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[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]
{| 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 32-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
| 59.333
| '''<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
| 118.666
| <small><small><small>[[19/18]]</small></small></small>, <small>[[18/17]]</small>, [[17/16]], '''[[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
| 177.999
| <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>
| vM2
| 12
|-
| 4
| 237.332
| <small><small><small>[[26/23]]</small></small></small>, <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, '''[[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>
| vvA2
| 16
|-
| 5
| 296.665
| <small>[[27/23]]</small>, <small>[[20/17]]</small>, '''[[13/11]]''', '''<u>[[32/27]]'''</u>, '''<u>[[19/16]]'''</u>, '''[[25/21]]''', '''[[31/26]]''', <small>[[6/5]]</small>
| vm3
| 20
|-
| 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>
| vvM3
| 24
|-
| 7
| 415.331
| <small><small><small>[[5/4]]</small></small></small>, [[29/23]], [[24/19]], '''[[19/15]]''', '''<u>[[14/11]]'''</u>, '''[[23/18]]''', [[32/25]], <small>[[9/7]]</small>, <small><small><small>[[31/24]]</small></small></small>
| ^^M3
| 28
|-
| 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>, <small><small>[[4/3]]</small></small>
| vv4
| 32
|-
| 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>
| ^^4
| 36
|-
| 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
| 40
|-
| 11
| 652.663
| <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>
| ^^d5
| 44
|-
| 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
| 48
|-
| 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>
| ^^d6
| 52
|-
| 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>
| ^m6
| 56
|-
| 15
| 889.995
| <small><small><small>[[28/17]]</small></small></small>, '''[[5/3]]''', [[32/19]], <small>[[27/16]]</small>, <small><small>[[22/13]]</small></small>, <small><small><small>[[17/10]]</small></small></small>
| M6
| 60
|-
| 16
| 949.328
| <small><small>[[29/17]]</small></small>, <small>[[12/7]]</small>, '''[[31/18]]''', '''<u>[[19/11]]'''</u>, '''<u>[[26/15]]'''</u>, <small>[[7/4]]</small>
| vA6, ^d7
| 64
|-
| 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
| 68
|-
| 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>
| vM7
| 72
|-
| 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>
| vvA7
| 76
|-
| 20
| 1186.660
| [[2/1]]
| v1 +1 oct
| 80
|-
| 21
| 1245.993
| [[31/15]], [[29/14]], <small>[[27/13]]</small>, <small><small>[[25/12]]</small></small>
| vvA1 +1 oct
| 84
|-
| 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>
| vm2 +1 oct
| 88
|-
| 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>
| vvM2 +1 oct
| 92
|-
| 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>
| ^^M2 +1 oct
| 96
|-
| 25
| 1483.325
| <small>[[7/3]]</small>, '''[[26/11]]''', [[19/8]], <small><small>[[31/13]]</small></small>
| vvm3 +1 oct
| 100
|-
| 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>
| ^^m3 +1 oct
| 104
|-
| 27
| 1601.990
| <small>[[5/2]]</small>, <small>[[28/11]]</small>, <small><small>[[23/9]]</small></small>
| ^M3 +1 oct
| 108
|-
| 28
| 1661.323
| <small><small><small>[[18/7]]</small></small></small>, <small>[[31/12]]</small>, '''[[13/5]]''', '''[[21/8]]''', <small>[[29/11]]</small>
| ^^d4 +1 oct
| 112
|-
| 29
| 1720.656
| <small><small>[[8/3]]</small></small>, '''<u>[[27/10]]'''</u>, '''[[19/7]]''', <small>[[30/11]]</small>
| ^4 +1 oct
| 116
|-
| 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>
| A4 +1 oct
| 120
|-
| 31
| 1839.322
| <small><small>[[20/7]]</small></small>, [[23/8]], '''<u>[[26/9]]'''</u>, '''<u>[[29/10]]'''</u>, '''[[32/11]]'''
| ^d5 +1 oct
| 124
|-
| 32
| 1898.655
| '''<u>[[3/1]]'''</u>
| P5 +1 oct
| 128
|-
| 33
| 1957.988
| '''<u>[[31/10]]'''</u>, '''[[28/9]]''', [[25/8]], <small><small>[[22/7]]</small></small>
| vA5 +1 oct, ^d6 +1 oct
| 132
|-
| 34
| 2017.321
| <small><small>[[19/6]]</small></small>, '''<u>[[16/5]]'''</u>, '''[[29/9]]''', <small><small>[[13/4]]</small></small>
| m6 +1 oct
| 136
|-
| 35
| 2076.654
| <small>[[23/7]]</small>, '''[[10/3]]''', <small><small><small>[[27/8]]</small></small></small>
| vM6 +1 oct
| 140
|-
| 36
| 2135.987
| <small>[[17/5]]</small>, '''<u>[[24/7]]'''</u>, '''[[31/9]]'''
| vvA6 +1 oct
| 144
|-
| 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
| 148
|-
| 38
| 2254.653
| <small><small><small>[[29/8]]</small></small></small>, '''[[11/3]]''', <small>[[26/7]]</small>
| vvM7 +1 oct
| 152
|-
| 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
| 156
|-
| 40
| 2373.319
| <small><small><small>[[31/8]]</small></small></small>, <small><small><small>[[4/1]]</small></small></small>
| vv1 +2 oct
| 160
|-
| 41
| 2432.652
| <small><small><small>[[29/7]]</small></small></small>
| ^^1 +2 oct
| 164
|-
| 42
| 2491.985
| <small><small>[[25/6]]</small></small>, '''[[21/5]]''', [[17/4]], <small><small><small>[[30/7]]</small></small></small>
| vvm2 +2 oct
| 168
|-
| 43
| 2551.318
| [[13/3]], [[22/5]], <small><small><small>[[31/7]]</small></small></small>
| ^^m2 +2 oct
| 172
|-
| 44
| 2610.651
| '''[[9/2]]''', <small><small>[[32/7]]</small></small>
| ^M2 +2 oct
| 176
|-
| 45
| 2669.984
| <small><small><small>[[23/5]]</small></small></small>, '''<u>[[14/3]]'''</u>, <small><small><small>[[19/4]]</small></small></small>
| ^^d3 +2 oct
| 180
|-
| 46
| 2729.317
| [[24/5]], '''<u>[[29/6]]'''</u>
| ^m3 +2 oct
| 184
|-
| 47
| 2788.650
| '''<u>[[5/1]]'''</u>
| M3 +2 oct
| 188
|-
| 48
| 2847.983
| '''<u>[[31/6]]'''</u>, '''[[26/5]]''', <small><small>[[21/4]]</small></small>
| vA3 +2 oct, ^d4 +2 oct
| 192
|-
| 49
| 2907.316
| '''[[16/3]]''', [[27/5]]
| P4 +2 oct
| 196
|-
| 50
| 2966.649
| <small>[[11/2]]</small>, <small>[[28/5]]</small>
| vA4 +2 oct
| 200
|-
| 51
| 3025.982
| <small><small>[[17/3]]</small></small>, '''<u>[[23/4]]'''</u>, <small>[[29/5]]</small>
| d5 +2 oct
| 204
|-
| 52
| 3085.315
| <small>[[6/1]]</small>
| v5 +2 oct
| 208
|-
| 53
| 3144.648
| [[31/5]], <small><small><small>[[25/4]]</small></small></small>
| vvA5 +2 oct
| 212
|-
| 54
| 3203.981
| '''[[19/3]]''', '''[[32/5]]'''
| vm6 +2 oct
| 216
|-
| 55
| 3263.314
| <small><small>[[13/2]]</small></small>, <small><small>[[20/3]]</small></small>
| vvM6 +2 oct
| 220
|-
| 56
| 3322.647
| <small>[[27/4]]</small>
| ^^M6 +2 oct
| 224
|-
| 57
| 3381.980
| [[7/1]]
| vvm7 +2 oct
| 228
|-
| 58
| 3441.313
| [[29/4]], '''[[22/3]]'''
| ^^m7 +2 oct
| 232
|-
| 59
| 3500.646
| [[15/2]], <small><small><small>[[23/3]]</small></small></small>
| ^M7 +2 oct
| 236
|-
| 60
| 3559.979
| <small>[[31/4]]</small>
| ^^d1 +3 oct
| 240
|-
| 61
| 3619.312
| <small>[[8/1]]</small>
| ^1 +3 oct
| 244
|-
| 62
| 3678.645
| '''[[25/3]]''', <small><small><small>[[17/2]]</small></small></small>
| ^^d2 +3 oct
| 248
|-
| 63
| 3737.978
| '''<u>[[26/3]]'''</u>
| ^m2 +3 oct
| 252
|-
| 64
| 3797.311
| '''[[9/1]]'''
| M2 +3 oct
| 256
|-
| 65
| 3856.644
| [[28/3]]
| vA2 +3 oct, ^d3 +3 oct
| 260
|-
| 66
| 3915.977
| <small>[[19/2]]</small>, [[29/3]]
| m3 +3 oct
| 264
|-
| 67
| 3975.310
| [[10/1]]
| vM3 +3 oct
| 268
|-
| 68
| 4034.643
| '''[[31/3]]'''
| vvA3 +3 oct
| 272
|-
| 69
| 4093.976
| <small><small>[[21/2]]</small></small>, '''<u>[[32/3]]'''</u>
| v4 +3 oct
| 276
|-
| 70
| 4153.309
| '''<u>[[11/1]]'''</u>
| vvA4 +3 oct
| 280
|-
| 71
| 4212.642
| <small>[[23/2]]</small>
| vd5 +3 oct
| 284
|-
| 72
| 4271.975
|
| vv5 +3 oct
| 288
|-
| 73
| 4331.308
| <small><small><small>[[12/1]]</small></small></small>
| ^^5 +3 oct
| 292
|-
| 74
| 4390.641
| <small>[[25/2]]</small>
| vvm6 +3 oct
| 296
|-
| 75
| 4449.974
| '''[[13/1]]'''
| ^^m6 +3 oct
| 300
|-
| 76
| 4509.307
| '''<u>[[27/2]]'''</u>
| ^M6 +3 oct
| 304
|-
| 77
| 4568.640
| '''<u>[[14/1]]'''</u>
| ^^d7 +3 oct
| 308
|-
| 78
| 4627.972
| '''<u>[[29/2]]'''</u>
| ^m7 +3 oct
| 312
|-
| 79
| 4687.305
| '''<u>[[15/1]]'''</u>
| M7 +3 oct
| 316
|-
| 80
| 4746.638
| '''<u>[[31/2]]'''</u>
| vA7 +3 oct, ^d1 +4 oct
| 320
|-
| 81
| 4805.971
| '''[[16/1]]'''
| P1 +4 oct
| 324
|-
| 82
| 4865.304
|
| vA1 +4 oct, ^d2 +4 oct
| 328
|-
| 83
| 4924.637
| <small>[[17/1]]</small>
| m2 +4 oct
| 332
|-
| 84
| 4983.970
| <small><small>[[18/1]]</small></small>
| vM2 +4 oct
| 336
|-
| 85
| 5043.303
|
| vvA2 +4 oct
| 340
|-
| 86
| 5102.636
| '''[[19/1]]'''
| vm3 +4 oct
| 344
|-
| 87
| 5161.969
| <small><small>[[20/1]]</small></small>
| vvM3 +4 oct
| 348
|-
| 88
| 5221.302
|
| ^^M3 +4 oct
| 352
|-
| 89
| 5280.635
| '''[[21/1]]'''
| vv4 +4 oct
| 356
|-
| 90
| 5339.968
| [[22/1]]
| ^^4 +4 oct
| 360
|-
| 91
| 5399.301
| <small><small><small>[[23/1]]</small></small></small>
| ^A4 +4 oct
| 364
|-
| 92
| 5458.634
|
| ^^d5 +4 oct
| 368
|-
| 93
| 5517.967
| <small>[[24/1]]</small>
| ^5 +4 oct
| 372
|-
| 94
| 5577.300
| '''<u>[[25/1]]'''</u>
| ^^d6 +4 oct
| 376
|-
| 95
| 5636.633
| '''<u>[[26/1]]'''</u>
| ^m6 +4 oct
| 380
|-
| 96
| 5695.966
| [[27/1]]
| M6 +4 oct
| 384
|-
| 97
| 5755.299
| [[28/1]]
| vA6 +4 oct, ^d7 +4 oct
| 388
|-
| 98
| 5814.632
| <small>[[29/1]]</small>
| m7 +4 oct
| 392
|-
| 99
| 5873.965
| [[30/1]]
| vM7 +4 oct
| 396
|-
| 100
| 5933.298
| [[31/1]]
| vvA7 +4 oct
| 400
|-
| 101
| 5992.631
| '''[[32/1]]'''
| v1 +5 oct
| 404
|}
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Intervals by direct approximation (even if inconsistent)
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[14/1]]
| +0.186
| +0.314
|-
| [[11/5]]
| +0.346
| +0.583
|-
| ''[[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
|-
| ''[[32/9]]''
| ''+0.770''
| ''+1.297''
|-
| [[15/14]]
| +0.777
| +1.309
|-
| ''[[19/16]]''
| ''+0.848''
| ''+1.429''
|-
| [[15/1]]
| +0.963
| +1.623
|-
| [[23/12]]
| -1.007
| -1.698
|-
| [[27/10]]
| -1.105
| -1.863
|-
| ''[[25/16]]''
| ''+1.299''
| ''+2.189''
|-
| [[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
|-
| ''[[32/27]]''
| ''-2.530''
| ''-4.264''
|-
| [[31/30]]
| -2.566
| -4.325
|-
| [[25/11]]
| -2.682
| -4.520
|-
| [[26/9]]
| -2.705
| -4.559
|-
| [[19/5]]
| -2.787
| -4.697
|-
| ''[[24/7]]''
| ''-2.858''
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Retrieved from "https://en.xen.wiki/w/71zpi"