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'''71 [[zeta peak index]]''' (abbreviated '''71zpi'''), is the [[tuning system]] obtained from the 71st peak of the [[The Riemann zeta function and tuning|Riemann zeta function]].
'''71 zeta peak index''' (abbreviated '''71zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 71st [[Zeta peak index|peak]] of the [[Riemann zeta function]].
{|class="wikitable sortable"
 
!colspan="3"|Tuning
{{ZPI
!colspan="3"|Strength
| zpi = 71
!colspan="2"|Closest EDO
| steps = 20.2248393119540
!colspan="2"|Integer limit
| step size = 59.3329806724710
| height = 3.531097
| integral = 0.613581
| gap = 12.986080
| octave = 1186.65961344942
| consistent = 6
| distinct = 6
}}
 
[[File:71zpi.png|thumb|right|The Riemann zeta function around 71zpi]]
 
== Theory ==
'''71zpi''' marks the most prominent [[zeta peak index]] in the [[vicinity]] of [[20edo]]. 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 may also be viewed as a tritave compression of [[32edt]], a [[Riemann zeta function#Removing_primes|no-2s zeta peak EDT]] (consistent in the [[Odd_limit#Nonoctave_equaves|no-2s 19-integer-limit]]), but with less extreme stretch than [[71zpi#Record on the Riemann zeta function with prime 2 removed|the no-2s peak]] at 59.271105 cents.
 
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 nearest zeta peaks to 71zpi that surpass its strength are [[65zpi]] and [[75zpi]].
 
71zpi is distinguished by its extensive [[EDO-span|EDO-deviation]] and substantial zeta strength, qualifying it as a strong candidate for no-octave tuning systems. It is noteworthy that only [[19zpi]] exhibits both a greater octave error and stronger zeta height and integral than 71zpi, although 71zpi still has a more pronounced zeta gap. Other notable [[Zeta peak index|zeta peak indices]] in this category include [[61zpi]], [[84zpi]], [[110zpi]], [[137zpi]], [[151zpi]], [[222zpi]], and [[273zpi]], each demonstrating characteristics that make them suitable for similar applications.
 
=== Harmonic series ===
{{Harmonics in cet|59.3329806724710|columns=15|title=Approximation of harmonics in 71zpi}}
{{Harmonics in cet|59.3329806724710|columns=17|start=16|title=Approximation of harmonics in 71zpi}}
 
== Intervals ==
 
There are multiple ways to approach notation. The simplest method is to use the notations from [[20edo]]. However, this approach will not preserve octave compression when the audio is rendered by notation software. If maintaining accurate step compression in notation software is important, consider using the ups and downs notation from [[182edo]] at every 9-degree step. With this method, the tonal difference will be less than 1 cent up to the 86th harmonic.
 
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ style="white-space:nowrap" | Intervals in 71zpi
|-
| colspan="3" style="text-align:left;" | JI ratios are comprised of 33-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* Normal: relative error < 25 %
* <small>Small:</small> relative error < 33.333 %
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
| colspan="2" style="text-align:right;" | <center>'''⟨182 288] at every 9 steps'''</center><br>[[9/8|Whole tone]] = 30 steps<br>[[256/243|Limma]] = 16 steps<br>[[2187/2048|Apotome]] = 14 steps
|-
! Degree
! Cents
! Ratios
! Ups and downs notation
! Step
|-
| 0
| 0.000
|
| P1
| 0
|-
| 1
| 59.333
| '''[[33/32]]''', '''<u>[[32/31]]'''</u>, '''<u>[[31/30]]'''</u>, '''<u>[[30/29]]'''</u>, '''<u>[[29/28]]'''</u>, '''<u>[[28/27]]'''</u>, '''[[27/26]]''', '''[[26/25]]''', [[25/24]], [[24/23]], <small>[[23/22]]</small>, <small><small>[[22/21]]</small></small>, <small><small><small>[[21/20]]</small></small></small>, <small><small><small>[[20/19]]</small></small></small>
| v<sup>7</sup>m2
| 9
|-
| 2
| 118.666
| <small><small><small>[[19/18]]</small></small></small>, <small>[[18/17]]</small>, [[17/16]], [[33/31]], '''[[16/15]]''', '''<u>[[31/29]]'''</u>, '''<u>[[15/14]]'''</u>, '''[[29/27]]''', '''[[14/13]]''', [[27/25]], <small><small>[[13/12]]</small></small>, <small><small><small>[[25/23]]</small></small></small>
| ^^m2
| 18
|-
| 3
| 177.999
| <small><small><small>[[12/11]]</small></small></small>, <small><small>[[23/21]]</small></small>, [[11/10]], '''[[32/29]]''', '''<u>[[21/19]]'''</u>, '''<u>[[31/28]]'''</u>, '''<u>[[10/9]]'''</u>, [[29/26]], [[19/17]], <small>[[28/25]]</small>, <small><small><small>[[9/8]]</small></small></small>
| vvvM2
| 27
|-
| 4
| 237.332
| <small><small><small>[[26/23]]</small></small></small>, <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, [[33/29]], '''[[8/7]]''', '''<u>[[31/27]]'''</u>, '''<u>[[23/20]]'''</u>, [[15/13]], <small>[[22/19]]</small>, <small>[[29/25]]</small>, <small><small><small>[[7/6]]</small></small></small>
| ^<sup>6</sup>M2
| 36
|-
| 5
| 296.665
| <small>[[27/23]]</small>, <small>[[20/17]]</small>, [[33/28]], '''[[13/11]]''', '''<u>[[32/27]]'''</u>, '''<u>[[19/16]]'''</u>, '''[[25/21]]''', '''[[31/26]]''', <small>[[6/5]]</small>
| vm3
| 45
|-
| 6
| 355.998
| <small><small><small>[[29/24]]</small></small></small>, <small><small><small>[[23/19]]</small></small></small>, <small><small>[[17/14]]</small></small>, <small>[[28/23]]</small>, '''[[11/9]]''', '''<u>[[27/22]]'''</u>, '''<u>[[16/13]]'''</u>, '''[[21/17]]''', [[26/21]], <small>[[31/25]]</small>
| v<sup>6</sup>M3
| 54
|-
| 7
| 415.331
| <small><small><small>[[5/4]]</small></small></small>, [[29/23]], [[24/19]], '''[[19/15]]''', '''<u>[[33/26]]'''</u>, '''<u>[[14/11]]'''</u>, '''[[23/18]]''', [[32/25]], <small>[[9/7]]</small>, <small><small><small>[[31/24]]</small></small></small>
| ^^^M3
| 63
|-
| 8
| 474.664
| <small><small><small>[[22/17]]</small></small></small>, <small><small>[[13/10]]</small></small>, [[30/23]], [[17/13]], '''<u>[[21/16]]'''</u>, '''<u>[[25/19]]'''</u>, '''<u>[[29/22]]'''</u>, '''[[33/25]]''', <small><small>[[4/3]]</small></small>
| v<sup>4</sup>4
| 72
|-
| 9
| 533.997
| <small>[[31/23]]</small>, [[27/20]], [[23/17]], '''[[19/14]]''', '''<u>[[15/11]]'''</u>, '''[[26/19]]''', <small>[[11/8]]</small>, <small><small><small>[[29/21]]</small></small></small>, <small><small><small>[[18/13]]</small></small></small>
| ^<sup>5</sup>4
| 81
|-
| 10
| 593.330
| <small><small>[[25/18]]</small></small>, <small><small>[[32/23]]</small></small>, [[7/5]], '''<u>[[31/22]]'''</u>, '''<u>[[24/17]]'''</u>, '''[[17/12]]''', <small>[[27/19]]</small>, <small><small>[[10/7]]</small></small>
| A4
| 90
|-
| 11
| 652.663
| <small><small><small>[[33/23]]</small></small></small>, <small><small>[[23/16]]</small></small>, <small>[[13/9]]</small>, '''[[29/20]]''', '''<u>[[16/11]]'''</u>, '''<u>[[19/13]]'''</u>, [[22/15]], <small>[[25/17]]</small>, <small>[[28/19]]</small>, <small><small>[[31/21]]</small></small>
| ~5
| 99
|-
| 12
| 711.996
| [[3/2]], <small>[[32/21]]</small>, <small><small>[[29/19]]</small></small>, <small><small>[[26/17]]</small></small>, <small><small><small>[[23/15]]</small></small></small>
| ^^5
| 108
|-
| 13
| 771.329
| <small><small><small>[[20/13]]</small></small></small>, <small>[[17/11]]</small>, [[31/20]], '''[[14/9]]''', '''<u>[[25/16]]'''</u>, [[11/7]], <small>[[30/19]]</small>, <small><small>[[19/12]]</small></small>, <small><small><small>[[27/17]]</small></small></small>
| v<sup>5</sup>m6
| 117
|-
| 14
| 830.662
| <small>[[8/5]]</small>, '''[[29/18]]''', '''<u>[[21/13]]'''</u>, '''[[13/8]]''', <small>[[31/19]]</small>, <small><small>[[18/11]]</small></small>, <small><small><small>[[23/14]]</small></small></small>
| ^<sup>4</sup>m6
| 126
|-
| 15
| 889.995
| <small><small><small>[[28/17]]</small></small></small>, <small><small>[[33/20]]</small></small>, '''[[5/3]]''', [[32/19]], <small>[[27/16]]</small>, <small><small>[[22/13]]</small></small>, <small><small><small>[[17/10]]</small></small></small>
| vM6
| 135
|-
| 16
| 949.328
| <small><small>[[29/17]]</small></small>, <small>[[12/7]]</small>, '''[[31/18]]''', '''<u>[[19/11]]'''</u>, '''<u>[[26/15]]'''</u>, '''[[33/19]]''', <small>[[7/4]]</small>
| v<sup>6</sup>A6, ^<sup>6</sup>d7
| 144
|-
| 17
| 1008.661
| <small><small><small>[[30/17]]</small></small></small>, <small><small>[[23/13]]</small></small>, [[16/9]], '''<u>[[25/14]]'''</u>, '''[[9/5]]''', <small><small>[[29/16]]</small></small>, <small><small><small>[[20/11]]</small></small></small>
| ^m7
| 153
|-
| 18
| 1067.994
| <small><small><small>[[31/17]]</small></small></small>, <small>[[11/6]]</small>, '''[[24/13]]''', '''<u>[[13/7]]'''</u>, [[28/15]], <small><small>[[15/8]]</small></small>, <small><small><small>[[32/17]]</small></small></small>
| v<sup>4</sup>M7
| 162
|-
| 19
| 1127.327
| <small><small><small>[[17/9]]</small></small></small>, <small>[[19/10]]</small>, '''[[21/11]]''', '''<u>[[23/12]]'''</u>, '''<u>[[25/13]]'''</u>, '''[[27/14]]''', [[29/15]], <small>[[31/16]]</small>, <small><small>[[33/17]]</small></small>
| ^<sup>5</sup>M7
| 171
|-
| 20
| 1186.660
| [[2/1]]
| vv1 +1 oct
| 180
|-
| 21
| 1245.993
| '''[[33/16]]''', [[31/15]], [[29/14]], <small>[[27/13]]</small>, <small><small>[[25/12]]</small></small>
| ^<sup>7</sup>1 +1 oct
| 189
|-
| 22
| 1305.326
| <small><small><small>[[23/11]]</small></small></small>, <small><small>[[21/10]]</small></small>, [[19/9]], '''<u>[[17/8]]'''</u>, '''[[32/15]]''', [[15/7]], <small><small>[[28/13]]</small></small>
| m2 +1 oct
| 198
|-
| 23
| 1364.659
| <small><small><small>[[13/6]]</small></small></small>, [[24/11]], '''<u>[[11/5]]'''</u>, [[31/14]], <small>[[20/9]]</small>, <small><small>[[29/13]]</small></small>
| v<sup>5</sup>M2 +1 oct
| 207
|-
| 24
| 1423.992
| <small><small>[[9/4]]</small></small>, '''<u>[[25/11]]'''</u>, '''[[16/7]]''', <small>[[23/10]]</small>, <small><small>[[30/13]]</small></small>
| ^<sup>4</sup>M2 +1 oct
| 216
|-
| 25
| 1483.325
| <small>[[7/3]]</small>, '''<u>[[33/14]]'''</u>, '''[[26/11]]''', [[19/8]], <small><small>[[31/13]]</small></small>
| vvvm3 +1 oct
| 225
|-
| 26
| 1542.657
| <small><small><small>[[12/5]]</small></small></small>, <small>[[29/12]]</small>, '''[[17/7]]''', '''<u>[[22/9]]'''</u>, [[27/11]], <small>[[32/13]]</small>
| ^<sup>6</sup>m3 +1 oct
| 234
|-
| 27
| 1601.990
| <small>[[5/2]]</small>, [[33/13]], <small>[[28/11]]</small>, <small><small>[[23/9]]</small></small>
| ^M3 +1 oct
| 243
|-
| 28
| 1661.323
| <small><small><small>[[18/7]]</small></small></small>, <small>[[31/12]]</small>, '''[[13/5]]''', '''[[21/8]]''', <small>[[29/11]]</small>
| v<sup>6</sup>4 +1 oct
| 252
|-
| 29
| 1720.656
| <small><small>[[8/3]]</small></small>, '''<u>[[27/10]]'''</u>, '''[[19/7]]''', <small>[[30/11]]</small>
| ^^^4 +1 oct
| 261
|-
| 30
| 1779.989
| <small><small><small>[[11/4]]</small></small></small>, [[25/9]], '''<u>[[14/5]]'''</u>, [[31/11]], <small><small>[[17/6]]</small></small>
| vvA4 +1 oct
| 270
|-
| 31
| 1839.322
| <small><small>[[20/7]]</small></small>, [[23/8]], '''<u>[[26/9]]'''</u>, '''<u>[[29/10]]'''</u>, '''[[32/11]]'''
| ^<sup>5</sup>d5 +1 oct
| 279
|-
| 32
| 1898.655
| '''<u>[[3/1]]'''</u>
| P5 +1 oct
| 288
|-
| 33
| 1957.988
| '''<u>[[31/10]]'''</u>, '''[[28/9]]''', [[25/8]], <small><small>[[22/7]]</small></small>
| v<sup>7</sup>m6 +1 oct
| 297
|-
| 34
| 2017.321
| <small><small>[[19/6]]</small></small>, '''<u>[[16/5]]'''</u>, '''[[29/9]]''', <small><small>[[13/4]]</small></small>
| ^^m6 +1 oct
| 306
|-
| 35
| 2076.654
| <small>[[23/7]]</small>, '''[[33/10]]''', '''[[10/3]]''', <small><small><small>[[27/8]]</small></small></small>
| vvvM6 +1 oct
| 315
|-
| 36
| 2135.987
| <small>[[17/5]]</small>, '''<u>[[24/7]]'''</u>, '''[[31/9]]'''
| ^<sup>6</sup>M6 +1 oct
| 324
|-
| 37
| 2195.320
| <small><small><small>[[7/2]]</small></small></small>, '''<u>[[32/9]]'''</u>, '''[[25/7]]''', <small><small>[[18/5]]</small></small>
| vm7 +1 oct
| 333
|-
| 38
| 2254.653
| <small><small><small>[[29/8]]</small></small></small>, '''[[11/3]]''', <small>[[26/7]]</small>
| v<sup>6</sup>M7 +1 oct
| 342
|-
| 39
| 2313.986
| <small><small><small>[[15/4]]</small></small></small>, '''<u>[[19/5]]'''</u>, [[23/6]], <small><small>[[27/7]]</small></small>
| ^^^M7 +1 oct
| 351
|-
| 40
| 2373.319
| <small><small><small>[[31/8]]</small></small></small>, <small><small><small>[[4/1]]</small></small></small>
| v<sup>4</sup>1 +2 oct
| 360
|-
| 41
| 2432.652
| <small><small>[[33/8]]</small></small>, <small><small><small>[[29/7]]</small></small></small>
| ^<sup>5</sup>1 +2 oct
| 369
|-
| 42
| 2491.985
| <small><small>[[25/6]]</small></small>, '''[[21/5]]''', [[17/4]], <small><small><small>[[30/7]]</small></small></small>
| vvm2 +2 oct
| 378
|-
| 43
| 2551.318
| [[13/3]], [[22/5]], <small><small><small>[[31/7]]</small></small></small>
| ~2 +2 oct
| 387
|-
| 44
| 2610.651
| '''[[9/2]]''', <small><small>[[32/7]]</small></small>
| ^^M2 +2 oct
| 396
|-
| 45
| 2669.984
| <small><small><small>[[23/5]]</small></small></small>, '''<u>[[14/3]]'''</u>, [[33/7]], <small><small><small>[[19/4]]</small></small></small>
| v<sup>5</sup>m3 +2 oct
| 405
|-
| 46
| 2729.317
| [[24/5]], '''<u>[[29/6]]'''</u>
| ^<sup>4</sup>m3 +2 oct
| 414
|-
| 47
| 2788.650
| '''<u>[[5/1]]'''</u>
| vM3 +2 oct
| 423
|-
| 48
| 2847.983
| '''<u>[[31/6]]'''</u>, '''[[26/5]]''', <small><small>[[21/4]]</small></small>
| v<sup>6</sup>A3 +2 oct, ^<sup>6</sup>d4 +2 oct
| 432
|-
| 49
| 2907.316
| '''[[16/3]]''', [[27/5]]
| ^4 +2 oct
| 441
|-
| 50
| 2966.649
| <small>[[11/2]]</small>, <small>[[28/5]]</small>
| v<sup>4</sup>A4 +2 oct
| 450
|-
| 51
| 3025.982
| <small><small>[[17/3]]</small></small>, '''<u>[[23/4]]'''</u>, <small>[[29/5]]</small>
| ^^^d5 +2 oct
| 459
|-
| 52
| 3085.315
| <small>[[6/1]]</small>
| vv5 +2 oct
| 468
|-
| 53
| 3144.648
| [[31/5]], <small><small><small>[[25/4]]</small></small></small>
| ^<sup>7</sup>5 +2 oct
| 477
|-
| 54
| 3203.981
| '''[[19/3]]''', '''[[32/5]]'''
| m6 +2 oct
| 486
|-
| 55
| 3263.314
| <small><small>[[13/2]]</small></small>, '''<u>[[33/5]]'''</u>, <small><small>[[20/3]]</small></small>
| v<sup>5</sup>M6 +2 oct
| 495
|-
| 56
| 3322.647
| <small>[[27/4]]</small>
| ^<sup>4</sup>M6 +2 oct
| 504
|-
| 57
| 3381.980
| [[7/1]]
| vvvm7 +2 oct
| 513
|-
| 58
| 3441.313
| [[29/4]], '''[[22/3]]'''
| ^<sup>6</sup>m7 +2 oct
| 522
|-
| 59
| 3500.646
| [[15/2]], <small><small><small>[[23/3]]</small></small></small>
| ^M7 +2 oct
| 531
|-
| 60
| 3559.979
| <small>[[31/4]]</small>
| v<sup>6</sup>1 +3 oct
| 540
|-
| 61
| 3619.312
| <small>[[8/1]]</small>
| ^^^1 +3 oct
| 549
|-
| 62
| 3678.645
| <small><small><small>[[33/4]]</small></small></small>, '''[[25/3]]''', <small><small><small>[[17/2]]</small></small></small>
| v<sup>4</sup>m2 +3 oct
| 558
|-
| 63
| 3737.978
| '''<u>[[26/3]]'''</u>
| ^<sup>5</sup>m2 +3 oct
| 567
|-
| 64
| 3797.311
| '''[[9/1]]'''
| M2 +3 oct
| 576
|-
| 65
| 3856.644
| [[28/3]]
| v<sup>7</sup>m3 +3 oct
| 585
|-
| 66
| 3915.977
| <small>[[19/2]]</small>, [[29/3]]
| ^^m3 +3 oct
| 594
|-
| 67
| 3975.310
| [[10/1]]
| vvvM3 +3 oct
| 603
|-
| 68
| 4034.643
| '''[[31/3]]'''
| ^<sup>6</sup>M3 +3 oct
| 612
|-
| 69
| 4093.976
| <small><small>[[21/2]]</small></small>, '''<u>[[32/3]]'''</u>
| v4 +3 oct
| 621
|-
| 70
| 4153.309
| '''<u>[[11/1]]'''</u>
| v<sup>6</sup>A4 +3 oct
| 630
|-
| 71
| 4212.642
| <small>[[23/2]]</small>
| ^d5 +3 oct
| 639
|-
| 72
| 4271.975
|
| v<sup>4</sup>5 +3 oct
| 648
|-
| 73
| 4331.308
| <small><small><small>[[12/1]]</small></small></small>
| ^<sup>5</sup>5 +3 oct
| 657
|-
| 74
| 4390.641
| <small>[[25/2]]</small>
| vvm6 +3 oct
| 666
|-
| 75
| 4449.974
| '''[[13/1]]'''
| ~6 +3 oct
| 675
|-
| 76
| 4509.307
| '''<u>[[27/2]]'''</u>
| ^^M6 +3 oct
| 684
|-
| 77
| 4568.640
| '''<u>[[14/1]]'''</u>
| v<sup>5</sup>m7 +3 oct
| 693
|-
| 78
| 4627.972
| '''<u>[[29/2]]'''</u>
| ^<sup>4</sup>m7 +3 oct
| 702
|-
| 79
| 4687.305
| '''<u>[[15/1]]'''</u>
| vM7 +3 oct
| 711
|-
| 80
| 4746.638
| '''<u>[[31/2]]'''</u>
| v<sup>6</sup>A7 +3 oct, ^<sup>6</sup>d1 +4 oct
| 720
|-
| 81
| 4805.971
| '''[[16/1]]'''
| ^1 +4 oct
| 729
|-
| 82
| 4865.304
| [[33/2]]
| v<sup>6</sup>m2 +4 oct
| 738
|-
| 83
| 4924.637
| <small>[[17/1]]</small>
| ^^^m2 +4 oct
| 747
|-
| 84
| 4983.970
| <small><small>[[18/1]]</small></small>
| vvM2 +4 oct
| 756
|-
| 85
| 5043.303
|
| ^<sup>7</sup>M2 +4 oct
| 765
|-
| 86
| 5102.636
| '''[[19/1]]'''
| m3 +4 oct
| 774
|-
| 87
| 5161.969
| <small><small>[[20/1]]</small></small>
| v<sup>5</sup>M3 +4 oct
| 783
|-
| 88
| 5221.302
|
| ^<sup>4</sup>M3 +4 oct
| 792
|-
| 89
| 5280.635
| '''[[21/1]]'''
| vvv4 +4 oct
| 801
|-
| 90
| 5339.968
| [[22/1]]
| ^<sup>6</sup>4 +4 oct
| 810
|-
| 91
| 5399.301
| <small><small><small>[[23/1]]</small></small></small>
| ^A4 +4 oct, vd5 +4 oct
| 819
|-
| 92
| 5458.634
|
| v<sup>6</sup>5 +4 oct
| 828
|-
| 93
| 5517.967
| <small>[[24/1]]</small>
| ^^^5 +4 oct
| 837
|-
| 94
| 5577.300
| '''<u>[[25/1]]'''</u>
| v<sup>4</sup>m6 +4 oct
| 846
|-
| 95
| 5636.633
| '''<u>[[26/1]]'''</u>
| ^<sup>5</sup>m6 +4 oct
| 855
|-
| 96
| 5695.966
| [[27/1]]
| M6 +4 oct
| 864
|-
| 97
| 5755.299
| [[28/1]]
| v<sup>7</sup>m7 +4 oct
| 873
|-
| 98
| 5814.632
| <small>[[29/1]]</small>
| ^^m7 +4 oct
| 882
|-
| 99
| 5873.965
| [[30/1]]
| vvvM7 +4 oct
| 891
|-
| 100
| 5933.298
| [[31/1]]
| ^<sup>6</sup>M7 +4 oct
| 900
|-
| 101
| 5992.631
| '''[[32/1]]'''
| v1 +5 oct
| 909
|-
| 102
| 6051.964
| '''<u>[[33/1]]'''</u>
| v<sup>6</sup>A1 +5 oct, ^<sup>6</sup>d2 +5 oct
| 918
|}
 
== Approximation to JI ==
 
=== Interval mappings ===
 
The following tables show how 33-integer-limit intervals are represented in 71zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 33-integer-limit intervals in 71zpi (by direct approximation)
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[14/1]]
| -0.186
| -0.314
|-
| [[11/5]]
| -0.346
| -0.583
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''+0.370''
| ''+0.624''
|-
| [[31/22]]
| -0.388
| -0.654
|-
| [[21/13]]
| +0.408
| +0.688
|-
| [[25/19]]
| -0.451
| -0.759
|-
| [[26/3]]
| -0.595
| -1.003
|-
| [[30/29]]
| +0.641
| +1.081
|-
| [[31/10]]
| -0.733
| -1.236
|- style="background-color: #cccccc;"
| ''[[32/9]]''
| ''-0.770''
| ''-1.297''
|-
| [[15/14]]
| -0.777
| -1.309
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''-0.848''
| ''-1.429''
|-
| [[15/1]]
| -0.963
| -1.623
|-
| [[23/12]]
| +1.007
| +1.698
|-
| [[27/10]]
| +1.105
| +1.863
|-
| [[33/14]]
| -1.123
| -1.892
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''-1.299''
| ''-2.189''
|-
| [[33/1]]
| -1.309
| -2.206
|-
| [[29/28]]
| -1.418
| -2.390
|-
| [[27/22]]
| +1.451
| +2.445
|-
| [[31/2]]
| +1.603
| +2.702
|-
| [[29/2]]
| -1.605
| -2.705
|-
| [[29/6]]
| +1.695
| +2.857
|-
| [[31/28]]
| +1.789
| +3.016
|-
| [[31/27]]
| -1.839
| -3.099
|-
| '''[[11/1]]'''
| '''+1.991'''
| '''+3.355'''
|-
| [[14/11]]
| -2.177
| -3.669
|-
| [[23/4]]
| -2.292
| -3.864
|-
| '''[[5/1]]'''
| '''+2.336'''
| '''+3.938'''
|-
| [[14/5]]
| -2.523
| -4.252
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''+2.530''
| ''+4.264''
|-
| [[31/30]]
| +2.566
| +4.325
|-
| [[33/26]]
| +2.586
| +4.358
|-
| [[25/11]]
| +2.682
| +4.520
|-
| [[26/9]]
| +2.705
| +4.559
|-
| [[19/5]]
| +2.787
| +4.697
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''+2.858''
| ''+4.817''
|-
| [[26/15]]
| -2.931
| -4.940
|-
| [[15/11]]
| -2.954
| -4.979
|-
| [[14/3]]
| +3.113
| +5.247
|-
| [[19/11]]
| +3.133
| +5.280
|-
| [[31/29]]
| +3.208
| +5.406
|-
| '''[[3/1]]'''
| '''-3.300'''
| '''-5.561'''
|-
| [[27/2]]
| +3.442
| +5.800
|- style="background-color: #cccccc;"
| ''[[16/13]]''
| ''-3.474''
| ''-5.856''
|-
| [[29/22]]
| -3.595
| -6.060
|-
| [[28/27]]
| -3.628
| -6.115
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''+3.635''
| ''+6.127''
|-
| [[33/5]]
| -3.645
| -6.144
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''-3.670''
| ''-6.185''
|-
| [[13/7]]
| -3.708
| -6.250
|- style="background-color: #cccccc;"
| ''[[21/16]]''
| ''+3.883''
| ''+6.544''
|-
| [[26/1]]
| -3.894
| -6.564
|-
| [[29/10]]
| -3.941
| -6.642
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''+3.981''
| ''+6.709''
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''-4.069''
| ''-6.858''
|-
| [[19/13]]
| -4.323
| -7.285
|- style="background-color: #cccccc;"
| ''[[32/31]]''
| ''+4.369''
| ''+7.363''
|-
| [[10/9]]
| -4.405
| -7.424
|-
| [[23/20]]
| -4.629
| -7.801
|-
| [[25/1]]
| +4.673
| +7.875
|-
| [[21/19]]
| +4.731
| +7.974
|-
| [[22/9]]
| -4.750
| -8.006
|-
| [[25/13]]
| -4.773
| -8.045
|-
| [[25/14]]
| +4.859
| +8.190
|-
| [[31/6]]
| +4.903
| +8.263
|-
| [[29/18]]
| +4.995
| +8.418
|-
| [[29/27]]
| -5.046
| -8.505
|-
| '''[[19/1]]'''
| '''+5.123'''
| '''+8.635'''
|-
| [[31/9]]
| -5.138
| -8.660
|-
| [[25/21]]
| -5.182
| -8.733
|-
| [[11/3]]
| +5.290
| +8.916
|-
| [[19/14]]
| +5.310
| +8.949
|-
| [[5/3]]
| +5.636
| +9.499
|-
| [[26/11]]
| -5.885
| -9.919
|- style="background-color: #cccccc;"
| ''[[16/1]]''
| ''+5.971''
| ''+10.064''
|-
| [[33/25]]
| -5.982
| -10.082
|-
| [[27/26]]
| -6.004
| -10.120
|- style="background-color: #cccccc;"
| ''[[33/32]]''
| ''+6.060''
| ''+10.214''
|-
| [[19/15]]
| +6.087
| +10.258
|- style="background-color: #cccccc;"
| ''[[8/7]]''
| ''+6.158''
| ''+10.378''
|-
| [[26/5]]
| -6.231
| -10.502
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''-6.406''
| ''-10.796''
|-
| [[14/9]]
| +6.413
| +10.808
|-
| [[33/19]]
| -6.432
| -10.841
|-
| [[17/7]]
| +6.528
| +11.002
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''+6.566''
| ''+11.067''
|-
| [[9/1]]
| -6.599
| -11.122
|-
| [[9/2]]
| +6.741
| +11.362
|-
| [[28/9]]
| -6.928
| -11.676
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''+6.935''
| ''+11.688''
|-
| [[13/5]]
| +7.110
| +11.982
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''-7.183''
| ''-12.106''
|- style="background-color: #cccccc;"
| ''[[33/16]]''
| ''-7.280''
| ''-12.270''
|- style="background-color: #cccccc;"
| ''[[32/1]]''
| ''-7.369''
| ''-12.420''
|-
| [[13/11]]
| +7.455
| +12.565
|-
| [[21/5]]
| +7.518
| +12.671
|- style="background-color: #cccccc;"
| ''[[32/29]]''
| ''+7.576''
| ''+12.769''
|-
| [[10/3]]
| -7.704
| -12.985
|-
| [[31/26]]
| -7.843
| -13.219
|-
| [[21/11]]
| +7.864
| +13.253
|-
| [[25/3]]
| +7.972
| +13.437
|-
| [[19/7]]
| -8.031
| -13.535
|-
| [[22/3]]
| -8.050
| -13.568
|-
| [[31/18]]
| +8.202
| +13.824
|-
| [[29/9]]
| -8.346
| -14.066
|-
| [[19/3]]
| +8.423
| +14.196
|-
| [[31/3]]
| -8.438
| -14.221
|-
| [[25/7]]
| -8.481
| -14.294
|-
| [[26/25]]
| -8.567
| -14.439
|-
| [[11/9]]
| +8.590
| +14.478
|-
| [[9/5]]
| -8.936
| -15.060
|-
| [[26/19]]
| -9.018
| -15.199
|-
| [[23/18]]
| -9.033
| -15.225
|- style="background-color: #cccccc;"
| ''[[16/3]]''
| ''+9.271''
| ''+15.625''
|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''-9.360''
| ''-15.775''
|-
| [[29/20]]
| +9.399
| +15.842
|-
| '''[[13/1]]'''
| '''+9.446'''
| '''+15.920'''
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''-9.457''
| ''-15.940''
|-
|-
!ZPI
| [[14/13]]
!Steps per octave
| -9.632
!Cents
| -16.234
!Height
|- style="background-color: #cccccc;"
!Integral
| ''[[17/12]]''
!Gap
| ''-9.671''
!EDO
| ''-16.299''
!Octave
|-
!Consistent
| [[33/10]]
!Distinct
| +9.695
| +16.340
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''-9.705''
| ''-16.357''
|-
| [[27/14]]
| -9.712
| -16.369
|-
| [[21/17]]
| -9.828
| -16.563
|-
| [[21/1]]
| +9.854
| +16.609
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''-9.866''
| ''-16.628''
|-
| [[27/1]]
| -9.899
| -16.684
|-
| [[3/2]]
| +10.041
| +16.923
|-
| [[28/3]]
| -10.227
| -17.237
|-
| [[17/13]]
| +10.236
| +17.252
|-
| [[22/15]]
| -10.386
| -17.505
|-
| [[15/13]]
| -10.409
| -17.544
|-
| [[33/31]]
| +10.429
| +17.576
|- style="background-color: #cccccc;"
| ''[[23/17]]''
| ''+10.678''
| ''+17.997''
|-
| [[33/13]]
| -10.755
| -18.126
|-
| [[31/15]]
| -10.774
| -18.159
|-
| [[7/5]]
| +10.818
| +18.232
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''+10.889''
| ''+18.352''
|-
| [[10/1]]
| -11.004
| -18.546
|-
| [[23/8]]
| +11.048
| +18.620
|-
| [[29/26]]
| -11.051
| -18.625
|-
| [[11/7]]
| -11.163
| -18.815
|-
| [[25/9]]
| +11.272
| +18.998
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''-11.339''
| ''-19.112''
|-
| [[22/1]]
| -11.350
| -19.129
|-
| [[31/14]]
| -11.551
| -19.468
|-
| [[29/3]]
| -11.645
| -19.627
|-
| [[19/9]]
| +11.723
| +19.757
|-
| [[29/4]]
| +11.736
| +19.779
|-
| '''[[31/1]]'''
| '''-11.738'''
| '''-19.782'''
|-
| [[27/11]]
| -11.890
| -20.039
|-
| [[33/2]]
| +12.031
| +20.278
|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''-12.042''
| ''-20.295''
|-
| [[33/28]]
| +12.218
| +20.592
|-
| [[27/5]]
| -12.235
| -20.621
|-
| [[23/6]]
| -12.333
| -20.786
|-
| [[15/2]]
| +12.377
| +20.860
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''-12.492''
| ''-21.055''
|-
| [[28/15]]
| -12.564
| -21.175
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''+12.571''
| ''+21.187''
|-
| [[31/20]]
| +12.607
| +21.248
|-
| [[13/3]]
| +12.746
| +21.481
|- style="background-color: #cccccc;"
| ''[[17/4]]''
| ''-12.970''
| ''-21.860''
|-
| [[11/10]]
| +12.995
| +21.901
|-
| '''[[7/1]]'''
| '''+13.154'''
| '''+22.170'''
|-
| '''[[2/1]]'''
| '''-13.340'''
| '''-22.484'''
|-
| [[28/1]]
| -13.527
| -22.798
|-
| [[33/29]]
| +13.636
| +22.982
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''+13.676''
| ''+23.049''
|-
| [[22/5]]
| -13.686
| -23.067
|- style="background-color: #cccccc;"
| ''[[17/16]]''
| ''+13.711''
| ''+23.108''
|-
| [[31/11]]
| -13.728
| -23.138
|-
| [[26/21]]
| -13.749
| -23.172
|-
| [[29/15]]
| -13.982
| -23.565
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''+14.021''
| ''+23.632''
|-
| [[29/23]]
| +14.028
| +23.643
|-
| [[31/5]]
| -14.074
| -23.720
|-
| [[15/7]]
| -14.117
| -23.793
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''-14.188''
| ''-23.913''
|-
| [[30/1]]
| -14.304
| -24.107
|-
| [[24/23]]
| -14.348
| -24.182
|-
| [[27/20]]
| +14.446
| +24.347
|-
| [[33/7]]
| -14.463
| -24.376
|-
| [[19/17]]
| -14.559
| -24.537
|-
| [[27/25]]
| -14.572
| -24.559
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''-14.639''
| ''-24.673''
|-
| [[30/23]]
| +14.669
| +24.724
|-
| [[29/14]]
| -14.759
| -24.874
|-
| [[31/4]]
| +14.943
| +25.185
|-
| '''[[29/1]]'''
| '''-14.945'''
| '''-25.189'''
|-
| [[25/17]]
| -15.009
| -25.297
|-
| [[27/19]]
| -15.022
| -25.318
|-
| [[29/12]]
| +15.035
| +25.341
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''+15.307''
| ''+25.798''
|-
| [[11/2]]
| +15.331
| +25.839
|-
| [[28/23]]
| +15.446
| +26.033
|-
| [[28/11]]
| -15.517
| -26.153
|-
| [[23/2]]
| -15.633
| -26.347
|-
| [[5/2]]
| +15.677
| +26.422
|-
| [[28/5]]
| -15.863
| -26.736
|- style="background-color: #cccccc;"
| ''[[27/16]]''
| ''-15.870''
| ''-26.748''
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''+16.012''
| ''+26.987''
|-
| [[25/22]]
| +16.022
| +27.004
|-
| [[13/9]]
| +16.045
| +27.043
|-
| [[19/10]]
| +16.127
| +27.181
|- style="background-color: #cccccc;"
| ''[[12/7]]''
| ''+16.199''
| ''+27.301''
|-
| [[30/11]]
| -16.294
| -27.463
|-
| [[31/25]]
| -16.410
| -27.658
|-
| [[7/3]]
| +16.454
| +27.731
|-
| [[22/19]]
| -16.473
| -27.764
|-
| [[6/1]]
| -16.640
| -28.045
|-
| [[27/4]]
| +16.782
| +28.284
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''-16.815''
| ''-28.340''
|-
| [[31/19]]
| -16.861
| -28.417
|-
| [[29/11]]
| -16.936
| -28.544
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''+16.975''
| ''+28.610''
|-
| [[26/7]]
| -17.048
| -28.734
|- style="background-color: #cccccc;"
| ''[[23/7]]''
| ''+17.206''
| ''+28.999''
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''-17.223''
| ''-29.028''
|-
| [[31/23]]
| +17.236
| +29.049
|-
| [[29/5]]
| -17.281
| -29.126
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''-17.321''
| ''-29.193''
|-
| [[17/5]]
| +17.346
| +29.234
|-
| [[23/22]]
| -17.623
| -29.703
|-
| [[17/11]]
| +17.691
| +29.817
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''-17.709''
| ''-29.847''
|-
| [[20/9]]
| -17.745
| -29.908
|-
| [[23/10]]
| -17.969
| -30.285
|-
| [[25/2]]
| +18.013
| +30.359
|-
| [[28/25]]
| -18.200
| -30.674
|-
| [[31/12]]
| +18.243
| +30.747
|-
| [[19/2]]
| +18.464
| +31.119
|-
| [[11/6]]
| +18.631
| +31.400
|-
| [[28/19]]
| -18.650
| -31.433
|-
| [[6/5]]
| -18.976
| -31.983
|-
| [[27/23]]
| +19.074
| +32.148
|- style="background-color: #cccccc;"
| ''[[8/1]]''
| ''+19.312''
| ''+32.548''
|-
| [[27/13]]
| -19.345
| -32.604
|-
| [[30/19]]
| -19.427
| -32.742
|- style="background-color: #cccccc;"
| ''[[7/4]]''
| ''-19.498''
| ''-32.862''
|-
| [[29/25]]
| -19.618
| -33.064
|-
| '''[[17/1]]'''
| '''+19.682'''
| '''+33.172'''
|- style="background-color: #cccccc;"
| ''[[18/17]]''
| ''+19.711''
| ''+33.222''
|-
| [[9/7]]
| -19.753
| -33.292
|-
| [[17/14]]
| +19.868
| +33.486
|- style="background-color: #cccccc;"
| ''[[13/12]]''
| ''-19.907''
| ''-33.551''
|-
| [[18/1]]
| -19.940
| -33.606
|-
| [[29/19]]
| -20.068
| -33.823
|-
| [[9/4]]
| +20.082
| +33.845
|- style="background-color: #cccccc;"
| ''[[15/8]]''
| ''-20.275''
| ''-34.172''
|-
| [[13/10]]
| +20.450
| +34.466
|- style="background-color: #cccccc;"
| ''[[23/21]]''
| ''+20.506''
| ''+34.560''
|- style="background-color: #cccccc;"
| ''[[32/7]]''
| ''-20.523''
| ''-34.589''
|- style="background-color: #cccccc;"
| ''[[33/8]]''
| ''-20.621''
| ''-34.754''
|-
| [[17/15]]
| +20.645
| +34.796
|-
| [[22/13]]
| -20.796
| -35.049
|-
| [[21/10]]
| +20.858
| +35.155
|- style="background-color: #cccccc;"
| ''[[23/13]]''
| ''+20.914''
| ''+35.249''
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''-20.917''
| ''-35.253''
|-
| [[33/17]]
| -20.991
| -35.378
|-
| [[20/3]]
| -21.045
| -35.469
|-
| [[31/13]]
| -21.183
| -35.703
|-
| [[22/21]]
| -21.204
| -35.737
|-
| [[25/6]]
| +21.313
| +35.921
|-
| [[31/21]]
| -21.592
| -36.391
|- style="background-color: #cccccc;"
| ''[[32/23]]''
| ''+21.604''
| ''+36.412''
|-
| [[19/6]]
| +21.763
| +36.680
|- style="background-color: #cccccc;"
| ''[[20/7]]''
| ''+21.835''
| ''+36.800''
|-
| [[18/11]]
| -21.930
| -36.961
|-
| [[18/5]]
| -22.276
| -37.544
|-
| [[23/9]]
| -22.374
| -37.709
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''+22.611''
| ''+38.109''
|-
| [[13/2]]
| +22.786
| +38.404
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''-22.798''
| ''-38.424''
|-
| [[28/13]]
| -22.973
| -38.718
|-
| [[17/3]]
| +22.982
| +38.733
|- style="background-color: #cccccc;"
| ''[[17/6]]''
| ''-23.011''
| ''-38.783''
|-
| [[33/20]]
| +23.035
| +38.824
|-
| [[27/7]]
| -23.053
| -38.853
|-
| [[21/2]]
| +23.195
| +39.093
|- style="background-color: #cccccc;"
| ''[[13/4]]''
| ''-23.206''
| ''-39.112''
|-
| [[4/3]]
| -23.381
| -39.407
|-
| [[26/17]]
| -23.576
| -39.736
|-
| [[30/13]]
| -23.750
| -40.028
|-
| [[10/7]]
| -24.158
| -40.716
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''-24.229''
| ''-40.836''
|-
| [[20/1]]
| -24.344
| -41.030
|-
| [[23/16]]
| +24.388
| +41.104
|-
| [[29/13]]
| -24.391
| -41.109
|-
| [[22/7]]
| -24.504
| -41.299
|-
| [[25/18]]
| +24.612
| +41.482
|- style="background-color: #cccccc;"
| ''[[25/12]]''
| ''-24.680''
| ''-41.595''
|- style="background-color: #cccccc;"
| ''[[29/17]]''
| ''+24.706''
| ''+41.639''
|-
| [[29/21]]
| -24.799
| -41.797
|-
| [[31/7]]
| -24.891
| -41.952
|-
| [[19/18]]
| +25.063
| +42.241
|-
| [[29/8]]
| +25.076
| +42.263
|-
| [[26/23]]
| +25.079
| +42.268
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''-25.134''
| ''-42.361''
|- style="background-color: #cccccc;"
| ''[[23/19]]''
| ''+25.237''
| ''+42.534''
|- style="background-color: #cccccc;"
| ''[[30/17]]''
| ''+25.347''
| ''+42.721''
|-
| [[33/4]]
| +25.372
| +42.762
|- style="background-color: #cccccc;"
| ''[[20/13]]''
| ''+25.543''
| ''+43.050''
|-
| [[23/3]]
| -25.673
| -43.270
|- style="background-color: #cccccc;"
| ''[[25/23]]''
| ''-25.687''
| ''-43.293''
|-
| [[15/4]]
| +25.718
| +43.344
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''-25.911''
| ''-43.671''
|-
| [[13/6]]
| +26.086
| +43.965
|- style="background-color: #cccccc;"
| ''[[28/17]]''
| ''+26.124''
| ''+44.030''
|- style="background-color: #cccccc;"
| ''[[18/7]]''
| ''+26.239''
| ''+44.224''
|-
| [[17/9]]
| +26.281
| +44.294
|- style="background-color: #cccccc;"
| ''[[17/2]]''
| ''-26.311''
| ''-44.344''
|-
| [[20/11]]
| -26.335
| -44.385
|-
| [[7/2]]
| +26.494
| +44.654
|-
| [[4/1]]
| -26.681
| -44.968
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''+27.016''
| ''+45.533''
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''-27.051''
| ''-45.592''
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''+27.362''
| ''+46.116''
|-
| [[30/7]]
| -27.458
| -46.277
|- style="background-color: #cccccc;"
| ''[[19/4]]''
| ''-27.529''
| ''-46.397''
|-
| [[33/23]]
| +27.664
| +46.625
|- style="background-color: #cccccc;"
| ''[[31/24]]''
| ''-27.750''
| ''-46.769''
|- style="background-color: #cccccc;"
| ''[[31/17]]''
| ''+27.913''
| ''+47.045''
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''-27.979''
| ''-47.157''
|-
| [[23/15]]
| -28.010
| -47.208
|- style="background-color: #cccccc;"
| ''[[23/5]]''
| ''+28.023''
| ''+47.231''
|-
| [[29/7]]
| -28.099
| -47.358
|-
| [[31/8]]
| +28.284
| +47.669
|- style="background-color: #cccccc;"
| ''[[22/17]]''
| ''+28.301''
| ''+47.699''
|- style="background-color: #cccccc;"
| ''[[23/11]]''
| ''+28.369''
| ''+47.813''
|-
| [[29/24]]
| +28.376
| +47.824
|- style="background-color: #cccccc;"
| ''[[17/10]]''
| ''-28.647''
| ''-48.282''
|-
| [[11/4]]
| +28.671
| +48.323
|-
| [[23/14]]
| -28.787
| -48.517
|-
| '''[[23/1]]'''
| '''-28.973'''
| '''-48.831'''
|-
| [[5/4]]
| +29.017
| +48.906
|- style="background-color: #cccccc;"
| ''[[27/8]]''
| ''-29.211''
| ''-49.232''
|- style="background-color: #cccccc;"
| ''[[12/1]]''
| ''+29.353''
| ''+49.471''
|-
| [[18/13]]
| -29.386
| -49.526
|-
| [[20/19]]
| -29.468
| -49.665
|- style="background-color: #cccccc;"
| ''[[7/6]]''
| ''-29.539''
| ''-49.785''
|-
| [[27/17]]
| -29.581
| -49.856
|}
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 33-integer-limit intervals in 71zpi (by patent val mapping)
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[14/1]]
| -0.186
| -0.314
|-
| [[11/5]]
| -0.346
| -0.583
|-
| [[31/22]]
| -0.388
| -0.654
|-
| [[21/13]]
| +0.408
| +0.688
|-
| [[25/19]]
| -0.451
| -0.759
|-
| [[26/3]]
| -0.595
| -1.003
|-
| [[30/29]]
| +0.641
| +1.081
|-
| [[31/10]]
| -0.733
| -1.236
|-
| [[15/14]]
| -0.777
| -1.309
|-
| [[15/1]]
| -0.963
| -1.623
|-
| [[23/12]]
| +1.007
| +1.698
|-
| [[27/10]]
| +1.105
| +1.863
|-
| [[33/14]]
| -1.123
| -1.892
|-
| [[33/1]]
| -1.309
| -2.206
|-
| [[29/28]]
| -1.418
| -2.390
|-
| [[27/22]]
| +1.451
| +2.445
|-
| [[31/2]]
| +1.603
| +2.702
|-
| [[29/2]]
| -1.605
| -2.705
|-
| [[29/6]]
| +1.695
| +2.857
|-
| [[31/28]]
| +1.789
| +3.016
|-
| [[31/27]]
| -1.839
| -3.099
|-
| '''[[11/1]]'''
| '''+1.991'''
| '''+3.355'''
|-
| [[14/11]]
| -2.177
| -3.669
|-
| [[23/4]]
| -2.292
| -3.864
|-
| '''[[5/1]]'''
| '''+2.336'''
| '''+3.938'''
|-
| [[14/5]]
| -2.523
| -4.252
|-
| [[31/30]]
| +2.566
| +4.325
|-
| [[33/26]]
| +2.586
| +4.358
|-
| [[25/11]]
| +2.682
| +4.520
|-
| [[26/9]]
| +2.705
| +4.559
|-
| [[19/5]]
| +2.787
| +4.697
|-
| [[26/15]]
| -2.931
| -4.940
|-
| [[15/11]]
| -2.954
| -4.979
|-
| [[14/3]]
| +3.113
| +5.247
|-
| [[19/11]]
| +3.133
| +5.280
|-
| [[31/29]]
| +3.208
| +5.406
|-
| '''[[3/1]]'''
| '''-3.300'''
| '''-5.561'''
|-
| [[27/2]]
| +3.442
| +5.800
|-
| [[29/22]]
| -3.595
| -6.060
|-
| [[28/27]]
| -3.628
| -6.115
|-
| [[33/5]]
| -3.645
| -6.144
|-
| [[13/7]]
| -3.708
| -6.250
|-
| [[26/1]]
| -3.894
| -6.564
|-
| [[29/10]]
| -3.941
| -6.642
|-
| [[19/13]]
| -4.323
| -7.285
|-
| [[10/9]]
| -4.405
| -7.424
|-
| [[23/20]]
| -4.629
| -7.801
|-
| [[25/1]]
| +4.673
| +7.875
|-
| [[21/19]]
| +4.731
| +7.974
|-
| [[22/9]]
| -4.750
| -8.006
|-
| [[25/13]]
| -4.773
| -8.045
|-
| [[25/14]]
| +4.859
| +8.190
|-
| [[31/6]]
| +4.903
| +8.263
|-
| [[29/18]]
| +4.995
| +8.418
|-
| [[29/27]]
| -5.046
| -8.505
|-
| '''[[19/1]]'''
| '''+5.123'''
| '''+8.635'''
|-
| [[31/9]]
| -5.138
| -8.660
|-
| [[25/21]]
| -5.182
| -8.733
|-
| [[11/3]]
| +5.290
| +8.916
|-
| [[19/14]]
| +5.310
| +8.949
|-
| [[5/3]]
| +5.636
| +9.499
|-
| [[26/11]]
| -5.885
| -9.919
|-
| [[33/25]]
| -5.982
| -10.082
|-
| [[27/26]]
| -6.004
| -10.120
|-
| [[19/15]]
| +6.087
| +10.258
|-
| [[26/5]]
| -6.231
| -10.502
|-
| [[14/9]]
| +6.413
| +10.808
|-
| [[33/19]]
| -6.432
| -10.841
|-
| [[17/7]]
| +6.528
| +11.002
|-
| [[9/1]]
| -6.599
| -11.122
|-
| [[9/2]]
| +6.741
| +11.362
|-
| [[28/9]]
| -6.928
| -11.676
|-
| [[13/5]]
| +7.110
| +11.982
|-
| [[13/11]]
| +7.455
| +12.565
|-
| [[21/5]]
| +7.518
| +12.671
|-
| [[10/3]]
| -7.704
| -12.985
|-
| [[31/26]]
| -7.843
| -13.219
|-
| [[21/11]]
| +7.864
| +13.253
|-
| [[25/3]]
| +7.972
| +13.437
|-
| [[19/7]]
| -8.031
| -13.535
|-
| [[22/3]]
| -8.050
| -13.568
|-
| [[31/18]]
| +8.202
| +13.824
|-
| [[29/9]]
| -8.346
| -14.066
|-
| [[19/3]]
| +8.423
| +14.196
|-
| [[31/3]]
| -8.438
| -14.221
|-
| [[25/7]]
| -8.481
| -14.294
|-
| [[26/25]]
| -8.567
| -14.439
|-
| [[11/9]]
| +8.590
| +14.478
|-
| [[9/5]]
| -8.936
| -15.060
|-
| [[26/19]]
| -9.018
| -15.199
|-
| [[23/18]]
| -9.033
| -15.225
|-
| [[29/20]]
| +9.399
| +15.842
|-
| '''[[13/1]]'''
| '''+9.446'''
| '''+15.920'''
|-
| [[14/13]]
| -9.632
| -16.234
|-
| [[33/10]]
| +9.695
| +16.340
|-
| [[27/14]]
| -9.712
| -16.369
|-
| [[21/17]]
| -9.828
| -16.563
|-
| [[21/1]]
| +9.854
| +16.609
|-
| [[27/1]]
| -9.899
| -16.684
|-
| [[3/2]]
| +10.041
| +16.923
|-
| [[28/3]]
| -10.227
| -17.237
|-
| [[17/13]]
| +10.236
| +17.252
|-
| [[22/15]]
| -10.386
| -17.505
|-
| [[15/13]]
| -10.409
| -17.544
|-
| [[33/31]]
| +10.429
| +17.576
|-
| [[33/13]]
| -10.755
| -18.126
|-
| [[31/15]]
| -10.774
| -18.159
|-
| [[7/5]]
| +10.818
| +18.232
|-
| [[10/1]]
| -11.004
| -18.546
|-
| [[23/8]]
| +11.048
| +18.620
|-
| [[29/26]]
| -11.051
| -18.625
|-
| [[11/7]]
| -11.163
| -18.815
|-
| [[25/9]]
| +11.272
| +18.998
|-
| [[22/1]]
| -11.350
| -19.129
|-
| [[31/14]]
| -11.551
| -19.468
|-
| [[29/3]]
| -11.645
| -19.627
|-
| [[19/9]]
| +11.723
| +19.757
|-
| [[29/4]]
| +11.736
| +19.779
|-
| '''[[31/1]]'''
| '''-11.738'''
| '''-19.782'''
|-
| [[27/11]]
| -11.890
| -20.039
|-
| [[33/2]]
| +12.031
| +20.278
|-
| [[33/28]]
| +12.218
| +20.592
|-
| [[27/5]]
| -12.235
| -20.621
|-
| [[23/6]]
| -12.333
| -20.786
|-
| [[15/2]]
| +12.377
| +20.860
|-
| [[28/15]]
| -12.564
| -21.175
|-
| [[31/20]]
| +12.607
| +21.248
|-
| [[13/3]]
| +12.746
| +21.481
|-
| [[11/10]]
| +12.995
| +21.901
|-
| '''[[7/1]]'''
| '''+13.154'''
| '''+22.170'''
|-
| '''[[2/1]]'''
| '''-13.340'''
| '''-22.484'''
|-
| [[28/1]]
| -13.527
| -22.798
|-
| [[33/29]]
| +13.636
| +22.982
|-
| [[22/5]]
| -13.686
| -23.067
|-
| [[31/11]]
| -13.728
| -23.138
|-
| [[26/21]]
| -13.749
| -23.172
|-
| [[29/15]]
| -13.982
| -23.565
|-
| [[29/23]]
| +14.028
| +23.643
|-
| [[31/5]]
| -14.074
| -23.720
|-
| [[15/7]]
| -14.117
| -23.793
|-
| [[30/1]]
| -14.304
| -24.107
|-
| [[24/23]]
| -14.348
| -24.182
|-
| [[27/20]]
| +14.446
| +24.347
|-
| [[33/7]]
| -14.463
| -24.376
|-
| [[19/17]]
| -14.559
| -24.537
|-
| [[27/25]]
| -14.572
| -24.559
|-
| [[30/23]]
| +14.669
| +24.724
|-
| [[29/14]]
| -14.759
| -24.874
|-
| [[31/4]]
| +14.943
| +25.185
|-
| '''[[29/1]]'''
| '''-14.945'''
| '''-25.189'''
|-
| [[25/17]]
| -15.009
| -25.297
|-
| [[27/19]]
| -15.022
| -25.318
|-
| [[29/12]]
| +15.035
| +25.341
|-
| [[11/2]]
| +15.331
| +25.839
|-
| [[28/23]]
| +15.446
| +26.033
|-
| [[28/11]]
| -15.517
| -26.153
|-
| [[23/2]]
| -15.633
| -26.347
|-
| [[5/2]]
| +15.677
| +26.422
|-
| [[28/5]]
| -15.863
| -26.736
|-
| [[25/22]]
| +16.022
| +27.004
|-
| [[13/9]]
| +16.045
| +27.043
|-
| [[19/10]]
| +16.127
| +27.181
|-
| [[30/11]]
| -16.294
| -27.463
|-
| [[31/25]]
| -16.410
| -27.658
|-
| [[7/3]]
| +16.454
| +27.731
|-
| [[22/19]]
| -16.473
| -27.764
|-
| [[6/1]]
| -16.640
| -28.045
|-
| [[27/4]]
| +16.782
| +28.284
|-
| [[31/19]]
| -16.861
| -28.417
|-
| [[29/11]]
| -16.936
| -28.544
|-
| [[26/7]]
| -17.048
| -28.734
|-
| [[31/23]]
| +17.236
| +29.049
|-
| [[29/5]]
| -17.281
| -29.126
|-
| [[17/5]]
| +17.346
| +29.234
|-
| [[23/22]]
| -17.623
| -29.703
|-
| [[17/11]]
| +17.691
| +29.817
|-
| [[20/9]]
| -17.745
| -29.908
|-
| [[23/10]]
| -17.969
| -30.285
|-
| [[25/2]]
| +18.013
| +30.359
|-
| [[28/25]]
| -18.200
| -30.674
|-
| [[31/12]]
| +18.243
| +30.747
|-
| [[19/2]]
| +18.464
| +31.119
|-
| [[11/6]]
| +18.631
| +31.400
|-
|-
|[[1zpi]]
| [[28/19]]
|1.12657363114120
| -18.650
|1065.17671533322
| -31.433
|1.552472
|
|
|[[1edo]]
|1065.17671533322
|4
|2
|-
|-
|[[2zpi]]
| [[6/5]]
|1.97276711441199
| -18.976
|608.282645849800
| -31.983
|2.340551
|1.103823
|10.222388
|[[2edo]]
|1216.56529169960
|4
|3
|-
|-
|[[3zpi]]
| [[27/23]]
|2.54885423138170
| +19.074
|470.799775532670
| +32.148
|1.459266
|0.414716
|7.471444
|[[3edo]]
|1412.39932659801
|3
|3
|-
|-
|[[4zpi]]
| [[27/13]]
|3.05976162780486
| -19.345
|392.187413913321
| -32.604
|2.847473
|1.044063
|11.592757
|[[3edo]]
|1176.56224173996
|6
|4
|-
|-
|[[5zpi]]
| [[30/19]]
|3.49684591978495
| -19.427
|343.166392665594
| -32.742
|0.925523
|0.167718
|5.858780
|[[3edo]]
|1029.49917799678
|2
|2
|-
|-
|[[6zpi]]
| [[29/25]]
|3.90444812410668
| -19.618
|307.341770682266
| -33.064
|2.942394
|0.927921
|11.574256
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|-
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| '''[[17/1]]'''
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|-
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| [[17/14]]
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|4
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|-
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| [[18/1]]
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| [[29/19]]
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| [[9/4]]
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| [[13/10]]
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| [[17/15]]
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| [[22/13]]
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| [[21/10]]
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| [[33/17]]
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| [[20/3]]
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| [[31/13]]
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|-
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| [[22/21]]
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| [[25/6]]
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| [[31/21]]
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| [[18/11]]
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| [[18/5]]
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| [[23/9]]
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| [[13/2]]
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| [[28/13]]
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| [[17/3]]
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| [[27/7]]
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| [[4/3]]
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| [[26/17]]
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| [[30/13]]
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| [[23/16]]
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| ''-67.452''
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''+41.624''
| ''+70.153''
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''+42.012''
| ''+70.807''
|- style="background-color: #cccccc;"
| ''[[23/7]]''
| ''-42.127''
| ''-71.001''
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''-42.358''
| ''-71.390''
|- style="background-color: #cccccc;"
| ''[[12/7]]''
| ''-43.134''
| ''-72.699''
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''-43.321''
| ''-73.013''
|- style="background-color: #cccccc;"
| ''[[27/16]]''
| ''+43.463''
| ''+73.252''
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''-44.026''
| ''-74.202''
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''+44.694''
| ''+75.327''
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''+45.144''
| ''+76.087''
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''-45.311''
| ''-76.368''
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''-45.657''
| ''-76.951''
|- style="background-color: #cccccc;"
| ''[[17/4]]''
| ''+46.363''
| ''+78.140''
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''-46.762''
| ''-78.813''
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''+47.994''
| ''+80.888''
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''-48.444''
| ''-81.648''
|- style="background-color: #cccccc;"
| ''[[23/17]]''
| ''-48.655''
| ''-82.003''
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''+49.467''
| ''+83.372''
|- style="background-color: #cccccc;"
| ''[[17/12]]''
| ''+49.662''
| ''+83.701''
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''+49.876''
| ''+84.060''
|- style="background-color: #cccccc;"
| ''[[16/3]]''
| ''-50.062''
| ''-84.375''
|- style="background-color: #cccccc;"
| ''[[32/29]]''
| ''-51.757''
| ''-87.231''
|- style="background-color: #cccccc;"
| ''[[33/16]]''
| ''+52.053''
| ''+87.730''
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''-52.398''
| ''-88.312''
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''-52.767''
| ''-88.933''
|- style="background-color: #cccccc;"
| ''[[8/7]]''
| ''-53.175''
| ''-89.622''
|- style="background-color: #cccccc;"
| ''[[16/1]]''
| ''-53.362''
| ''-89.936''
|- style="background-color: #cccccc;"
| ''[[32/31]]''
| ''-54.964''
| ''-92.637''
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''-55.352''
| ''-93.291''
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''-55.698''
| ''-93.873''
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''-56.475''
| ''-95.183''
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''-56.803''
| ''-95.736''
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''+58.034''
| ''+97.811''
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''+58.485''
| ''+98.571''
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''+59.703''
| ''+100.624''
|- style="background-color: #cccccc;"
| ''[[32/9]]''
| ''-60.103''
| ''-101.297''
|- style="background-color: #cccccc;"
| ''[[16/13]]''
| ''-62.807''
| ''-105.856''
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''-63.003''
| ''-106.185''
|- style="background-color: #cccccc;"
| ''[[21/16]]''
| ''+63.216''
| ''+106.544''
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''-63.402''
| ''-106.858''
|- style="background-color: #cccccc;"
| ''[[33/32]]''
| ''+65.393''
| ''+110.214''
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''-65.739''
| ''-110.796''
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''-66.516''
| ''-112.106''
|- style="background-color: #cccccc;"
| ''[[32/1]]''
| ''-66.702''
| ''-112.420''
|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''-68.693''
| ''-115.775''
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''-69.038''
| ''-116.357''
|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''-71.375''
| ''-120.295''
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''-71.825''
| ''-121.055''
|- style="background-color: #cccccc;"
| ''[[17/16]]''
| ''+73.044''
| ''+123.108''
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''-76.148''
| ''-128.340''
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''-76.556''
| ''-129.028''
|- style="background-color: #cccccc;"
| ''[[32/7]]''
| ''-79.856''
| ''-134.589''
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''-86.384''
| ''-145.592''
|}
 
== Record on the Riemann zeta function with prime 2 removed ==
'''[[71zpi]]''' sets a height record on the Riemann zeta function with prime 2 removed. The previous record is [[53zpi]] and the next one is [[93zpi]]. It is important to highlight that the optimal equal tunings obtained by excluding the prime number 2 from the Riemann zeta function differs slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.
{| class="wikitable"
! colspan="6" |Unmodified Riemann zeta function
! colspan="5" |Riemann zeta function with prime 2 removed
|-
|-
|[[68zpi]]
! colspan="3" | Tuning
|19.5727176089709
! colspan="1" |Strength
|61.3098305495399
! colspan="2" |Closest EDO
|1.766973
! colspan="2" |Tuning
|0.238290
! colspan="1" |Strength
|9.330313
! colspan="2" |Closest EDO
|[[20edo]]
|1226.19661099080
|3
|3
|-
|-
|[[69zpi]]
!ZPI
|19.7669547333089
!Steps per octave
|60.7073783589894
!Step size (cents)
|1.419909
! colspan="1" | Height
|0.155680
!EDO
|7.439130
!Octave (cents)
|[[20edo]]
!Steps per octave
|1214.14756717979
!Step size (cents)
|2
! colspan="1" |Height
|2
!EDO
!Octave (cents)
|-
|-
|[[70zpi]]
|[[53zpi]]
|19.9819046661574
| 16.3979501311478
|60.0543351621727
|73.1798786069366
|3.392542
|2.518818
|0.534897
| [[16edo]]
|11.106731
|1170.87805771099
|[[20edo]]
| 16.4044889390925
|1201.08670324345
|73.1507092025500
|4
|4.100909
|4
|[[16edo]]
|1170.41134724080
|-
|-
|[[71zpi]]
|[[71zpi]]
|20.2248393119540
|20.2248393119540
|59.3329806724710
|59.3329806724710
|3.531097
| 3.531097
|0.613581
|12.986080
|[[20edo]]
|[[20edo]]
|1186.65961344942
|1186.65961344942
|6
|20.2459529213541
|6
|59.2711049295348
|4.137236
|[[20edo]]
|1185.42209859070
|-
| [[93zpi]]
| 24.5782550666850
|48.8236449961234
|2.810487
|[[25edo]]
|1220.59112490308
|24.5738316304204
|48.8324335434323
|4.665720
|[[25edo]]
|1220.81083858581
|}
 
=== Harmonic series in 71zpi with prime 2 removed ===
 
{{Harmonics in cet|59.2711049295348|columns=15|title=Approximation of harmonics in 71zpi with prime 2 removed }}
{{Harmonics in cet|59.2711049295348|columns=18|start=16|title=Approximation of harmonics in 71zpi with prime 2 removed }}
 
=== Intervals in 71zpi with prime 2 removed ===
 
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ style="white-space:nowrap" | Intervals in 71zpi with prime 2 removed
|-
| colspan="3" style="text-align:left;" | JI ratios are comprised of 34-integer-limit ratios,<br>and are stylized as follows to indicate their accuracy:
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* Normal: relative error < 25 %
* <small>Small:</small> relative error < 33.333 %
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
| colspan="2" style="text-align:right;" | <center>'''⟨81 128] at every 4 steps'''</center><br>[[9/8|Whole tone]] = 13 steps<br>[[256/243|Limma]] = 8 steps<br>[[2187/2048|Apotome]] = 5 steps
|-
! Degree
! Cents
! Ratios
! Ups and downs notation
! Step
|-
| 0
| 0.000
|
| P1
| 0
|-
| 1
| 59.271
| '''[[34/33]]''', '''[[33/32]]''', '''<u>[[32/31]]'''</u>, '''<u>[[31/30]]'''</u>, '''<u>[[30/29]]'''</u>, '''<u>[[29/28]]'''</u>, '''<u>[[28/27]]'''</u>, '''[[27/26]]''', '''[[26/25]]''', [[25/24]], [[24/23]], <small>[[23/22]]</small>, <small><small>[[22/21]]</small></small>, <small><small><small>[[21/20]]</small></small></small>, <small><small><small>[[20/19]]</small></small></small>
| vA1, ^d2
| 4
|-
| 2
| 118.542
| <small><small><small>[[19/18]]</small></small></small>, <small>[[18/17]]</small>, [[17/16]], [[33/31]], '''[[16/15]]''', '''<u>[[31/29]]'''</u>, '''<u>[[15/14]]'''</u>, '''[[29/27]]''', '''[[14/13]]''', [[27/25]], <small><small>[[13/12]]</small></small>, <small><small><small>[[25/23]]</small></small></small>
| m2
| 8
|-
| 3
| 177.813
| <small><small><small>[[12/11]]</small></small></small>, <small><small>[[23/21]]</small></small>, <small>[[34/31]]</small>, [[11/10]], '''[[32/29]]''', '''<u>[[21/19]]'''</u>, '''<u>[[31/28]]'''</u>, '''<u>[[10/9]]'''</u>, [[29/26]], [[19/17]], <small>[[28/25]]</small>, <small><small><small>[[9/8]]</small></small></small>
| vM2
| 12
|-
| 4
| 237.084
| <small><small><small>[[26/23]]</small></small></small>, <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, [[33/29]], '''[[8/7]]''', '''<u>[[31/27]]'''</u>, '''<u>[[23/20]]'''</u>, [[15/13]], <small>[[22/19]]</small>, <small><small>[[29/25]]</small></small>
| vvA2
| 16
|-
| 5
| 296.356
| <small><small><small>[[7/6]]</small></small></small>, <small><small>[[34/29]]</small></small>, <small>[[27/23]]</small>, <small>[[20/17]]</small>, [[33/28]], '''[[13/11]]''', '''<u>[[32/27]]'''</u>, '''<u>[[19/16]]'''</u>, '''[[25/21]]''', '''[[31/26]]''', <small>[[6/5]]</small>
| vm3
| 20
|-
| 6
| 355.627
| <small><small><small>[[29/24]]</small></small></small>, <small><small><small>[[23/19]]</small></small></small>, <small>[[17/14]]</small>, <small>[[28/23]]</small>, '''[[11/9]]''', '''<u>[[27/22]]'''</u>, '''<u>[[16/13]]'''</u>, [[21/17]], [[26/21]], <small>[[31/25]]</small>
| vvM3
| 24
|-
| 7
| 414.898
| <small><small><small>[[5/4]]</small></small></small>, <small>[[34/27]]</small>, [[29/23]], [[24/19]], '''[[19/15]]''', '''<u>[[33/26]]'''</u>, '''<u>[[14/11]]'''</u>, '''[[23/18]]''', [[32/25]], <small><small>[[9/7]]</small></small>, <small><small><small>[[31/24]]</small></small></small>
| ^^M3
| 28
|-
| 8
| 474.169
| <small><small><small>[[22/17]]</small></small></small>, <small><small>[[13/10]]</small></small>, [[30/23]], '''[[17/13]]''', '''<u>[[21/16]]'''</u>, '''<u>[[25/19]]'''</u>, '''<u>[[29/22]]'''</u>, '''[[33/25]]''', <small><small>[[4/3]]</small></small>
| vv4
| 32
|-
| 9
| 533.440
| <small>[[31/23]]</small>, [[27/20]], [[23/17]], '''<u>[[19/14]]'''</u>, '''<u>[[34/25]]'''</u>, '''<u>[[15/11]]'''</u>, '''[[26/19]]''', <small>[[11/8]]</small>, <small><small><small>[[29/21]]</small></small></small>
| ^^4
| 36
|-
| 10
| 592.711
| <small><small><small>[[18/13]]</small></small></small>, <small><small>[[25/18]]</small></small>, <small><small>[[32/23]]</small></small>, [[7/5]], '''<u>[[31/22]]'''</u>, '''<u>[[24/17]]'''</u>, [[17/12]], <small>[[27/19]]</small>, <small><small><small>[[10/7]]</small></small></small>
| ^A4
| 40
|-
| 11
| 651.982
| <small><small><small>[[33/23]]</small></small></small>, <small><small>[[23/16]]</small></small>, <small>[[13/9]]</small>, '''[[29/20]]''', '''<u>[[16/11]]'''</u>, '''[[19/13]]''', [[22/15]], <small>[[25/17]]</small>, <small>[[28/19]]</small>, <small><small>[[31/21]]</small></small>, <small><small><small>[[34/23]]</small></small></small>
| ^^d5
| 44
|-
| 12
| 711.253
| '''[[3/2]]''', <small>[[32/21]]</small>, <small><small>[[29/19]]</small></small>, <small><small>[[26/17]]</small></small>, <small><small><small>[[23/15]]</small></small></small>
| ^5
| 48
|-
| 13
| 770.524
| <small><small><small>[[20/13]]</small></small></small>, <small>[[17/11]]</small>, [[31/20]], '''[[14/9]]''', '''<u>[[25/16]]'''</u>, [[11/7]], <small><small>[[30/19]]</small></small>, <small><small><small>[[19/12]]</small></small></small>
| ^^d6
| 52
|-
| 14
| 829.795
| <small><small><small>[[27/17]]</small></small></small>, <small>[[8/5]]</small>, '''<u>[[29/18]]'''</u>, '''<u>[[21/13]]'''</u>, '''<u>[[34/21]]'''</u>, [[13/8]], <small>[[31/19]]</small>, <small><small>[[18/11]]</small></small>
| ^m6
| 56
|-
| 15
| 889.067
| <small><small><small>[[23/14]]</small></small></small>, <small><small><small>[[28/17]]</small></small></small>, <small><small>[[33/20]]</small></small>, '''<u>[[5/3]]'''</u>, [[32/19]], <small>[[27/16]]</small>, <small><small>[[22/13]]</small></small>, <small><small><small>[[17/10]]</small></small></small>
| M6
| 60
|-
| 16
| 948.338
| <small><small>[[29/17]]</small></small>, <small>[[12/7]]</small>, '''[[31/18]]''', '''<u>[[19/11]]'''</u>, '''<u>[[26/15]]'''</u>, '''[[33/19]]''', <small><small>[[7/4]]</small></small>
| vA6, ^d7
| 64
|-
| 17
| 1007.609
| <small><small>[[30/17]]</small></small>, <small><small>[[23/13]]</small></small>, [[16/9]], '''<u>[[25/14]]'''</u>, '''<u>[[34/19]]'''</u>, [[9/5]], <small><small>[[29/16]]</small></small>, <small><small><small>[[20/11]]</small></small></small>
| m7
| 68
|-
| 18
| 1066.880
| <small><small><small>[[31/17]]</small></small></small>, <small>[[11/6]]</small>, '''[[24/13]]''', '''<u>[[13/7]]'''</u>, [[28/15]], <small><small>[[15/8]]</small></small>, <small><small><small>[[32/17]]</small></small></small>
| vM7
| 72
|-
| 19
| 1126.151
| <small><small><small>[[17/9]]</small></small></small>, <small>[[19/10]]</small>, '''[[21/11]]''', '''<u>[[23/12]]'''</u>, '''[[25/13]]''', [[27/14]], <small>[[29/15]]</small>, <small>[[31/16]]</small>, <small><small>[[33/17]]</small></small>
| vvA7
| 76
|-
| 20
| 1185.422
| [[2/1]]
| v1 +1 oct
| 80
|-
| 21
| 1244.693
| '''[[33/16]]''', [[31/15]], <small>[[29/14]]</small>, <small><small>[[27/13]]</small></small>, <small><small><small>[[25/12]]</small></small></small>
| vvA1 +1 oct
| 84
|-
| 22
| 1303.964
| <small><small><small>[[23/11]]</small></small></small>, <small>[[21/10]]</small>, [[19/9]], '''<u>[[17/8]]'''</u>, '''[[32/15]]''', <small>[[15/7]]</small>, <small><small>[[28/13]]</small></small>
| vm2 +1 oct
| 88
|-
| 23
| 1363.235
| <small><small>[[13/6]]</small></small>, [[24/11]], '''<u>[[11/5]]'''</u>, [[31/14]], <small>[[20/9]]</small>, <small><small><small>[[29/13]]</small></small></small>
| vvM2 +1 oct
| 92
|-
| 24
| 1422.507
| <small>[[9/4]]</small>, '''[[34/15]]''', '''<u>[[25/11]]'''</u>, '''[[16/7]]''', <small>[[23/10]]</small>, <small><small><small>[[30/13]]</small></small></small>
| ^^M2 +1 oct
| 96
|-
| 25
| 1481.778
| <small>[[7/3]]</small>, '''<u>[[33/14]]'''</u>, '''[[26/11]]''', <small>[[19/8]]</small>, <small><small>[[31/13]]</small></small>
| vvm3 +1 oct
| 100
|-
| 26
| 1541.049
| <small><small><small>[[12/5]]</small></small></small>, [[29/12]], '''<u>[[17/7]]'''</u>, '''[[22/9]]''', [[27/11]], <small>[[32/13]]</small>
| ^^m3 +1 oct
| 104
|-
| 27
| 1600.320
| [[5/2]], [[33/13]], <small>[[28/11]]</small>, <small><small>[[23/9]]</small></small>
| ^M3 +1 oct
| 108
|-
| 28
| 1659.591
| <small><small>[[18/7]]</small></small>, <small>[[31/12]]</small>, '''[[13/5]]''', '''<u>[[34/13]]'''</u>, [[21/8]], <small>[[29/11]]</small>
| ^^d4 +1 oct
| 112
|-
| 29
| 1718.862
| <small><small>[[8/3]]</small></small>, '''<u>[[27/10]]'''</u>, '''[[19/7]]''', <small>[[30/11]]</small>
| ^4 +1 oct
| 116
|-
| 30
| 1778.133
| <small><small><small>[[11/4]]</small></small></small>, '''[[25/9]]''', '''<u>[[14/5]]'''</u>, <small>[[31/11]]</small>, <small><small><small>[[17/6]]</small></small></small>
| A4 +1 oct
| 120
|-
| 31
| 1837.404
| <small><small>[[20/7]]</small></small>, '''[[23/8]]''', '''<u>[[26/9]]'''</u>, '''[[29/10]]''', [[32/11]]
| ^d5 +1 oct
| 124
|-
| 32
| 1896.675
| '''[[3/1]]'''
| P5 +1 oct
| 128
|-
| 33
| 1955.946
| '''<u>[[34/11]]'''</u>, '''<u>[[31/10]]'''</u>, '''[[28/9]]''', <small>[[25/8]]</small>, <small><small><small>[[22/7]]</small></small></small>
| vA5 +1 oct, ^d6 +1 oct
| 132
|-
| 34
| 2015.218
| <small>[[19/6]]</small>, '''<u>[[16/5]]'''</u>, [[29/9]], <small><small><small>[[13/4]]</small></small></small>
| m6 +1 oct
| 136
|-
| 35
| 2074.489
| <small>[[23/7]]</small>, '''[[33/10]]''', '''[[10/3]]'''
| vM6 +1 oct
| 140
|-
| 36
| 2133.760
| <small><small><small>[[27/8]]</small></small></small>, <small>[[17/5]]</small>, '''<u>[[24/7]]'''</u>, '''[[31/9]]'''
| vvA6 +1 oct
| 144
|-
| 37
| 2193.031
| <small><small>[[7/2]]</small></small>, '''<u>[[32/9]]'''</u>, [[25/7]], <small><small>[[18/5]]</small></small>
| vm7 +1 oct
| 148
|-
| 38
| 2252.302
| <small><small>[[29/8]]</small></small>, '''<u>[[11/3]]'''</u>, <small>[[26/7]]</small>
| vvM7 +1 oct
| 152
|-
| 39
| 2311.573
| <small><small>[[15/4]]</small></small>, [[34/9]], '''<u>[[19/5]]'''</u>, [[23/6]], <small><small><small>[[27/7]]</small></small></small>
| ^^M7 +1 oct
| 156
|-
| 40
| 2370.844
| <small><small><small>[[31/8]]</small></small></small>, <small><small><small>[[4/1]]</small></small></small>
| vv1 +2 oct
| 160
|-
| 41
| 2430.115
| <small><small>[[33/8]]</small></small>
| ^^1 +2 oct
| 164
|-
| 42
| 2489.386
| <small><small><small>[[29/7]]</small></small></small>, <small>[[25/6]]</small>, '''<u>[[21/5]]'''</u>, <small>[[17/4]]</small>
| vvm2 +2 oct
| 168
|-
| 43
| 2548.658
| <small><small><small>[[30/7]]</small></small></small>, [[13/3]], <small>[[22/5]]</small>, <small><small><small>[[31/7]]</small></small></small>
| ^^m2 +2 oct
| 172
|-
| 44
| 2607.929
| '''<u>[[9/2]]'''</u>, <small><small>[[32/7]]</small></small>
| ^M2 +2 oct
| 176
|-
| 45
| 2667.200
| <small><small><small>[[23/5]]</small></small></small>, '''<u>[[14/3]]'''</u>, <small>[[33/7]]</small>
| ^^d3 +2 oct
| 180
|-
| 46
| 2726.471
| <small><small><small>[[19/4]]</small></small></small>, [[24/5]], '''<u>[[29/6]]'''</u>, '''[[34/7]]'''
| ^m3 +2 oct
| 184
|-
| 47
| 2785.742
| '''<u>[[5/1]]'''</u>
| M3 +2 oct
| 188
|-
| 48
| 2845.013
| '''<u>[[31/6]]'''</u>, '''[[26/5]]''', <small><small><small>[[21/4]]</small></small></small>
| vA3 +2 oct, ^d4 +2 oct
| 192
|-
| 49
| 2904.284
| '''[[16/3]]''', <small>[[27/5]]</small>
| P4 +2 oct
| 196
|-
| 50
| 2963.555
| [[11/2]], <small>[[28/5]]</small>
| vA4 +2 oct
| 200
|-
| 51
| 3022.826
| <small><small>[[17/3]]</small></small>, '''[[23/4]]''', <small><small>[[29/5]]</small></small>
| d5 +2 oct
| 204
|-
| 52
| 3082.097
| <small><small>[[6/1]]</small></small>
| v5 +2 oct
| 208
|-
| 53
| 3141.369
| <small>[[31/5]]</small>
| vvA5 +2 oct
| 212
|-
| 54
| 3200.640
| <small><small><small>[[25/4]]</small></small></small>, '''[[19/3]]''', [[32/5]]
| vm6 +2 oct
| 216
|-
| 55
| 3259.911
| <small>[[13/2]]</small>, '''[[33/5]]''', <small><small>[[20/3]]</small></small>
| vvM6 +2 oct
| 220
|-
| 56
| 3319.182
| [[27/4]], '''<u>[[34/5]]'''</u>
| ^^M6 +2 oct
| 224
|-
| 57
| 3378.453
| '''[[7/1]]'''
| vvm7 +2 oct
| 228
|-
| 58
| 3437.724
| '''[[29/4]]''', [[22/3]]
| ^^m7 +2 oct
| 232
|-
| 59
| 3496.995
| '''[[15/2]]''', <small><small><small>[[23/3]]</small></small></small>
| ^M7 +2 oct
| 236
|-
| 60
| 3556.266
| [[31/4]]
| ^^d1 +3 oct
| 240
|-
| 61
| 3615.537
| <small>[[8/1]]</small>
| ^1 +3 oct
| 244
|-
| 62
| 3674.809
| <small><small>[[33/4]]</small></small>, '''<u>[[25/3]]'''</u>
| ^^d2 +3 oct
| 248
|-
| 63
| 3734.080
| <small><small><small>[[17/2]]</small></small></small>, '''<u>[[26/3]]'''</u>
| ^m2 +3 oct
| 252
|-
| 64
| 3793.351
| [[9/1]]
| M2 +3 oct
| 256
|-
| 65
| 3852.622
| [[28/3]]
| vA2 +3 oct, ^d3 +3 oct
| 260
|-
| 66
| 3911.893
| [[19/2]], <small>[[29/3]]</small>
| m3 +3 oct
| 264
|-
| 67
| 3971.164
| <small>[[10/1]]</small>
| vM3 +3 oct
| 268
|-
| 68
| 4030.435
| [[31/3]]
| vvA3 +3 oct
| 272
|-
| 69
| 4089.706
| <small>[[21/2]]</small>, '''[[32/3]]'''
| v4 +3 oct
| 276
|-
| 70
| 4148.977
| '''<u>[[11/1]]'''</u>
| vvA4 +3 oct
| 280
|-
| 71
| 4208.248
| '''[[34/3]]''', <small><small>[[23/2]]</small></small>
| vd5 +3 oct
| 284
|-
| 72
| 4267.520
|
| vv5 +3 oct
| 288
|-
| 73
| 4326.791
| <small><small><small>[[12/1]]</small></small></small>
| ^^5 +3 oct
| 292
|-
| 74
| 4386.062
| [[25/2]]
| vvm6 +3 oct
| 296
|-
| 75
| 4445.333
| '''<u>[[13/1]]'''</u>
| ^^m6 +3 oct
| 300
|-
| 76
| 4504.604
| '''<u>[[27/2]]'''</u>
| ^M6 +3 oct
| 304
|-
| 77
| 4563.875
| '''[[14/1]]'''
| ^^d7 +3 oct
| 308
|-
| 78
| 4623.146
| '''[[29/2]]'''
| ^m7 +3 oct
| 312
|-
| 79
| 4682.417
| '''[[15/1]]'''
| M7 +3 oct
| 316
|-
| 80
| 4741.688
| '''<u>[[31/2]]'''</u>
| vA7 +3 oct, ^d1 +4 oct
| 320
|-
| 81
| 4800.959
| '''<u>[[16/1]]'''</u>
| P1 +4 oct
| 324
|-
| 82
| 4860.231
| '''[[33/2]]'''
| vA1 +4 oct, ^d2 +4 oct
| 328
|-
| 83
| 4919.502
| [[17/1]]
| m2 +4 oct
| 332
|-
| 84
| 4978.773
| <small><small><small>[[18/1]]</small></small></small>
| vM2 +4 oct
| 336
|-
| 85
| 5038.044
|
| vvA2 +4 oct
| 340
|-
| 86
| 5097.315
| '''<u>[[19/1]]'''</u>
| vm3 +4 oct
| 344
|-
| 87
| 5156.586
|
| vvM3 +4 oct
| 348
|-
| 88
| 5215.857
| <small><small><small>[[20/1]]</small></small></small>
| ^^M3 +4 oct
| 352
|-
| 89
| 5275.128
| '''<u>[[21/1]]'''</u>
| vv4 +4 oct
| 356
|-
| 90
| 5334.399
| <small>[[22/1]]</small>
| ^^4 +4 oct
| 360
|-
| 91
| 5393.671
|
| ^A4 +4 oct
| 364
|-
|-
|[[72zpi]]
| 92
|20.4330900105668
| 5452.942
|58.7282686749499
| <small><small>[[23/1]]</small></small>
|0.257023
| ^^d5 +4 oct
|0.013560
| 368
|3.535914
|-
|[[20edo]]
| 93
|1174.56537349900
| 5512.213
|3
| [[24/1]]
|3
| ^5 +4 oct
| 372
|-
| 94
| 5571.484
| '''<u>[[25/1]]'''</u>
| ^^d6 +4 oct
| 376
|-
| 95
| 5630.755
| '''[[26/1]]'''
| ^m6 +4 oct
| 380
|-
| 96
| 5690.026
| <small>[[27/1]]</small>
| M6 +4 oct
| 384
|-
| 97
| 5749.297
| <small>[[28/1]]</small>
| vA6 +4 oct, ^d7 +4 oct
| 388
|-
| 98
| 5808.568
| <small><small>[[29/1]]</small></small>
| m7 +4 oct
| 392
|-
| 99
| 5867.839
| <small><small>[[30/1]]</small></small>
| vM7 +4 oct
| 396
|-
| 100
| 5927.110
| <small>[[31/1]]</small>
| vvA7 +4 oct
| 400
|-
| 101
| 5986.382
| [[32/1]]
| v1 +5 oct
| 404
|-
| 102
| 6045.653
| '''[[33/1]]'''
| vvA1 +5 oct
| 408
|-
| 103
| 6104.924
| '''<u>[[34/1]]'''</u>
| vm2 +5 oct
| 412
|}
 
=== Approximation to JI in 71zpi with prime 2 removed ===
 
==== Interval mappings in 71zpi with prime 2 removed ====
 
The following tables show how 34-integer-limit intervals are represented in 71zpi with prime 2 removed. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 34-integer-limit intervals in 71zpi with prime 2 removed (by direct approximation)
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[34/1]]
| -0.032
| -0.053
|-
| [[34/19]]
| +0.166
| +0.281
|- style="background-color: #cccccc;"
| ''[[23/12]]''
| ''-0.168''
| ''-0.284''
|-
| '''[[19/1]]'''
| '''-0.198'''
| '''-0.334'''
|-
| [[14/3]]
| +0.329
| +0.555
|-
| [[19/5]]
| +0.374
| +0.631
|-
|-
|[[73zpi]]
| [[21/13]]
|20.5774567453445
| -0.458
|58.3162445607613
| -0.772
|1.051613
|0.117999
|7.972796
|[[21edo]]
|1224.64113577599
|3
|3
|-
|-
|[[74zpi]]
| [[34/5]]
|20.7874292468999
| +0.540
|57.7271958810858
| +0.911
|2.915475
|0.437980
|10.729630
|[[21edo]]
|1212.27111350280
|4
|4
|-
|-
|[[75zpi]]
| '''[[5/1]]'''
|21.0279383259393
| '''-0.572'''
|57.0669354931351
| '''-0.965'''
|4.107322
|0.716469
|12.853639
|[[21edo]]
|1198.40564535584
|4
|4
|-
|-
|[[76zpi]]
| [[30/29]]
|21.2400913171162
| +0.580
|56.4969322440242
| +0.978
|0.730362
|- style="background-color: #cccccc;"
|0.055707
| ''[[24/7]]''
|5.199658
| ''+0.631''
|[[21edo]]
| ''+1.064''
|1186.43557712451
|2
|2
|-
|-
|[[77zpi]]
| [[27/10]]
|21.4234529823551
| -0.689
|56.0133794019270
| -1.163
|2.177870
|0.324040
|10.818410
|[[21edo]]
|1176.28096744047
|3
|3
|-
|-
|[[78zpi]]
| [[26/9]]
|21.6259104051269
| +0.787
|55.4889934120653
| +1.327
|1.264778
|0.143334
|7.997001
|[[22edo]]
|1220.75785506544
|2
|2
|-
|-
|[[79zpi]]
| [[15/14]]
|21.7869242868810
| -0.901
|55.0789080734347
| -1.519
|0.827778
|0.067771
|5.664322
|[[22edo]]
|1211.73597761556
|5
|5
|-
|-
|[[80zpi]]
| [[25/19]]
|22.0251467420146
| -0.946
|54.4831784348982
| -1.595
|6.062600
|- style="background-color: #cccccc;"
|1.258178
| ''[[16/1]]''
|16.213941
| ''+0.959''
|[[22edo]]
| ''+1.619''
|1198.62992556776
|- style="background-color: #cccccc;"
|12
| ''[[17/8]]''
|8
| ''-0.991''
| ''-1.672''
|-
|-
|[[81zpi]]
| [[31/22]]
|22.2647624440801
| -1.007
|53.8968247702578
| -1.698
|0.951934
|0.083763
|6.151404
|[[22edo]]
|1185.73014494567
|3
|3
|-
|-
|[[82zpi]]
| [[27/22]]
|22.4309325986632
| +1.080
|53.4975527531796
| +1.821
|1.218056
|0.143958
|8.507974
|[[22edo]]
|1176.94616056995
|2
|2
|-
|-
|[[83zpi]]
| [[34/25]]
|22.5965359597246
| +1.112
|53.1054849353390
| +1.876
|0.817326
|0.070665
|6.057085
|[[23edo]]
|1221.42615351280
|3
|3
|-
|-
|[[84zpi]]
| [[25/1]]
|22.8071262132237
| -1.144
|52.6151339182853
| -1.929
|3.709236
|0.623853
|12.657148
|[[23edo]]
|1210.14808012056
|3
|3
|-
|-
|[[85zpi]]
| [[29/6]]
|23.0261914398016
| -1.151
|52.1145671500740
| -1.943
|2.161963
|- style="background-color: #cccccc;"
|0.256306
| ''[[19/16]]''
|8.441576
| ''-1.157''
|[[23edo]]
| ''-1.953''
|1198.63504445170
|5
|5
|-
|-
|[[86zpi]]
| [[25/11]]
|23.2320841524373
| +1.197
|51.6527054622479
| +2.020
|2.750907
|0.400877
|10.713630
|[[23edo]]
|1188.01222563170
|3
|3
|-
|-
|[[87zpi]]
| [[27/2]]
|23.4368797826083
| -1.261
|51.2013549214209
| -2.128
|1.402248
|0.162427
|8.417773
|[[23edo]]
|1177.63116319268
|3
|3
|-
|-
|[[88zpi]]
| [[29/28]]
|23.6030639552002
| -1.480
|50.8408570293103
| -2.497
|0.731504
|- style="background-color: #cccccc;"
|0.062917
| ''[[16/5]]''
|6.103089
| ''+1.531''
|[[24edo]]
| ''+2.584''
|1220.18056870345
|2
|2
|-
|-
|[[89zpi]]
| [[31/28]]
|23.7696274252429
| +1.604
|50.4845944167228
| +2.706
|1.614140
|0.182679
|8.273256
|[[24edo]]
|1211.63026600135
|4
|4
|-
|-
|[[90zpi]]
| [[11/5]]
|24.0057421830853
| -1.769
|49.9880399800983
| -2.984
|5.721613
|1.092055
|14.821136
|[[24edo]]
|1199.71295952236
|6
|6
|-
|-
|[[91zpi]]
| [[31/6]]
|24.2420113390111
| +1.932
|49.5008431115168
| +3.260
|1.430838
|0.160980
|8.449365
|[[24edo]]
|1188.02023467640
|5
|5
|-
|-
|[[92zpi]]
| [[31/27]]
|24.3891186689229
| -2.086
|49.2022699257709
| -3.520
|0.289192
|- style="background-color: #cccccc;"
|0.015088
| ''[[25/16]]''
|3.676912
| ''-2.103''
|[[24edo]]
| ''-3.548''
|1180.85447821850
|2
|2
|-
|-
|[[93zpi]]
| [[19/11]]
|24.5782550666850
| +2.143
|48.8236449961234
| +3.615
|2.810487
|0.469100
|13.261693
|[[25edo]]
|1220.59112490308
|3
|3
|-
|-
|[[94zpi]]
| [[33/26]]
|24.7668980969992
| +2.152
|48.4517679727278
| +3.632
|0.721507
|- style="background-color: #cccccc;"
|0.051118
| ''[[32/27]]''
|5.036901
| ''+2.221''
|[[25edo]]
| ''+3.746''
|1211.29419931819
|3
|3
|-
|-
|[[95zpi]]
| [[34/11]]
|24.9650888246290
| +2.309
|48.0671231906915
| +3.896
|3.915820
|0.639164
|12.605015
|[[25edo]]
|1201.67807976729
|6
|6
|-
|-
|[[96zpi]]
| '''[[11/1]]'''
|25.1878832117586
| '''-2.341'''
|47.6419550587640
| '''-3.949'''
|2.736945
|0.365926
|9.931986
|[[25edo]]
|1191.04887646910
|4
|4
|-
|-
|[[97zpi]]
| [[31/30]]
|25.3904920234491
| +2.504
|47.2617859823966
| +4.225
|1.732315
|0.223731
|9.938467
|[[25edo]]
|1181.54464955991
|3
|3
|-
|-
|[[98zpi]]
| [[14/11]]
|25.5515957282057
| -2.610
|46.9637987687538
| -4.404
|0.285465
|0.015320
|3.835673
|[[26edo]]
|1221.05876798760
|2
|2
|-
|-
|[[99zpi]]
| [[33/14]]
|25.7034869501596
| -2.669
|46.6862726573583
| -4.504
|1.550016
|0.179635
|8.892042
|[[26edo]]
|1213.84308909132
|3
|3
|-
|-
|[[100zpi]]
| [[31/10]]
|25.9356996537225
| -2.775
|46.2682717652372
| -4.683
|5.545073
|1.031155
|14.793013
|[[26edo]]
|1202.97506589617
|14
|9
|-
|-
|[[101zpi]]
| [[11/3]]
|26.1569708443492
| +2.939
|45.8768718725410
| +4.959
|1.203870
|- style="background-color: #cccccc;"
|0.107517
| ''[[32/9]]''
|6.524581
| ''-3.059''
|[[26edo]]
| ''-5.161''
|1192.79866868607
|4
|4
|-
|-
|[[102zpi]]
| [[31/29]]
|26.3282726958943
| +3.084
|45.5783793285888
| +5.203
|1.761035
|- style="background-color: #cccccc;"
|0.218588
| ''[[16/11]]''
|9.369937
| ''+3.300''
|[[26edo]]
| ''+5.568''
|1185.03786254331
|2
|2
|-
|-
|[[103zpi]]
| [[31/2]]
|26.5097255289111
| -3.347
|45.2664060475201
| -5.647
|1.315212
|- style="background-color: #cccccc;"
|0.139268
| ''[[21/16]]''
|7.852592
| ''+3.388''
|[[27edo]]
| ''+5.716''
|1222.19296328304
|2
|2
|-
|-
|[[104zpi]]
| [[15/11]]
|26.6907769881100
| -3.511
|44.9593505852065
| -5.923
|1.774617
|0.218962
|9.344236
|[[27edo]]
|1213.90246580058
|2
|2
|-
|-
|[[105zpi]]
| [[28/27]]
|26.8614449800848
| -3.690
|44.6736949888469
| -6.225
|1.256485
|0.112342
|6.582438
|[[27edo]]
|1206.18976469887
|4
|4
|-
|-
|[[106zpi]]
| [[25/14]]
|27.0866140827635
| +3.807
|44.3023257293579
| +6.423
|6.069233
|- style="background-color: #cccccc;"
|1.185939
| ''[[16/13]]''
|16.215619
| ''-3.846''
|[[27edo]]
| ''-6.488''
|1196.16279469266
|10
|8
|-
|-
|[[107zpi]]
| [[26/15]]
|27.3120290844743
| -3.921
|43.9366843191503
| -6.616
|0.602637
|0.041871
|5.114968
|[[27edo]]
|1186.29047661706
|3
|3
|-
|-
|[[108zpi]]
| [[9/2]]
|27.4542642328809
| +4.019
|43.7090569909648
| +6.780
|0.984736
|0.101571
|7.811143
|[[27edo]]
|1180.14453875605
|2
|2
|-
|-
|[[109zpi]]
| [[29/22]]
|27.6183280003205
| -4.090
|43.4494079433800
| -6.901
|1.239508
|0.126212
|7.661708
|[[28edo]]
|1216.58342241464
|3
|3
|-
|-
|[[110zpi]]
| [[29/18]]
|27.8137942668253
| +4.128
|43.1440596880840
| +6.965
|3.162449
|0.446881
|10.945193
|[[28edo]]
|1208.03367126635
|4
|4
|-
|-
|[[111zpi]]
| [[25/3]]
|28.0320347788478
| +4.136
|42.8081660666847
| +6.978
|3.688692
|- style="background-color: #cccccc;"
|0.558839
| ''[[24/17]]''
|11.937782
| ''-4.289''
|[[28edo]]
| ''-7.235''
|1198.62864986717
|- style="background-color: #cccccc;"
|6
| ''[[32/31]]''
|6
| ''+4.307''
| ''+7.266''
|-
|-
|[[112zpi]]
| [[21/1]]
|28.2227703035949
| +4.347
|42.5188593143583
| +7.335
|0.923641
|0.071711
|5.745791
|[[28edo]]
|1190.52806080203
|3
|3
|-
|-
|[[113zpi]]
| [[34/21]]
|28.4036873861268
| -4.379
|42.2480357457431
| -7.388
|2.614796
|0.391266
|11.944435
|[[28edo]]
|1182.94500088081
|3
|3
|-
|-
|[[114zpi]]
| [[14/5]]
|28.5934669867681
| -4.379
|41.9676284990313
| -7.388
|0.825416
|0.073811
|6.783286
|[[29edo]]
|1217.06122647191
|2
|2
|-
|-
|[[115zpi]]
| [[26/3]]
|28.7248803560996
| -4.493
|41.7756309207807
| -7.581
|0.551753
|0.036944
|5.000303
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| ''[[31/24]]''
|4
| ''-28.183''
| ''-47.549''
|-
|-
|[[314zpi]]
| [[5/4]]
|61.9380472360525
| +28.584
|19.3741981471691
| +48.226
|6.262952
|- style="background-color: #cccccc;"
|0.952068
| ''[[29/7]]''
|15.026453
| ''+28.635''
|[[62edo]]
| ''+48.312''
|1201.20028512448
|- style="background-color: #cccccc;"
|8
| ''[[23/15]]''
|8
| ''-28.752''
| ''-48.510''
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''+28.886''
| ''+48.735''
|-
|-
|[[315zpi]]
| [[19/4]]
|62.1297615103406
| +28.958
|19.3144150376350
| +48.857
|2.249577
|0.236225
|10.389110
|[[62edo]]
|1197.49373233337
|5
|5
|-
|-
|[[316zpi]]
| [[17/2]]
|62.2561204986878
| +29.124
|19.2752132704012
| +49.137
|0.124634
|0.003155
|2.239821
|[[62edo]]
|1195.06322276487
|2
|2
|-
|-
|[[317zpi]]
| [[4/1]]
|62.4054836742562
| -29.156
|19.2290793909034
| -49.191
|3.147820
|- style="background-color: #cccccc;"
|0.438058
| ''[[30/7]]''
|14.235540
| ''+29.215''
|[[62edo]]
| ''+49.290''
|1192.20292223601
|- style="background-color: #cccccc;"
|3
| ''[[23/3]]''
|3
| ''-29.324''
| ''-49.475''
|- style="background-color: #cccccc;"
| ''[[18/13]]''
| ''+29.329''
| ''+49.482''
|-
|-
|[[318zpi]]
| [[7/6]]
|62.5706008969214
| +29.485
|19.1783358765705
| +49.745
|0.930376
|0.068609
|6.710439
|[[63edo]]
|1208.23516022394
|2
|2
|-
|-
|[[319zpi]]
| [[20/19]]
|62.6989493884242
| -29.530
|19.1390766783973
| -49.821
|1.097917
|- style="background-color: #cccccc;"
|0.092231
| ''[[20/1]]''
|7.748190
| ''+29.544''
|[[63edo]]
| ''+49.845''
|1205.76183073903
|- style="background-color: #cccccc;"
|2
| ''[[17/10]]''
|2
| ''-29.575''
| ''-49.898''
|-
|-
|[[320zpi]]
| [[23/14]]
|62.8317086673125
| +29.618
|19.0986370648279
| +49.971
|1.423082
|}
|0.113490
 
|7.328819
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|[[63edo]]
|+ style="white-space: nowrap;" | 34-integer-limit intervals in 71zpi with prime 2 removed (by patent val mapping)
|1203.21413508416
|5
|5
|-
|-
|[[321zpi]]
! Ratio
|63.0192885705350
! Error (abs, [[Cent|¢]])
|19.0417890652143
! Error (rel, [[Relative cent|%]])
|6.768662
|1.049023
|15.412920
|[[63edo]]
|1199.63271110850
|8
|8
|-
|-
|[[322zpi]]
| [[34/1]]
|63.2073304209154
| -0.032
|18.9851397299785
| -0.053
|1.735228
|0.146786
|7.778139
|[[63edo]]
|1196.06380298865
|4
|4
|-
|-
|[[323zpi]]
| [[34/19]]
|63.3523599407441
| +0.166
|18.9416779599435
| +0.281
|1.487248
|0.149872
|9.636446
|[[63edo]]
|1193.32571147644
|3
|3
|-
|-
|[[324zpi]]
| '''[[19/1]]'''
|63.4820900240111
| '''-0.198'''
|18.9029693185293
| '''-0.334'''
|0.364339
|0.018823
|4.649012
|[[63edo]]
|1190.88706706735
|2
|2
|-
|-
|[[325zpi]]
| [[14/3]]
|63.6001794885619
| +0.329
|18.8678712803918
| +0.555
|1.154569
|0.098289
|8.030421
|[[64edo]]
|1207.54376194507
|3
|3
|-
|-
|[[326zpi]]
| [[19/5]]
|63.7755578116328
| +0.374
|18.8159859541224
| +0.631
|4.294126
|0.588980
|13.437518
|[[64edo]]
|1204.22310106383
|3
|3
|-
|-
|[[327zpi]]
| [[21/13]]
|63.9417017997285
| -0.458
|18.7670951229687
| -0.772
|1.537264
|0.114781
|6.776320
|[[64edo]]
|1201.09408786999
|4
|4
|-
|-
|[[328zpi]]
| [[34/5]]
|64.0993554529598
| +0.540
|18.7209370752665
| +0.911
|3.612776
|0.445177
|11.818611
|[[64edo]]
|1198.13997281706
|2
|2
|-
|-
|[[329zpi]]
| '''[[5/1]]'''
|64.2659524894239
| '''-0.572'''
|18.6724066712849
| '''-0.965'''
|1.814599
|0.165176
|8.426760
|[[64edo]]
|1195.03402696224
|3
|3
|-
|-
|[[330zpi]]
| [[30/29]]
|64.4123850539735
| +0.580
|18.6299575616471
| +0.978
|1.543630
|0.143805
|8.666993
|[[64edo]]
|1192.31728394542
|3
|3
|-
|-
|[[331zpi]]
| [[27/10]]
|64.5606141595703
| -0.689
|18.5871837748327
| -1.163
|1.391085
|0.136370
|9.307579
|[[65edo]]
|1208.16694536413
|2
|2
|-
|-
|[[332zpi]]
| [[26/9]]
|64.6874683930590
| +0.787
|18.5507337017499
| +1.327
|0.489027
|0.026821
|4.961836
|[[65edo]]
|1205.79769061374
|3
|3
|-
|-
|[[333zpi]]
| [[15/14]]
|64.8189580509998
| -0.901
|18.5131022787475
| -1.519
|2.021407
|0.192939
|9.145175
|[[65edo]]
|1203.35164811858
|7
|7
|-
|-
|[[334zpi]]
| [[25/19]]
|65.0158450885860
| -0.946
|18.4570391781413
| -1.595
|7.813349
|1.269821
|16.514861
|[[65edo]]
|1199.70754657919
|6
|6
|-
|-
|[[335zpi]]
| [[31/22]]
|65.2099287191200
| -1.007
|18.4021056849914
| -1.698
|1.097627
|0.081935
|6.985148
|[[65edo]]
|1196.13686952444
|5
|5
|-
|-
|[[336zpi]]
| [[27/22]]
|65.3248895418838
| +1.080
|18.3697210728631
| +1.821
|0.549360
|0.033412
|5.545061
|[[65edo]]
|1194.03186973610
|2
|2
|-
|-
|[[337zpi]]
| [[34/25]]
|65.4558787632399
| +1.112
|18.3329598910514
| +1.876
|1.497773
|0.145255
|9.207500
|[[65edo]]
|1191.64239291834
|2
|2
|-
|-
|[[338zpi]]
| [[25/1]]
|65.6180369970471
| -1.144
|18.2876546589469
| -1.929
|2.423098
|0.285838
|11.511133
|[[66edo]]
|1206.98520749050
|3
|3
|-
|-
|[[339zpi]]
| [[29/6]]
|65.7553795181244
| -1.151
|18.2494574405010
| -1.943
|0.486400
|0.022483
|4.168011
|[[66edo]]
|1204.46419107306
|3
|3
|-
|-
|[[340zpi]]
| [[25/11]]
|65.9158158482913
| +1.197
|18.2050390267772
| +2.020
|4.469113
|0.620786
|13.998526
|[[66edo]]
|1201.53257576729
|2
|2
|-
|-
|[[341zpi]]
| [[27/2]]
|66.0821618610393
| -1.261
|18.1592122019769
| -2.128
|1.668099
|0.126261
|6.920563
|[[66edo]]
|1198.50800533048
|4
|4
|-
|-
|[[342zpi]]
| [[29/28]]
|66.2463426513037
| -1.480
|18.1142075467676
| -2.497
|4.114058
|0.559460
|13.529076
|[[66edo]]
|1195.53769808666
|4
|4
|-
|-
|[[343zpi]]
| [[31/28]]
|66.4154889670582
| +1.604
|18.0680744606909
| +2.706
|0.782645
|0.054315
|6.431152
|[[66edo]]
|1192.49291440560
|3
|3
|-
|-
|[[344zpi]]
| [[11/5]]
|66.5330134017830
| -1.769
|18.0361588727896
| -2.984
|0.678268
|0.050255
|6.890632
|[[67edo]]
|1208.42264447691
|2
|2
|-
|-
|[[345zpi]]
| [[31/6]]
|66.6511016677143
| +1.932
|18.0042035311365
| +3.260
|0.801667
|0.056352
|6.525275
|[[67edo]]
|1206.28163658615
|3
|3
|-
|-
|[[346zpi]]
| [[31/27]]
|66.8108104662562
| -2.086
|17.9611651411724
| -3.520
|3.637876
|0.434417
|11.646984
|[[67edo]]
|1203.39806445855
|4
|4
|-
|-
|[[347zpi]]
| [[19/11]]
|66.9983955140918
| +2.143
|17.9108766828245
| +3.615
|5.331365
|0.724895
|13.386253
|[[67edo]]
|1200.02873774924
|4
|4
|-
|-
|[[348zpi]]
| [[33/26]]
|67.1687953903058
| +2.152
|17.8654387506433
| +3.632
|1.145201
|0.080143
|6.442564
|[[67edo]]
|1196.98439629310
|5
|5
|-
|-
|[[349zpi]]
| [[34/11]]
|67.3040949286566
| +2.309
|17.8295243591347
| +3.896
|1.654031
|0.165479
|9.569366
|[[67edo]]
|1194.57813206203
|2
|2
|-
|-
|[[350zpi]]
| '''[[11/1]]'''
|67.4393002044230
| '''-2.341'''
|17.7937789443625
| '''-3.949'''
|0.830230
|0.055816
|6.175288
|[[67edo]]
|1192.18318927228
|2
|2
|-
|-
|[[351zpi]]
| [[31/30]]
|67.5914903650132
| +2.504
|17.7537141660830
| +4.225
|2.639332
|0.323579
|12.062466
|[[68edo]]
|1207.25256329365
|2
|2
|-
|-
|[[352zpi]]
| [[14/11]]
|67.7458991176146
| -2.610
|17.7132492981850
| -4.404
|0.997211
|0.074197
|6.918024
|[[68edo]]
|1204.50095227658
|2
|2
|-
|-
|[[353zpi]]
| [[33/14]]
|67.8609531907493
| -2.669
|17.6832175732477
| -4.504
|0.915682
|0.058404
|5.901094
|[[68edo]]
|1202.45879498085
|5
|5
|-
|-
|[[354zpi]]
| [[31/10]]
|68.0493056282519
| -2.775
|17.6342725163943
| -4.683
|7.666604
|1.254592
|17.034505
|[[68edo]]
|1199.13053111481
|10
|10
|-
|-
|[[355zpi]]
| [[11/3]]
|68.2404318270010
| +2.939
|17.5848828600934
| +4.959
|1.291664
|0.097854
|7.095918
|[[68edo]]
|1195.77203448635
|6
|6
|-
|-
|[[356zpi]]
| [[31/29]]
|68.3661063759451
| +3.084
|17.5525573067040
| +5.203
|0.940770
|0.072706
|7.209631
|[[68edo]]
|1193.57389685587
|3
|3
|-
|-
|[[357zpi]]
| [[31/2]]
|68.5032557648893
| -3.347
|17.5174155826773
| -5.647
|1.284558
|0.126358
|9.518932
|[[69edo]]
|1208.70167520473
|3
|3
|-
|-
|[[358zpi]]
| [[15/11]]
|68.6242507456349
| -3.511
|17.4865297174313
| -5.923
|0.419056
|0.020242
|4.413228
|[[69edo]]
|1206.57055050276
|3
|3
|-
|-
|[[359zpi]]
| [[28/27]]
|68.7793781502555
| -3.690
|17.4470899893639
| -6.225
|3.727725
|0.466649
|12.567601
|[[69edo]]
|1203.84920926611
|6
|6
|-
|-
|[[360zpi]]
| [[25/14]]
|68.9600161044447
| +3.807
|17.4013880475683
| +6.423
|4.142538
|0.497993
|11.609870
|[[69edo]]
|1200.69577528221
|6
|6
|-
|-
|[[361zpi]]
| [[26/15]]
|69.1246112837247
| -3.921
|17.3599529561845
| -6.616
|1.817851
|0.159901
|8.294120
|[[69edo]]
|1197.83675397673
|2
|2
|-
|-
|[[362zpi]]
| [[9/2]]
|69.2585753964037
| +4.019
|17.3263742884078
| +6.780
|1.244724
|0.094118
|7.024382
|[[69edo]]
|1195.51982590014
|3
|3
|-
|-
|[[363zpi]]
| [[29/22]]
|69.4191373621103
| -4.090
|17.2862995075904
| -6.901
|3.169090
|0.429442
|14.276498
|[[69edo]]
|1192.75466602374
|3
|3
|-
|-
|[[364zpi]]
| [[29/18]]
|69.5704026167013
| +4.128
|17.2487143219712
| +6.965
|0.096808
|0.002355
|2.206818
|[[70edo]]
|1207.41000253799
|2
|2
|-
|-
|[[365zpi]]
| [[25/3]]
|69.6807229795223
| +4.136
|17.2214057014399
| +6.978
|1.263704
|0.119115
|9.440418
|[[70edo]]
|1205.49839910079
|2
|2
|-
|-
|[[366zpi]]
| [[21/1]]
|69.8265874613323
| +4.347
|17.1854309887981
| +7.335
|2.112555
|0.195535
|8.795110
|[[70edo]]
|1202.98016921587
|5
|5
|-
|-
|[[367zpi]]
| [[34/21]]
|70.0040185665629
| -4.379
|17.1418730606013
| -7.388
|5.698371
|0.763911
|13.162600
|[[70edo]]
|1199.93111424209
|10
|10
|-
|-
|[[368zpi]]
| [[14/5]]
|70.1911982193248
| -4.379
|17.0961606361297
| -7.388
|3.437073
|0.416756
|12.481351
|[[70edo]]
|1196.73124452908
|7
|7
|-
|-
|[[369zpi]]
| [[26/3]]
|70.3434069622478
| -4.493
|17.0591680417757
| -7.581
|0.213396
|0.008189
|3.521338
|[[70edo]]
|1194.14176292430
|3
|3
|-
|-
|[[370zpi]]
| [[21/19]]
|70.4373071391135
| +4.545
|17.0364264157629
| +7.669
|0.619653
|0.043294
|6.683044
|[[70edo]]
|1192.54984910341
|2
|2
|-
|-
|[[371zpi]]
| [[10/9]]
|70.5909931918320
| -4.590
|16.9993358322496
| -7.745
|2.606389
|0.309753
|11.784944
|[[71edo]]
|1206.95284408972
|3
|3
|-
|-
|[[372zpi]]
| [[5/3]]
|70.7491415154812
| +4.708
|16.9613365518706
| +7.943
|1.837153
|0.162767
|8.346461
|[[71edo]]
|1204.25489518282
|3
|3
|-
|-
|[[373zpi]]
| [[19/14]]
|70.8951562521128
| +4.753
|16.9264032049332
| +8.019
|2.285630
|0.214583
|8.902084
|[[71edo]]
|1201.77462755026
|3
|3
|-
|-
|[[374zpi]]
| '''[[13/1]]'''
|71.0593309545342
| '''+4.805'''
|16.8872966277686
| '''+8.107'''
|3.793904
|0.446694
|11.433644
|[[71edo]]
|1198.99806057157
|6
|6
|-
|-
|[[375zpi]]
| [[13/7]]
|71.2245551379515
| -4.822
|16.8481220791871
| -8.135
|2.274247
|0.217081
|9.073141
|[[71edo]]
|1196.21666762229
|3
|3
|-
|-
|[[376zpi]]
| [[34/13]]
|71.3758515821207
| -4.837
|16.8124088665948
| -8.160
|1.790062
|0.175495
|9.451423
|[[71edo]]
|1193.68102952823
|3
|3
|-
|-
|[[377zpi]]
| [[21/5]]
|71.5145608508210
| +4.919
|16.7797996061696
| +8.300
|0.854020
|0.062425
|6.853833
|[[72edo]]
|1208.14557164421
|2
|2
|-
|-
|[[378zpi]]
| [[17/7]]
|71.6470716535280
| +4.919
|16.7487654736676
| +8.300
|1.218607
|0.116828
|9.442741
|[[72edo]]
|1205.91111410407
|3
|3
|-
|-
|[[379zpi]]
| [[14/1]]
|71.7560971542458
| -4.951
|16.7233175658996
| -8.353
|0.256297
|0.008806
|3.153863
|[[72edo]]
|1204.07886474477
|5
|5
|-
|-
|[[380zpi]]
| [[19/13]]
|71.9506065993786
| -5.003
|16.6781081733140
| -8.441
|9.157547
|1.625363
|19.964746
|[[72edo]]
|1200.82378847861
|18
|13
|-
|-
|[[381zpi]]
| [[19/3]]
|72.1424720620339
| +5.082
|16.6337521532135
| +8.574
|0.568366
|0.026895
|4.371780
|[[72edo]]
|1197.63015503137
|4
|4
|-
|-
|[[382zpi]]
| [[29/27]]
|72.2612976521753
| -5.170
|16.6063998155156
| -8.723
|1.591014
|0.154252
|9.435978
|[[72edo]]
|1195.66078671712
|2
|2
|-
|-
|[[383zpi]]
| [[34/3]]
|72.4050722040381
| +5.248
|16.5734245332757
| +8.854
|1.378597
|0.121775
|8.414491
|[[72edo]]
|1193.28656639585
|2
|2
|-
|-
|[[384zpi]]
| '''[[3/1]]'''
|72.5434989197956
| '''-5.280'''
|16.5417993048106
| '''-8.908'''
|1.365896
|0.116955
|8.128764
|[[73edo]]
|1207.55134925117
|3
|3
|-
|-
|[[385zpi]]
| [[13/5]]
|72.6913620787328
| +5.377
|16.5081512532434
| +9.072
|2.069179
|0.213104
|9.989699
|[[73edo]]
|1205.09504148677
|2
|2
|-
|-
|[[386zpi]]
| [[25/21]]
|72.8328565155552
| -5.491
|16.4760804039549
| -9.264
|1.354260
|0.101953
|7.070388
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|-
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|-
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| [[29/10]]
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| [[25/13]]
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| [[33/10]]
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| [[34/33]]
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| [[29/4]]
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| [[31/26]]
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| [[29/20]]
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| [[15/2]]
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| [[28/9]]
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|10
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| [[26/5]]
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| [[3/2]]
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| [[25/9]]
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| [[26/19]]
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|3
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|-
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| [[34/7]]
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| [[17/13]]
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| [[14/13]]
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| [[26/1]]
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| [[10/3]]
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| [[9/5]]
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| [[13/3]]
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| [[23/17]]
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| [[33/31]]
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| [[29/9]]
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| [[34/9]]
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| [[9/1]]
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| [[25/7]]
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| [[27/14]]
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| [[22/15]]
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| [[31/4]]
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| [[29/26]]
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| [[22/3]]
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| [[31/20]]
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| [[31/15]]
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| [[33/13]]
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| [[31/3]]
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| [[31/14]]
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| [[27/4]]
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| [[33/29]]
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| [[29/12]]
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| [[25/2]]
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| [[28/15]]
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| [[6/5]]
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| [[28/19]]
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|-
|-
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|14.332919
|[[95edo]]
|1198.52584768461
|7
|7
|-
|-
|[[541zpi]]
| [[26/17]]
|95.2826493877981
| -24.319
|12.5941082422680
| -41.030
|1.758458
|0.142811
|8.176292
|[[95edo]]
|1196.44028301546
|3
|3
|-
|-
|[[542zpi]]
| [[28/13]]
|95.4156589931259
| -24.334
|12.5765520320564
| -41.055
|1.337395
|0.116246
|8.908544
|[[95edo]]
|1194.77244304536
|3
|3
|-
|-
|[[543zpi]]
| [[20/3]]
|95.5361940130413
| -24.448
|12.5606845907656
| -41.248
|0.585756
|0.034891
|5.892027
|[[96edo]]
|1205.82572071350
|2
|2
|-
|-
|[[544zpi]]
| [[18/5]]
|95.6568645286242
| -24.565
|12.5448393684377
| -41.446
|1.326531
|0.116452
|9.023393
|[[96edo]]
|1204.30457937002
|3
|3
|-
|-
|[[545zpi]]
| [[13/6]]
|95.7816928430132
| +24.663
|12.5284901987148
| +41.610
|1.342276
|0.093325
|6.949461
|[[96edo]]
|1202.73505907662
|4
|4
|-
|-
|[[546zpi]]
| '''[[23/1]]'''
|95.9543940692998
| '''+24.667'''
|12.5059410946136
| '''+41.618'''
|7.327322
|1.045052
|15.480737
|[[96edo]]
|1200.57034508290
|6
|6
|-
|-
|[[547zpi]]
| [[34/23]]
|96.1324479947499
| -24.699
|12.4827779280679
| -41.671
|2.431095
|0.224252
|9.548447
|[[96edo]]
|1198.34668109452
|6
|6
|-
|-
|[[548zpi]]
| [[10/7]]
|96.2640257554220
| -24.777
|12.4657159368011
| -41.802
|0.763738
|0.049355
|6.478779
|[[96edo]]
|1196.70872993291
|2
|2
|-
|-
|[[549zpi]]
| [[23/19]]
|96.3664598543133
| +24.865
|12.4524653267761
| +41.952
|0.635305
|0.036834
|5.762332
|[[96edo]]
|1195.43667137051
|2
|2
|-
|-
|[[550zpi]]
| [[19/18]]
|96.5200797471850
| +24.939
|12.4326461721039
| +42.076
|3.549272
|0.471966
|14.790729
|[[97edo]]
|1205.96667869407
|3
|3
|-
|-
|[[551zpi]]
| [[17/9]]
|96.6691581811906
| +25.106
|12.4134731550139
| +42.357
|0.404643
|0.018066
|4.384973
|[[97edo]]
|1204.10689603635
|2
|2
|-
|-
|[[552zpi]]
| [[18/1]]
|96.7709136556901
| -25.137
|12.4004202778284
| -42.411
|1.100851
|0.080757
|7.508997
|[[97edo]]
|1202.84076694935
|2
|2
|-
|-
|[[553zpi]]
| [[30/13]]
|96.9251251346284
| -25.235
|12.3806907479687
| -42.575
|4.250052
|0.495809
|12.303755
|[[97edo]]
|1200.92700255296
|5
|5
|-
|-
|[[554zpi]]
| [[23/5]]
|97.0894142430262
| +25.239
|12.3597408569822
| +42.582
|3.739770
|0.380211
|10.364917
|[[97edo]]
|1198.89486312727
|4
|4
|-
|-
|[[555zpi]]
| [[29/21]]
|97.2477095492293
| -25.356
|12.3396222447021
| -42.780
|3.012654
|0.318839
|11.069984
|[[97edo]]
|1196.94335773610
|4
|4
|-
|-
|[[556zpi]]
| [[27/7]]
|97.3932499632846
| -25.466
|12.3211824274514
| -42.965
|0.907034
|0.066183
|7.445945
|[[97edo]]
|1195.15469546278
|3
|3
|-
|-
|[[557zpi]]
| [[31/8]]
|97.5007120641918
| +25.809
|12.3076024225336
| +43.543
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|0.023978
|5.483463
|[[98edo]]
|1206.14503740829
|3
|3
|-
|-
|[[558zpi]]
| [[25/23]]
|97.6100413764871
| -25.811
|12.2938171429673
| -43.547
|0.992912
|0.074301
|7.662658
|[[98edo]]
|1204.79408001079
|3
|3
|-
|-
|[[559zpi]]
| [[29/13]]
|97.7583854312732
| -25.814
|12.2751618155931
| -43.553
|3.322076
|0.357937
|11.284386
|[[98edo]]
|1202.96585792813
|6
|6
|-
|-
|[[560zpi]]
| [[22/7]]
|97.9232407224070
| -26.546
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| -44.787
|4.310922
|0.481970
|11.590393
|[[98edo]]
|1200.94064629022
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|4
|-
|-
|[[561zpi]]
| [[11/4]]
|98.0791975025252
| +26.815
|12.2350103850422
| +45.242
|2.326577
|0.205633
|9.000394
|[[98edo]]
|1199.03101773413
|4
|4
|-
|-
|[[562zpi]]
| [[23/11]]
|98.2125880281967
| +27.008
|12.2183930195942
| +45.567
|1.519368
|0.116527
|7.702886
|[[98edo]]
|1197.40251592023
|2
|2
|-
|-
|[[563zpi]]
| [[20/11]]
|98.3540669893026
| -27.387
|12.2008172791728
| -46.206
|2.366811
|0.251909
|11.247147
|[[98edo]]
|1195.68009335893
|3
|3
|-
|-
|[[564zpi]]
| [[31/7]]
|98.4863571145854
| -27.552
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| -46.485
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|[[98edo]]
|1194.07401639576
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|3
|-
|-
|[[565zpi]]
| [[27/8]]
|98.6209462564991
| +27.895
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| +47.063
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|[[99edo]]
|1204.61225033289
|2
|2
|-
|-
|[[566zpi]]
| [[29/24]]
|98.7500793162469
| +28.004
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| +47.248
|0.294291
|0.010980
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|[[99edo]]
|1203.03700840121
|4
|4
|-
|-
|[[567zpi]]
| [[25/4]]
|98.8605032450577
| +28.012
|12.1383157136618
| +47.261
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|0.151623
|8.832735
|[[99edo]]
|1201.69325565252
|8
|8
|-
|-
|[[568zpi]]
| [[5/4]]
|99.0473345956631
| +28.584
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| +48.226
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|1.510412
|18.536483
|[[99edo]]
|1199.42652152097
|12
|12
|-
|-
|[[569zpi]]
| [[19/4]]
|99.2313264966420
| +28.958
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| +48.857
|0.491001
|0.022527
|4.564498
|[[99edo]]
|1197.20257900634
|5
|5
|-
|-
|[[570zpi]]
| [[17/2]]
|99.3276816516566
| +29.124
|12.0812242875900
| +49.137
|0.783378
|0.054725
|7.097350
|[[99edo]]
|1196.04120447141
|3
|3
|-
|-
|[[571zpi]]
| [[4/1]]
|99.4575461197234
| -29.156
|12.0654494989800
| -49.191
|1.521422
|0.145458
|9.983865
|[[99edo]]
|1194.47950039902
|2
|2
|-
|-
|[[572zpi]]
| [[7/6]]
|99.5827149010666
| +29.485
|12.0502840396767
| +49.745
|0.815515
|0.050203
|6.137922
|[[100edo]]
|1205.02840396767
|3
|3
|-
|-
|[[573zpi]]
| [[20/19]]
|99.7229394185531
| -29.530
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| -49.821
|2.909787
|0.316222
|11.492782
|[[100edo]]
|1203.33396407762
|3
|3
|-
|-
|[[574zpi]]
| [[23/14]]
|99.8687655581762
| +29.618
|12.0157688271512
| +49.971
|2.104342
|- style="background-color: #cccccc;"
|0.168871
| ''[[17/10]]''
|8.081654
| ''+29.696''
|[[100edo]]
| ''+50.102''
|1201.57688271512
|- style="background-color: #cccccc;"
|3
| ''[[20/1]]''
|3
| ''-29.728''
| ''-50.155''
|- style="background-color: #cccccc;"
| ''[[18/13]]''
| ''-29.942''
| ''-50.518''
|- style="background-color: #cccccc;"
| ''[[23/3]]''
| ''+29.947''
| ''+50.525''
|- style="background-color: #cccccc;"
| ''[[30/7]]''
| ''-30.056''
| ''-50.710''
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''-30.385''
| ''-51.265''
|- style="background-color: #cccccc;"
| ''[[23/15]]''
| ''+30.519''
| ''+51.490''
|- style="background-color: #cccccc;"
| ''[[29/7]]''
| ''-30.636''
| ''-51.688''
|- style="background-color: #cccccc;"
| ''[[31/24]]''
| ''+31.088''
| ''+52.451''
|- style="background-color: #cccccc;"
| ''[[22/17]]''
| ''-31.465''
| ''-53.086''
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''-32.095''
| ''-54.149''
|- style="background-color: #cccccc;"
| ''[[33/23]]''
| ''-32.288''
| ''-54.474''
|- style="background-color: #cccccc;"
| ''[[31/17]]''
| ''-32.471''
| ''-54.785''
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''+33.174''
| ''+55.971''
|- style="background-color: #cccccc;"
| ''[[25/12]]''
| ''+33.292''
| ''+56.169''
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''+33.503''
| ''+56.525''
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''-33.864''
| ''-57.134''
|- style="background-color: #cccccc;"
| ''[[13/4]]''
| ''+33.961''
| ''+57.298''
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''+34.075''
| ''+57.490''
|- style="background-color: #cccccc;"
| ''[[28/17]]''
| ''-34.075''
| ''-57.490''
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''+34.237''
| ''+57.764''
|- style="background-color: #cccccc;"
| ''[[17/6]]''
| ''+34.404''
| ''+58.045''
|- style="background-color: #cccccc;"
| ''[[12/1]]''
| ''-34.435''
| ''-58.098''
|- style="background-color: #cccccc;"
| ''[[26/23]]''
| ''-34.440''
| ''-58.106''
|- style="background-color: #cccccc;"
| ''[[20/13]]''
| ''-34.533''
| ''-58.262''
|- style="background-color: #cccccc;"
| ''[[18/7]]''
| ''-34.764''
| ''-58.653''
|- style="background-color: #cccccc;"
| ''[[30/17]]''
| ''-34.976''
| ''-59.010''
|- style="background-color: #cccccc;"
| ''[[23/9]]''
| ''+35.227''
| ''+59.433''
|- style="background-color: #cccccc;"
| ''[[29/17]]''
| ''-35.555''
| ''-59.987''
|- style="background-color: #cccccc;"
| ''[[33/8]]''
| ''+36.113''
| ''+60.929''
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''+37.303''
| ''+62.936''
|- style="background-color: #cccccc;"
| ''[[15/8]]''
| ''+37.882''
| ''+63.914''
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''-38.454''
| ''-64.878''
|- style="background-color: #cccccc;"
| ''[[7/4]]''
| ''+38.783''
| ''+65.433''
|- style="background-color: #cccccc;"
| ''[[13/12]]''
| ''+39.241''
| ''+66.205''
|- style="background-color: #cccccc;"
| ''[[23/2]]''
| ''+39.245''
| ''+66.213''
|- style="background-color: #cccccc;"
| ''[[20/7]]''
| ''-39.355''
| ''-66.398''
|- style="background-color: #cccccc;"
| ''[[18/17]]''
| ''-39.683''
| ''-66.953''
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''+39.817''
| ''+67.178''
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''+40.387''
| ''+68.139''
|- style="background-color: #cccccc;"
| ''[[27/23]]''
| ''-40.506''
| ''-68.341''
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''+41.393''
| ''+69.837''
|- style="background-color: #cccccc;"
| ''[[23/22]]''
| ''+41.586''
| ''+70.162''
|- style="background-color: #cccccc;"
| ''[[27/16]]''
| ''+42.473''
| ''+71.658''
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''+42.590''
| ''+71.856''
|- style="background-color: #cccccc;"
| ''[[31/23]]''
| ''-42.592''
| ''-71.860''
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''-43.162''
| ''-72.821''
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''+43.536''
| ''+73.452''
|- style="background-color: #cccccc;"
| ''[[17/4]]''
| ''+43.702''
| ''+73.733''
|- style="background-color: #cccccc;"
| ''[[8/1]]''
| ''-43.734''
| ''-73.786''
|- style="background-color: #cccccc;"
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| ''-44.063''
| ''-74.341''
|- style="background-color: #cccccc;"
| ''[[28/23]]''
| ''-44.196''
| ''-74.566''
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''-44.274''
| ''-74.697''
|- style="background-color: #cccccc;"
| ''[[23/6]]''
| ''+44.525''
| ''+75.121''
|- style="background-color: #cccccc;"
| ''[[30/23]]''
| ''-45.097''
| ''-76.085''
|- style="background-color: #cccccc;"
| ''[[29/23]]''
| ''-45.676''
| ''-77.063''
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''-46.673''
| ''-78.745''
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''-47.752''
| ''-80.566''
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''+47.870''
| ''+80.764''
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''+48.081''
| ''+81.121''
|- style="background-color: #cccccc;"
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| ''-81.729''
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''+48.539''
| ''+81.893''
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''-48.815''
| ''-82.359''
|- style="background-color: #cccccc;"
| ''[[17/12]]''
| ''+48.982''
| ''+82.640''
|- style="background-color: #cccccc;"
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| ''-82.693''
|- style="background-color: #cccccc;"
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| ''+49.804''
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|- style="background-color: #cccccc;"
| ''[[33/16]]''
| ''+50.691''
| ''+85.525''
|- style="background-color: #cccccc;"
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| ''-51.881''
| ''-87.531''
|- style="background-color: #cccccc;"
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| ''-88.509''
|- style="background-color: #cccccc;"
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|- style="background-color: #cccccc;"
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|- style="background-color: #cccccc;"
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|- style="background-color: #cccccc;"
| ''[[23/4]]''
| ''+53.823''
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|- style="background-color: #cccccc;"
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| ''+91.773''
|- style="background-color: #cccccc;"
| ''[[32/31]]''
| ''-54.964''
| ''-92.734''
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''-55.971''
| ''-94.432''
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''-57.051''
| ''-96.254''
|- style="background-color: #cccccc;"
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| ''+57.168''
| ''+96.452''
|- style="background-color: #cccccc;"
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| ''-97.416''
|- style="background-color: #cccccc;"
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| ''+58.114''
| ''+98.047''
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''+58.280''
| ''+98.328''
|- style="background-color: #cccccc;"
| ''[[16/1]]''
| ''-58.312''
| ''-98.381''
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''-58.640''
| ''-98.936''
|- style="background-color: #cccccc;"
| ''[[23/12]]''
| ''+59.103''
| ''+99.716''
|- style="background-color: #cccccc;"
| ''[[32/9]]''
| ''-62.330''
| ''-105.161''
|- style="background-color: #cccccc;"
| ''[[21/16]]''
| ''+62.659''
| ''+105.716''
|- style="background-color: #cccccc;"
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| ''-63.117''
| ''-106.488''
|- style="background-color: #cccccc;"
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| ''-107.235''
|- style="background-color: #cccccc;"
| ''[[33/32]]''
| ''+65.269''
| ''+110.120''
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''-67.038''
| ''-113.104''
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''-67.610''
| ''-114.069''
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''-67.939''
| ''-114.624''
|- style="background-color: #cccccc;"
| ''[[23/8]]''
| ''+68.401''
| ''+115.404''
|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''-70.549''
| ''-119.027''
|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''-71.746''
| ''-121.047''
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''-72.318''
| ''-122.012''
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''-72.692''
| ''-122.642''
|- style="background-color: #cccccc;"
| ''[[17/16]]''
| ''+72.858''
| ''+122.923''
|- style="background-color: #cccccc;"
| ''[[32/1]]''
| ''-72.890''
| ''-122.976''
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''-73.681''
| ''-124.311''
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''-77.237''
| ''-130.311''
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''-77.695''
| ''-131.084''
|- style="background-color: #cccccc;"
| ''[[32/7]]''
| ''-82.517''
| ''-139.219''
|- style="background-color: #cccccc;"
| ''[[23/16]]''
| ''+82.979''
| ''+139.999''
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''-87.436''
| ''-147.518''
|- style="background-color: #cccccc;"
| ''[[32/23]]''
| ''-97.557''
| ''-164.594''
|}
|}


{{Harmonics in cet|59.3329806724710|columns=15|title=71zpi}}
[[Category:Zeta peak indexes]]
{{Harmonics in cet|59.3329806724710|columns=16|start=16|title=71zpi}}
 
 
{{Stub}}
Retrieved from "https://en.xen.wiki/w/71zpi"