the authors, Oscar Reutesvald had also created an impossible staircase in the s. 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. Roger Shepard achieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship.
Such tones are well defined in terms of pitch class, but poorly defined in terms of height. Journal of the Acoustical Society of America.
We begin with a bank of twelve harmonic complex tones, whose fundamental frequencies range over an octave in semitone steps. Counterclockwise movement creates the impression of an eternally descending scale.
When such tones are played traversing the pitch class circle in clockwise felative, 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. 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.
Pitch circularities are based on the same principle. Subjects judged for each pair whether it ascended or descended in pitch. However pitch also varies in a circular fashion, known as pitch class: Since each stair that is jdugments step clockwise from its neighbor is also one step downward, the staircase appears to be eternally descending.
This continuum is known as pitch height. Paradoxes of musical pitch. From Wikipedia, the free encyclopedia.
Views Read Edit View history. 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. This page was last edited on 16 Aprilat 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.
Diana Deutsch – Pitch Circularity
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. The figure on the left below represents an impossible staircasesimilar to one originally published by Penrose and Penrose in 1.
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.