Zeta peak index: Difference between revisions
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ZPIs are a kind of [[equal-step tuning]]. | ZPIs are a kind of [[equal-step tuning]]. | ||
[[Category:Edonoi]][[Category:Zeta]] | |||
Revision as of 12:20, 27 March 2024
A zeta peak index (ZPI or zpi) is a tuning obtained from one of the peaks of the Riemann zeta function.
For instance, the closest zeta peak of 12edo, which has a value of 12.023edo, is the 34th peak of the Riemann zeta function: this tuning is 34zpi.
ZPIs are particularly useful when dealing with zeta peak tunings that are not closely associated with an integer EDO. For example, 22.597edo is 83zpi, 22.807edo is 84zpi, 23.026edo is 85zpi, 23.232edo is 86zpi, and 23.437edo is 87zpi.
ZPIs are a kind of equal-step tuning.