Pitch circularity
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Pitch circularity is a fixed series of tones that are perceived to ascend or descend endlessly in pitch. It's an example of an
auditory illusion Auditory illusions are Illusion, illusions of real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the Stimulus (physiology), stimulus, or sound ...
.


Explanation

Pitch is often defined as extending along a one-dimensional continuum from high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height. However pitch also varies in a circular fashion, known as
pitch class In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
: as one plays up a keyboard in semitone steps, C, C, D, D, E, F, F, G, G, A, A and B sound in succession, followed by C again, but one
octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
higher. Because the octave is the most consonant interval after the
unison Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...
, tones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence—all Cs sound more alike to other Cs than to any other pitch class, as do all Ds, and so on; this creates the auditory equivalent of a
Barber's pole A barber's pole is a type of Signage, sign used by barbers to signify the place or shop where they perform their craft. The trade sign is, by a tradition dating back to the Middle Ages, a staff or :wikt:pole, pole with a helix of colored Strip ...
, where all tones of the same pitch class are located on the same side of the pole, but at different heights.


Research on pitch perception

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.
Roger Shepard Roger Newland Shepard (January 30, 1929 – May 30, 2022) was an American cognitive science, cognitive scientist and author of the "universal law of generalization" (1987). He was considered a father of research on spatial relations. He studied m ...
achieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship. In other words, the components of the complex tone C consisted only of Cs, but in different octaves, and the components of the complex tone F consisted only of Fs, but in different octaves. When such complex tones are played in semitone steps the listener perceives a scale that appears to ascend endlessly in pitch. 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. Circularity effects based on this principle have been produced in orchestral music and electronic music, by having multiple instruments playing simultaneously in different octaves. Normann et al.PDF Document
showed that pitch circularity can be created using a bank of single tones; here the relative amplitudes of the odd and even harmonics of each tone are manipulated so as to create ambiguities 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 Diana Deutsch (born 15 February 1938) is a British-American psychologist from London, England. She is a professor of psychology at the University of California, San Diego, and is a prominent researcher on the psychology of music. Deutsch is ...
and colleagues.WeblinkPDF Document
Using this algorithm, gliding tones that appear to ascend or descend endlessly are also produced. 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. This development opens up new avenues for music composition and performance.WeblinkPDF Document


See also

* Chromatic circle * Shepard tone * Tritone paradox


References

{{Pitch (music) Auditory illusions