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			Strength	Closest EDO		Tuning		Strength	Closest EDO
ZPI	Steps per octave	Step size (cents)	Height	EDO	Octave (cents)	Steps per octave	Step size (cents)	Height	EDO	Octave (cents)
125zpi	30.6006474885974	39.2148564976330	1.468164	31edo	1215.66055142662	30.5974484926723	39.2189564527704	3.769318	31edo	1215.78765003588
186zpi	41.3438354846780	29.0248832971658	1.876590	41edo	1190.02021518380	41.3477989230936	29.0221010852836	4.469823	41edo	1189.90614449663
565zpi	98.6209462564991	12.1678005084130	2.305330	99edo	1204.61225033289	98.6257548378926	12.1672072570942	4.883729	99edo	1204.55351845233