The Riemann zeta function and tuning: Difference between revisions
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Another use for the Riemann zeta function is to determine the optimal tuning for an edo, meaning the optimal octave stretch. This is because the zeta peaks are typically not integers. The fractional part can give us the degree to which the generator diverges from what you would need to have the octave be a perfect 1200 cents. | Another use for the Riemann zeta function is to determine the optimal tuning for an edo, meaning the optimal octave stretch. This is because the zeta peaks are typically not integers. The fractional part can give us the degree to which the generator diverges from what you would need to have the octave be a perfect 1200 cents. | ||
For all edos 1 through 100, and for a list of successively higher zeta peaks, taken to five decimal places, see [[table of zeta-stretched edos]]. | |||
=== Zeta peak index === | === Zeta peak index === | ||