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 tone with the lowest fundamental is therefore heard as displaced up an octave, and pitch circularity is achieved. Here is an eternally descending scale based on this principle, with the amplitudes of the odd-numbered harmonics reduced by 3. Risset 3 has created intriguing variants using gliding tones that appear to ascend or descend continuously 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.
Pitch circularities are based on the same principle. 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. Journal of the Acoustical Society of America, See the review by Deutsch 4 for details.
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. 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.
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.
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.
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. Hudgments continuum is known as pitch height.
Pitch circularity from tones comprising full harmonic series. For the tone with the highest fundamental, the odd and even harmonics are equal in amplitude.
At some point, listeners 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.
The pitch class circle. 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. Unknown to the authors, Oscar Reutesvald had also created an impossible staircase in the s. 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.
This page was last edited on 16 Aprilat 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.
From Wikipedia, the free encyclopedia. This development opens up new avenues for music composition and performance. Paradoxes of musical pitch. We created a bank of twelve tones, and from this bank we paired each tone sequentially with every other tone e. 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. 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.
Counterclockwise movement creates the impression of an eternally descending scale.
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. 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. 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.
Subjects judged for each pair whether it ascended or descended in pitch. Such tones are well defined in terms of pitch class, but poorly defined in terms of height.
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. Retrieved from ” https: We begin with a bank of twelve harmonic complex tones, whose fundamental frequencies range over an octave rrelative semitone circularityy. Journal of the Acoustical Society of America. Since each stair that is one step clockwise from its neighbor is also one step downward, the staircase appears to be eternally descending.
I further reasoned that we should be able to produce pitch circularities on this principle.
Pitch circularity is a fixed series of tones that appear to ascend or descend endlessly in pitch. 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. If you take a harmonic complex tone and gradually reduce the amplitudes of the odd-numbered harmonics 1, 3, 5, etc. The figure on the left below represents an impossible staircasesimilar to one originally published by Penrose and Penrose in 1.
The paradox of pitch circularity. 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. This is acknowledged in our musical scale, which is based on the circular configuration shown on the right below. However pitch also judgmenys in a circular ciircularity, known as pitch class: