The Riemann zeta function and tuning: Difference between revisions
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Finally, taking the midpoints of the successively larger normalized gaps between the zeros of Z leads to a list of ''zeta gap edos''. These are {{EDOs|2, 3, 5, 7, 12, 19, 31, 46, 53, 72, 270, 311, 954, 1178, 1308, 1395, 1578, 3395, 4190,}} ... Since the density of the zeros increases logarithmically, the normalization is to divide through by the log of the midpoint. These edos are listed in the OEIS as {{OEIS|A117537}}. The zeta gap edos seem to weight higher primes more heavily and have the advantage of being easy to compute from a table of zeros on the critical line. | Finally, taking the midpoints of the successively larger normalized gaps between the zeros of Z leads to a list of ''zeta gap edos''. These are {{EDOs|2, 3, 5, 7, 12, 19, 31, 46, 53, 72, 270, 311, 954, 1178, 1308, 1395, 1578, 3395, 4190,}} ... Since the density of the zeros increases logarithmically, the normalization is to divide through by the log of the midpoint. These edos are listed in the OEIS as {{OEIS|A117537}}. The zeta gap edos seem to weight higher primes more heavily and have the advantage of being easy to compute from a table of zeros on the critical line. | ||
We may define the ''strict zeta edos'' to be the edos that are in all four of the zeta edo lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578}}... . | We may define the ''strict zeta edos'' to be the edos that are in all four of the zeta edo lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578}}... . [[16808edo]] is also known to be strict zeta. | ||
==Optimal Octave Stretch== | ==Optimal Octave Stretch== | ||