The uncertainty of the scale the Shepard tones pertain allows composers to experiment with deceiving and disconcerting melodies. Regardless of the tempo and the envelope of the notes, the auditory illusion is effectively maintained. Pedro Patricio observed in 2012 that, by using a Shepard tone as a sound source and applying it to a melody, he could reproduce the illusion of a continuously ascending or descending movement characteristic of the Shepard Scale. Interestingly, different listeners may perceive the same pattern as being either ascending or descending, depending on the language or dialect of the listener (Deutsch, Henthorn, and Dolson found that native speakers of Vietnamese, a tonal language, heard the tritone paradox differently from Californians who were native speakers of English). In 1986, Diana Deutsch discovered that the perception of which tone was higher depended on the absolute frequencies involved and that an individual would usually hear the same pitch as the highest (this is determined by the absolute pitch of the notes).
Sequence of Shepard tones producing the tritone paradox The illusion is more convincing if there is a short time between successive notes ( staccato or marcato rather than legato or portamento). The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale. The theory behind the illusion was demonstrated during an episode of the BBC's show Bang Goes the Theory, where the effect was described as "a musical barber's pole". According to Shepard, "almost any smooth distribution that tapers off to subthreshold levels at low and high frequencies would have done as well as the cosine curve actually employed." a raised cosine function of its separation in semitones from a peak frequency, which in the above example would be B 4. (In other words, each tone consists of two sine waves with frequencies separated by octaves the intensity of each is e.g. The thirteenth tone would then be the same as the first, and the cycle could continue indefinitely. The two frequencies would be equally loud at the middle of the octave (F ♯ 4 and F ♯ 5), and the twelfth tone would be a loud B 4 and an almost inaudible B 5 with the addition of an almost inaudible B 3. The next would be a slightly louder C ♯ 4 and a slightly quieter C ♯ 5 the next would be a still louder D 4 and a still quieter D 5.
Shepard scale, diatonic in C Major, repeated 5 timesĪs a conceptual example of an ascending Shepard scale, the first tone could be an almost inaudible C 4 ( middle C) and a loud C 5 (an octave higher).
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