The Riemann zeta function and tuning: Difference between revisions
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Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime ''p'' removed from consideration. Zeta peak and zeta integral tunings may then be found as before. | Multiplying the Z-function by this factor of adjustment gives a Z-function with the prime ''p'' removed from consideration. Zeta peak and zeta integral tunings may then be found as before. Note that multiplying this factor is technically only accurate for sums whose result is related to the Z function rather than the real part of the zeta function. | ||
For example, if we want to find zeta peak [[EDT]]s (division of the [[3/1|{{ordinal|3}}]] harmonic, or "tritave") - noting that here we must substitute <math>t = \frac{2\pi x}{\ln(3)}</math> instead of <math>\frac{2\pi x}{\ln(2)}</math> - in the no-twos subgroup, our modified Z function is: | For example, if we want to find zeta peak [[EDT]]s (division of the [[3/1|{{ordinal|3}}]] harmonic, or "tritave") - noting that here we must substitute <math>t = \frac{2\pi x}{\ln(3)}</math> instead of <math>\frac{2\pi x}{\ln(2)}</math> - in the no-twos subgroup, our modified Z function is: | ||