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## Technique for Producing Shepard-Tones

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The method for producing the frequencies of Shepard-tones (in this unit we consider Shepard-tones that are based on the chromatic scale, but they need not necessarily be based on it) derives from the following equation:

F(t,c)=F(min) * 2^((c-1)*t(max)+t-1)/t(max)

where F(t,c)is the frequency of the partial c of tone t;t(max) is 12 (i.e. based on the chromatic scale); and F(min) is the frequency of the lowest partial of the first (and presumably lowest) tone.  The symbol ^ indicates exponentiation.