The Riemann zeta function and tuning: Difference between revisions
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<math>\displaystyle{ | <math>\displaystyle{ | ||
\left| 1 - p^{-\frac{1}{2} - it} \right| = \sqrt{1 + \frac{1}{p} - \frac{2 \cos(t \ln p)}{\sqrt{p}}} | \left| 1 - p^{-\frac{1}{2} - it} \right| = \sqrt{1 + \frac{1}{p} - \frac{2 \cos(t \ln p)}{\sqrt{p}}} | ||
}</math> | }</math>. | ||
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. | ||
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: | ||
<math> | <math> | ||