The Riemann zeta function and tuning: Difference between revisions
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== Zeta EDO lists == | == Zeta EDO lists == | ||
The prime-approximating strength of an EDO can be determined by the magnitude of Z(x). Since a higher |Z(x)| correlates to a stronger tuning, we would like to find a sequence with succesively larger |Z(x)| values satisfying some property. | |||
=== Peak EDOs === | === Peak EDOs === | ||
If we examine the increasingly larger peak values of |Z(x)|, we find they occur with values of x such that Z'(x) = 0 near to integers, so that there is a sequence of [[EDO|edo]]s | If we examine the increasingly larger peak values of |Z(x)|, we find they occur with values of x such that Z'(x) = 0 near to integers, so that there is a sequence of [[EDO|edo]]s | ||
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=== Strict zeta EDOs === | === Strict zeta EDOs === | ||
We may define the ''strict zeta edos'' to be the edos that are in all four of the above lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578, 8539, 14348, 58973}}... . | We may define the ''strict zeta edos'' to be the edos that are in all four of the above lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578, 8539, 14348, 58973}}... . | ||
The following list of edos are not determined by successively large measured values, they are edos that purely satisfies some property relating to zeta peaks instead. | |||
=== Local zeta edos === | === Local zeta edos === | ||