Sequence of Shepard tones producing the tritone paradox Shepard had predicted that the two tones would constitute a bistable figure, the auditory equivalent of the Necker cube, that could be heard ascending or descending, but never both at the same time. An example of Risset's accelerating rhythm effect using a breakbeat loop Tritone paradox Ī sequentially played pair of Shepard tones separated by an interval of a tritone (half an octave) produces the tritone paradox. Risset has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly. When done correctly, the tone appears to rise (or fall) continuously in pitch, yet return to its starting note. Jean-Claude Risset subsequently created a version of the scale where the tones glide continuously, and it is appropriately called the continuous Risset scale or Shepard–Risset glissando. See and hear the higher tones as they fade out. Variants Moving audio and video visualization of a rising Shepard–Risset glissando. 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 tone as of the root note A (A 4 = 440 Hz) 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). Overlapping notes that play at the same time are exactly one octave apart, and each scale fades in and fades out so that hearing the beginning or end of any given scale is impossible. The color of each square indicates the loudness of the note, with purple being the quietest and green the loudest. Construction Figure 1: Shepard tones forming a Shepard scale, illustrated in a sequencerĮach square in Figure 1 indicates a tone, with any set of squares in vertical alignment together making one Shepard tone. This creates the auditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower. When played with the bass pitch of the tone moving upward or downward, it is referred to as the Shepard scale. A spectrum view of ascending Shepard tones on a linear frequency scaleĪ Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves.
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