Pitch circularity
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

 is often defined as extending along a one-dimensional continuum
Continuum (theory)
Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...

 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
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...

: 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 is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

 higher. Tones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence—all Cs tend to sound somewhat alike, as do all D#s, and so on; this creates the auditory equivalent of a Barber's pole
Barber's pole
A barber's pole is a type of 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 pole with a helix of colored stripes...


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 Shepard
Roger Newland Shepard is a cognitive scientist and author of Toward a Universal Law of Generalization for Psychological Science. He is seen as a father of research on spatial relations....

 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 F#s, 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
Jean-Claude Risset
Jean-Claude Risset is a French composer, best known for his pioneering contributions to computer music. He is a former student of André Jolivet and former co-worker of Max Mathews at Bell Labs....

 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.

Recently, Diana Deutsch
Diana Deutsch
Diana Deutsch is a British-American perceptual and cognitive psychologist, born in London, England. She is currently Professor of Psychology at the University of California, San Diego, and is one of the most prominent researchers on the psychology of music...

and colleagues have shown 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.
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.
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