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Shepard tone

A Shepard tone is a sound consisting of a superposition of tones separated by octaves. When played with the base pitch of the tone moving upward or downward, it is referred to as the Shepard scale. This auditory illusion can be constructed by creating a series of overlapping ascending or descending scales. Similar to the Penrose triangle optical illusion (M.C. Escher's Ascending and Descending) or a barber's pole, the basic concept is shown in this illustration:


Each square indicates a tone, any set of squares in vertical alignment together making one Shepard tone. The color of each square indicates the velocity (volume) of the note, with purple being the quietest. Overlapping notes that play at the same time should be exactly one octave apart, and each scale should fade in and fade out, so that it is impossible to hear the beginning or end of any given scale. The scale as described, with discrete steps between each tone, is known as the discrete Shepard scale, but, after Shepard, Jean-Claude Risset created a version of the scale where the steps between each tone are continuous, and it is appropriately called the continuous Risset scale or Shepard-Risset glissando. He has also created a similar effect with rhythm in which tempo seems to increase or decrease endlessly.

To make the illusion more convincing, it helps to have some amount of space between each note (staccato or marcato instead of legato or portamento. When done correctly, the tone appears to rise (or descend) continuously in pitch, yet return to its starting note.

Although it is implausible to create the illusion with acoustic instruments James Tenney, who worked with Roger Shepard at Bell Labratories in the early sixties, has created a piece utilizing this effect, For Ann (rising). The piece, in which up to twelve closely but not quite consistently spaced computer generated sine waves rise steadily from an A pitched below audibility to an A above, fading in, and back out, of audible volume, was then scored for twelve string players. The effect of the electronic work consists both of the Shepard scale, seamless endlessly (rising) glissandos, and of a shimmering caused by the highest perceivable frequency and the inability to focus on the multitude of rising tones. Tenney has also proposed that the piece be revised and realized so that all entrances are timed in such a way that the ratio between succesive pitches is the golden mean, which would make each lower first order combination tone of each successive pair coincide with subsequently spaced, lower, tones.


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