Zeta peak index: Difference between revisions

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A '''zeta peak index''' ('''ZPI''' or '''zpi''') is a [[tuning]] obtained from one of the peaks of the [[The Riemann zeta function and tuning|Riemann zeta function]].
A '''zeta peak index''' ('''ZPI''' or '''zpi''') is an [[equal-step tuning]] obtained from one of the peaks of the [[The Riemann zeta function and tuning|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.  
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 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]].


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