186zpi

186 zeta peak index (abbreviated 186zpi), is the equal-step tuning system obtained from the 186st peak of the Riemann zeta function.

Tuning			Strength			Closest EDO		Integer limit
ZPI	Steps per octave	Step size (cents)	Height	Integral	Gap	EDO	Octave (cents)	Consistent	Distinct
186zpi	41.3438354846780	29.0248832971658	1.876590	0.241233	11.567493	41edo	1190.02021518380	2	2

Theory

186zpi sets a height record on the Riemann zeta function with primes 2 and 3 removed. The last record is 125zpi and the next is 565zpi. It is important to highlight that the optimal equal tunings obtained by excluding the prime numbers 2 and 3 from the Riemann zeta function differs very slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.

Unmodified Riemann zeta function					Riemann zeta function with primes 2 and 3 removed
Tuning			Height	Closest EDO		Tuning		Height	Closest EDO
ZPI	Steps per octave	Step size (cents)		EDO	Octave (cents)	Steps per octave	Step size (cents)		EDO	Octave (cents)
186zpi	41.3438354846780	29.0248832971658		41edo	1190.02021518380	41.3477989230936	29.0221010852836		41edo	1189.90614449663