71zpi

71 zeta peak index (abbreviated 71zpi), is the equal-step tuning system obtained from the 71st 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
71zpi	20.2248393119540	59.3329806724710	3.531097	0.613581	12.986080	20edo	1186.65961344942	6	6

71zpi marks the most prominent zeta peak index in the vicinity of 20edo, ranging between 19.5 EDO and 20.5 EDO. It surpasses 70zpi in peak height, integral, and gap. However, while 70zpi is the closest peak to 20 EDO and closely rivals in strength, it does not match the overall superiority of 71zpi.

71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs from the harmonic characteristics of 20edo.

All harmonics starting from the fifth have a different mapping than 20edo.

The nearest zeta peaks to 71zpi that surpass its strength are 65zpi and 75zpi.

71zpi

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	-13.3	-3.3	-26.7	+2.3	-16.6	+13.2	+19.3	-6.6	-11.0	+2.0	+29.4	+9.4	-0.2	-1.0	+6.0
	Relative (%)	-22.5	-5.6	-45.0	+3.9	-28.0	+22.2	+32.5	-11.1	-18.5	+3.4	+49.5	+15.9	-0.3	-1.6	+10.1
Step		20	32	40	47	52	57	61	64	67	70	73	75	77	79	81

71zpi

Harmonic		17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32
Error	Absolute (¢)	+19.7	-19.9	+5.1	-24.3	+9.9	-11.3	-29.0	+16.0	+4.7	-3.9	-9.9	-13.5	-14.9	-14.3	-11.7	-7.4
	Relative (%)	+33.2	-33.6	+8.6	-41.0	+16.6	-19.1	-48.8	+27.0	+7.9	-6.6	-16.7	-22.8	-25.2	-24.1	-19.8	-12.4
Step		83	84	86	87	89	90	91	93	94	95	96	97	98	99	100	101

This page is a stub. You can help the Xenharmonic Wiki by expanding it.