71zpi: Difference between revisions

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!Consistent
!Consistent
!Distinct
!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]].[[File:71zpi.png|thumb|The Riemann zeta function around 71zpi]]The nearest zeta peaks to 71zpi that surpass its strength are [[65zpi]] and [[75zpi]].{{Harmonics in cet|59.3329806724710|columns=15|title=71zpi}}
{{Harmonics in cet|59.3329806724710|columns=16|start=16|title=71zpi}}
{|class="wikitable"
|-
!Step
!Cents
!Ratios
|-
|-
|1
|1
Line 127: Line 104:
|1364.659
|1364.659
|11/5
|11/5
|-
|24
|1423.992
|9/4, 25/11, 16/7
|-
|-
|25
|25
|1483.325
|1483.325
|7/3
|7/3
|-
|26
|1542.657
|17/7, 22/9
|-
|-
|27
|27
Line 150: Line 119:
|29
|29
|1720.656
|1720.656
|8/3, 27/10, 19/7
|8/3, 27/10
|-
|-
|30
|30
|1779.989
|1779.989
|14/5
|14/5
|-
|31
|1839.322
|26/9, 29/10
|-
|-
|32
|32
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|2373.319
|2373.319
|4/1
|4/1
|-
|42
|2491.985
|21/5, 17/4
|-
|43
|2551.318
|13/3
|-
|-
|44
|44
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|2788.650
|2788.650
|5/1
|5/1
|-
|48
|2847.983
|31/6, 26/5
|-
|49
|2907.316
|16/3
|-
|50
|2966.649
|11/2
|-
|-
|51
|51
|3025.982
|3025.982
|17/3, 23/4
|23/4
|-
|-
|52
|52
|3085.315
|3085.315
|6/1
|6/1
|-
|54
|3203.981
|19/3
|-
|55
|3263.314
|13/2
|-
|-
|57
|57
|3381.980
|3381.980
|7/1
|7/1
|-
|58
|3441.313
|22/3
|-
|59
|3500.646
|15/2
|-
|-
|61
|61
|3619.312
|3619.312
|8/1
|8/1
|-
|62
|3678.645
|25/3, 17/2
|-
|-
|63
|63
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|3797.311
|3797.311
|9/1
|9/1
|-
|65
|3856.644
|28/3
|-
|66
|3915.977
|19/2, 29/3
|-
|-
|67
|67
|3975.310
|3975.310
|10/1
|10/1
|-
|68
|4034.643
|31/3
|-
|69
|4093.976
|21/2, 32/3
|-
|-
|70
|70
|4153.309
|4153.309
|11/1
|11/1
|-
|71
|4212.642
|23/2
|-
|73
|4331.308
|12/1
|-
|74
|4390.641
|25/2
|-
|-
|75
|75
|4449.974
|4449.974
|13/1
|13/1
|-
|76
|4509.307
|27/2
|-
|-
|77
|77
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|4805.971
|4805.971
|16/1
|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
|}
|}


{{Stub}}
{{Stub}}
[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]

Revision as of 21:41, 20 April 2024

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
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
25 1483.325 7/3
27 1601.990 5/2
28 1661.323 13/5
29 1720.656 8/3, 27/10
30 1779.989 14/5
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
44 2610.651 9/2
45 2669.984 14/3
46 2729.317 29/6
47 2788.650 5/1
51 3025.982 23/4
52 3085.315 6/1
57 3381.980 7/1
61 3619.312 8/1
63 3737.978 26/3
64 3797.311 9/1
67 3975.310 10/1
70 4153.309 11/1
75 4449.974 13/1
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
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