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. While 70zpi is the nearest peak to 20edo and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength.

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

The Riemann zeta function around 71zpi

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

Step	Cents	Ratios
1	59.333	30/29, 29/28
2	118.666	15/14
3	177.999	10/9
4	237.332	8/7
5	296.665	13/11, 19/16, 6/5
6	355.998	11/9, 27/22, 16/13
7	415.331	5/4, 14/11
8	474.664	25/19, 4/3
9	533.997	15/11
10	593.330	7/5, 31/22
11	652.663	16/11, 19/13
12	711.996	3/2
13	771.329	14/9, 25/16, 11/7
14	830.662	8/5, 21/13, 13/8
15	889.995	5/3
16	949.328	19/11, 26/15, 7/4
17	1008.661	9/5
18	1067.994	13/7
19	1127.327	23/12
20	1186.660	2/1
22	1305.326	17/8
23	1364.659	11/5
24	1423.992	9/4, 25/11, 16/7
25	1483.325	7/3
26	1542.657	17/7, 22/9
27	1601.990	5/2
28	1661.323	13/5
29	1720.656	8/3, 27/10, 19/7
30	1779.989	14/5
31	1839.322	26/9, 29/10
32	1898.655	3/1
33	1957.988	31/10
34	2017.321	16/5
35	2076.654	10/3
36	2135.987	24/7
37	2195.320	7/2, 32/9
38	2254.653	11/3
39	2313.986	19/5
40	2373.319	4/1
42	2491.985	21/5, 17/4
43	2551.318	13/3
44	2610.651	9/2
45	2669.984	14/3
46	2729.317	29/6
47	2788.650	5/1
48	2847.983	31/6, 26/5
49	2907.316	16/3
50	2966.649	11/2
51	3025.982	17/3, 23/4
52	3085.315	6/1
54	3203.981	19/3
55	3263.314	13/2
57	3381.980	7/1
58	3441.313	22/3
59	3500.646	15/2
61	3619.312	8/1
62	3678.645	25/3, 17/2
63	3737.978	26/3
64	3797.311	9/1
65	3856.644	28/3
66	3915.977	19/2, 29/3
67	3975.310	10/1
68	4034.643	31/3
69	4093.976	21/2, 32/3
70	4153.309	11/1
71	4212.642	23/2
73	4331.308	12/1
74	4390.641	25/2
75	4449.974	13/1
76	4509.307	27/2
77	4568.640	14/1
78	4627.972	29/2
79	4687.305	15/1
80	4746.638	31/2
81	4805.971	16/1
83	4924.637	17/1
84	4983.970	18/1
86	5102.636	19/1
87	5161.969	20/1
89	5280.635	21/1
90	5339.968	22/1
91	5399.301	23/1
93	5517.967	24/1
94	5577.300	25/1
95	5636.633	26/1
96	5695.966	27/1
97	5755.299	28/1
98	5814.632	29/1
99	5873.965	30/1
100	5933.298	31/1
101	5992.631	32/1

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