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== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ style="white-space:nowrap" | Intervals in 45zpi
|-
|-
|+ style="white-space:nowrap" | Intervals in 45zpi
| 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:
| 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 %
* '''<u>Bold Underlined:</u>''' relative error < 8.333 %
* '''Bold:''' relative error < 16.667 %
* '''Bold:''' relative error < 16.667 %
Line 510: Line 511:


== Approximation to JI ==
== Approximation to JI ==
=== Interval mappings ===
The following tables show how 32-integer-limit intervals are represented in 45zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.


{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Intervals by direct approximation (even if inconsistent)
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 45zpi (by direct approximation)
|-
|-
! Ratio
! Ratio
Line 519: Line 524:
|-
|-
| [[23/15]]
| [[23/15]]
| -0.002
| +0.002
| -0.003
| +0.003
|-
|- style="background-color: #cccccc;"
| ''[[32/7]]''
| ''[[32/7]]''
| ''+0.034''
| ''-0.034''
| ''+0.042''
| ''-0.042''
|-
|-
| '''[[19/1]]'''
| '''[[19/1]]'''
| '''-0.321'''
| '''+0.321'''
| '''-0.390'''
| '''+0.390'''
|-
|-
| '''[[13/1]]'''
| '''[[13/1]]'''
| '''+0.479'''
| '''-0.479'''
| '''+0.583'''
| '''-0.583'''
|-
|- style="background-color: #cccccc;"
| ''[[11/10]]''
| ''[[11/10]]''
| ''+0.558''
| ''-0.558''
| ''+0.679''
| ''-0.679''
|-
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''[[25/8]]''
| ''-0.728''
| ''+0.728''
| ''-0.885''
| ''+0.885''
|-
|-
| [[19/13]]
| [[19/13]]
| -0.800
| +0.800
| -0.973
| +0.973
|-
|-
| [[29/5]]
| [[29/5]]
| +1.008
| -1.008
| +1.226
| -1.226
|-
|-
| [[23/13]]
| [[23/13]]
| +1.069
| -1.069
| +1.300
| -1.300
|-
|-
| [[15/13]]
| [[15/13]]
| +1.072
| -1.072
| +1.303
| -1.303
|-
|- style="background-color: #cccccc;"
| ''[[29/24]]''
| ''[[29/24]]''
| ''-1.270''
| ''+1.270''
| ''-1.545''
| ''+1.545''
|-
|- style="background-color: #cccccc;"
| ''[[31/12]]''
| ''[[31/12]]''
| ''-1.382''
| ''+1.382''
| ''-1.681''
| ''+1.681''
|-
|- style="background-color: #cccccc;"
| ''[[27/16]]''
| ''[[27/16]]''
| ''+1.411''
| ''-1.411''
| ''+1.716''
| ''-1.716''
|-
|-
| '''[[23/1]]'''
| '''[[23/1]]'''
| '''+1.548'''
| '''-1.548'''
| '''+1.883'''
| '''-1.883'''
|-
|-
| [[15/1]]
| [[15/1]]
| +1.551
| -1.551
| +1.886
| -1.886
|-
|-
| [[22/21]]
| [[22/21]]
| -1.686
| +1.686
| -2.051
| +2.051
|-
|-
| [[23/19]]
| [[23/19]]
| +1.869
| -1.869
| +2.273
| -2.273
|-
|-
| [[19/15]]
| [[19/15]]
| -1.871
| +1.871
| -2.276
| +2.276
|-
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''[[32/19]]''
| ''-1.967''
| ''+1.967''
| ''-2.393''
| ''+2.393''
|-
|-
| [[19/7]]
| [[19/7]]
| +2.002
| -2.002
| +2.434
| -2.434
|-
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''[[21/20]]''
| ''+2.244''
| ''-2.244''
| ''+2.729''
| ''-2.729''
|-
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''[[24/5]]''
| ''+2.278''
| ''-2.278''
| ''+2.771''
| ''-2.771''
|-
|- style="background-color: #cccccc;"
| ''[[32/1]]''
| ''[[32/1]]''
| ''-2.288''
| ''+2.288''
| ''-2.783''
| ''+2.783''
|-
|-
| '''[[7/1]]'''
| '''[[7/1]]'''
| '''-2.322'''
| '''+2.322'''
| '''-2.824'''
| '''+2.824'''
|-
|- style="background-color: #cccccc;"
| ''[[28/3]]''
| ''[[28/3]]''
| ''+2.384''
| ''-2.384''
| ''+2.900''
| ''-2.900''
|-
|-
| [[18/5]]
| [[18/5]]
| -2.428
| +2.428
| -2.953
| +2.953
|-
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''[[32/13]]''
| ''-2.767''
| ''+2.767''
| ''-3.365''
| ''+3.365''
|-
|-
| [[13/7]]
| [[13/7]]
| +2.801
| -2.801
| +3.407
| -3.407
|-
|-
| [[31/9]]
| [[31/9]]
| +3.324
| -3.324
| +4.043
| -4.043
|-
|-
| [[30/17]]
| [[30/17]]
| -3.364
| +3.364
| -4.092
| +4.092
|-
|-
| [[29/18]]
| [[29/18]]
| +3.436
| -3.436
| +4.179
| -4.179
|-
|- style="background-color: #cccccc;"
| ''[[32/23]]''
| ''[[32/23]]''
| ''-3.836''
| ''+3.836''
| ''-4.666''
| ''+4.666''
|-
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''[[32/15]]''
| ''-3.839''
| ''+3.839''
| ''-4.669''
| ''+4.669''
|-
|-
| [[23/7]]
| [[23/7]]
| +3.870
| -3.870
| +4.707
| -4.707
|-
|-
| [[15/7]]
| [[15/7]]
| +3.873
| -3.873
| +4.710
| -4.710
|-
|-
| [[25/6]]
| [[25/6]]
| +3.979
| -3.979
| +4.839
| -4.839
|-
|-
| [[22/3]]
| [[22/3]]
| -4.008
| +4.008
| -4.875
| +4.875
|-
|-
| [[26/17]]
| [[26/17]]
| -4.436
| +4.436
| -5.395
| +5.395
|-
|- style="background-color: #cccccc;"
| ''[[20/3]]''
| ''[[20/3]]''
| ''-4.566''
| ''+4.566''
| ''-5.553''
| ''+5.553''
|-
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''[[24/7]]''
| ''-4.672''
| ''+4.672''
| ''-5.682''
| ''+5.682''
|-
|- style="background-color: #cccccc;"
| ''[[4/3]]''
| ''[[4/3]]''
| ''+4.706''
| ''-4.706''
| ''+5.724''
| ''-5.724''
|-
|- style="background-color: #cccccc;"
| ''[[23/20]]''
| ''[[23/20]]''
| ''-4.709''
| ''+4.709''
| ''-5.727''
| ''+5.727''
|-
|-
| [[17/2]]
| [[17/2]]
| +4.915
| -4.915
| +5.977
| -5.977
|-
|-
| [[22/15]]
| [[22/15]]
| +5.264
| -5.264
| +6.402
| -6.402
|-
|-
| [[23/22]]
| [[23/22]]
| -5.267
| +5.267
| -6.405
| +6.405
|-
|- style="background-color: #cccccc;"
| ''[[20/13]]''
| ''[[20/13]]''
| ''+5.778''
| ''-5.778''
| ''+7.027''
| ''-7.027''
|-
|-
| [[17/6]]
| [[17/6]]
| -5.908
| +5.908
| -7.186
| +7.186
|-
|-
| [[29/7]]
| [[29/7]]
| -5.942
| +5.942
| -7.227
| +7.227
|-
|- style="background-color: #cccccc;"
| ''[[32/29]]''
| ''[[32/29]]''
| ''+5.977''
| ''-5.977''
| ''+7.269''
| ''-7.269''
|-
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''[[31/16]]''
| ''-6.088''
| ''+6.088''
| ''-7.404''
| ''+7.404''
|-
|- style="background-color: #cccccc;"
| ''[[9/4]]''
| ''[[9/4]]''
| ''+6.117''
| ''-6.117''
| ''+7.439''
| ''-7.439''
|-
|- style="background-color: #cccccc;"
| ''[[20/1]]''
| ''[[20/1]]''
| ''+6.257''
| ''-6.257''
| ''+7.610''
| ''-7.610''
|-
|-
| [[22/13]]
| [[22/13]]
| +6.336
| -6.336
| +7.706
| -7.706
|-
|- style="background-color: #cccccc;"
| ''[[14/11]]''
| ''[[14/11]]''
| ''+6.392''
| ''-6.392''
| ''+7.774''
| ''-7.774''
|-
|- style="background-color: #cccccc;"
| ''[[20/19]]''
| ''[[20/19]]''
| ''+6.578''
| ''-6.578''
| ''+8.000''
| ''-8.000''
|-
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''[[24/19]]''
| ''-6.674''
| ''+6.674''
| ''-8.116''
| ''+8.116''
|-
|-
| [[22/1]]
| [[22/1]]
| +6.815
| -6.815
| +8.288
| -8.288
|-
|-
| [[25/18]]
| [[25/18]]
| -6.844
| +6.844
| -8.324
| +8.324
|-
|-
| [[7/5]]
| [[7/5]]
| +6.950
| -6.950
| +8.453
| -8.453
|-
|-
| [[23/21]]
| [[23/21]]
| -6.953
| +6.953
| -8.456
| +8.456
|-
|- style="background-color: #cccccc;"
| ''[[32/5]]''
| ''[[32/5]]''
| ''+6.984''
| ''-6.984''
| ''+8.495''
| ''-8.495''
|-
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''[[24/1]]''
| ''-6.994''
| ''+6.994''
| ''-8.506''
| ''+8.506''
|-
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''[[21/4]]''
| ''-7.028''
| ''+7.028''
| ''-8.548''
| ''+8.548''
|-
|- style="background-color: #cccccc;"
| ''[[27/10]]''
| ''[[27/10]]''
| ''-7.134''
| ''+7.134''
| ''-8.677''
| ''+8.677''
|-
|-
| [[22/19]]
| [[22/19]]
| +7.136
| -7.136
| +8.678
| -8.678
|-
|-
| [[17/14]]
| [[17/14]]
| +7.237
| -7.237
| +8.802
| -8.802
|-
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''[[24/13]]''
| ''-7.473''
| ''+7.473''
| ''-9.089''
| ''+9.089''
|-
|-
| [[31/27]]
| [[31/27]]
| -7.499
| +7.499
| -9.120
| +9.120
|-
|-
| [[27/11]]
| [[27/11]]
| -7.692
| +7.692
| -9.355
| +9.355
|-
|-
| [[29/19]]
| [[29/19]]
| -7.944
| +7.944
| -9.661
| +9.661
|-
|-
| [[21/13]]
| [[21/13]]
| +8.022
| -8.022
| +9.756
| -9.756
|-
|-
| '''[[29/1]]'''
| '''[[29/1]]'''
| '''-8.265'''
| '''+8.265'''
| '''-10.051'''
| '''+10.051'''
|-
|- style="background-color: #cccccc;"
| ''[[28/9]]''
| ''[[28/9]]''
| ''-8.439''
| ''+8.439''
| ''-10.264''
| ''+10.264''
|-
|-
| [[21/1]]
| [[21/1]]
| +8.501
| -8.501
| +10.339
| -10.339
|-
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''[[24/23]]''
| ''-8.542''
| ''+8.542''
| ''-10.389''
| ''+10.389''
|-
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''[[8/5]]''
| ''-8.545''
| ''+8.545''
| ''-10.392''
| ''+10.392''
|-
|- style="background-color: #cccccc;"
| ''[[20/7]]''
| ''[[20/7]]''
| ''+8.579''
| ''-8.579''
| ''+10.434''
| ''-10.434''
|-
|- style="background-color: #cccccc;"
| ''[[11/2]]''
| ''[[11/2]]''
| ''-8.714''
| ''+8.714''
| ''-10.599''
| ''+10.599''
|-
|-
| [[29/13]]
| [[29/13]]
| -8.744
| +8.744
| -10.634
| +10.634
|-
|-
| [[21/19]]
| [[21/19]]
| +8.822
| -8.822
| +10.729
| -10.729
|-
|-
| [[19/5]]
| [[19/5]]
| +8.952
| -8.952
| +10.887
| -10.887
|-
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''[[16/11]]''
| ''-9.103''
| ''+9.103''
| ''-11.071''
| ''+11.071''
|-
|-
| [[22/7]]
| [[22/7]]
| +9.137
| -9.137
| +11.113
| -11.113
|-
|- style="background-color: #cccccc;"
| ''[[26/11]]''
| ''[[26/11]]''
| ''+9.194''
| ''-9.194''
| ''+11.181''
| ''-11.181''
|-
|-
| '''[[5/1]]'''
| '''[[5/1]]'''
| '''-9.272'''
| '''+9.272'''
| '''-11.277'''
| '''+11.277'''
|-
|-
| [[23/3]]
| [[23/3]]
| -9.275
| +9.275
| -11.280
| +11.280
|-
|-
| [[18/7]]
| [[18/7]]
| -9.378
| +9.378
| -11.406
| +11.406
|-
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''[[16/9]]''
| ''+9.413''
| ''-9.413''
| ''+11.448''
| ''-11.448''
|-
|- style="background-color: #cccccc;"
| ''[[31/4]]''
| ''[[31/4]]''
| ''+9.441''
| ''-9.441''
| ''+11.483''
| ''-11.483''
|-
|- style="background-color: #cccccc;"
| ''[[29/8]]''
| ''[[29/8]]''
| ''+9.553''
| ''-9.553''
| ''+11.618''
| ''-11.618''
|-
|-
| [[13/5]]
| [[13/5]]
| +9.751
| -9.751
| +11.860
| -11.860
|-
|-
| [[29/23]]
| [[29/23]]
| -9.813
| +9.813
| -11.934
| +11.934
|-
|-
| [[29/15]]
| [[29/15]]
| -9.815
| +9.815
| -11.937
| +11.937
|-
|-
| [[25/17]]
| [[25/17]]
| +9.887
| -9.887
| +12.025
| -12.025
|-
|- style="background-color: #cccccc;"
| ''[[30/11]]''
| ''[[30/11]]''
| ''+10.265''
| ''-10.265''
| ''+12.485''
| ''-12.485''
|-
|-
| [[29/25]]
| [[29/25]]
| +10.280
| -10.280
| +12.503
| -12.503
|-
|-
| [[13/3]]
| [[13/3]]
| -10.344
| +10.344
| -12.581
| +12.581
|-
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''[[17/8]]''
| ''-10.615''
| ''+10.615''
| ''-12.909''
| ''+12.909''
|-
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''[[32/21]]''
| ''-10.789''
| ''+10.789''
| ''-13.122''
| ''+13.122''
|-
|-
| [[23/5]]
| [[23/5]]
| +10.821
| -10.821
| +13.160
| -13.160
|-
|-
| '''[[3/1]]'''
| '''[[3/1]]'''
| '''+10.823'''
| '''-10.823'''
| '''+13.163'''
| '''-13.163'''
|-
|-
| [[19/3]]
| [[19/3]]
| -11.144
| +11.144
| -13.553
| +13.553
|-
|-
| [[19/18]]
| [[19/18]]
| +11.380
| -11.380
| +13.840
| -13.840
|-
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''[[25/24]]''
| ''-11.551''
| ''+11.551''
| ''-14.048''
| ''+14.048''
|-
|- style="background-color: #cccccc;"
| ''[[28/15]]''
| ''[[28/15]]''
| ''+11.657''
| ''-11.657''
| ''+14.177''
| ''-14.177''
|-
|- style="background-color: #cccccc;"
| ''[[28/23]]''
| ''[[28/23]]''
| ''+11.659''
| ''-11.659''
| ''+14.180''
| ''-14.180''
|-
|-
| [[18/1]]
| [[18/1]]
| -11.701
| +11.701
| -14.230
| +14.230
|-
|- style="background-color: #cccccc;"
| ''[[31/28]]''
| ''[[31/28]]''
| ''+11.763''
| ''-11.763''
| ''+14.307''
| ''-14.307''
|-
|-
| [[18/13]]
| [[18/13]]
| -12.180
| +12.180
| -14.813
| +14.813
|-
|- style="background-color: #cccccc;"
| ''[[28/13]]''
| ''[[28/13]]''
| ''+12.728''
| ''-12.728''
| ''+15.480''
| ''-15.480''
|-
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''[[32/3]]''
| ''-13.111''
| ''+13.111''
| ''-15.946''
| ''+15.946''
|-
|-
| [[7/3]]
| [[7/3]]
| -13.145
| +13.145
| -15.987
| +15.987
|-
|- style="background-color: #cccccc;"
| ''[[28/1]]''
| ''[[28/1]]''
| ''+13.207''
| ''-13.207''
| ''+16.063''
| ''-16.063''
|-
|-
| [[23/18]]
| [[23/18]]
| +13.249
| -13.249
| +16.113
| -16.113
|-
|-
| [[6/5]]
| [[6/5]]
| -13.251
| +13.251
| -16.116
| +16.116
|-
|- style="background-color: #cccccc;"
| ''[[28/19]]''
| ''[[28/19]]''
| ''+13.528''
| ''-13.528''
| ''+16.453''
| ''-16.453''
|-
|- style="background-color: #cccccc;"
| ''[[17/11]]''
| ''[[17/11]]''
| ''+13.629''
| ''-13.629''
| ''+16.576''
| ''-16.576''
|-
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''[[12/11]]''
| ''-13.809''
| ''+13.809''
| ''-16.795''
| ''+16.795''
|-
|- style="background-color: #cccccc;"
| ''[[15/4]]''
| ''[[15/4]]''
| ''-13.979''
| ''+13.979''
| ''-17.001''
| ''+17.001''
|-
|- style="background-color: #cccccc;"
| ''[[23/4]]''
| ''[[23/4]]''
| ''-13.981''
| ''+13.981''
| ''-17.004''
| ''+17.004''
|-
|- style="background-color: #cccccc;"
| ''[[27/14]]''
| ''[[27/14]]''
| ''-14.085''
| ''+14.085''
| ''-17.130''
| ''+17.130''
|-
|-
| [[31/3]]
| [[31/3]]
| +14.148
| -14.148
| +17.206
| -17.206
|-
|-
| [[17/10]]
| [[17/10]]
| +14.187
| -14.187
| +17.255
| -17.255
|-
|-
| [[29/6]]
| [[29/6]]
| +14.259
| -14.259
| +17.342
| -17.342
|-
|-
| [[26/25]]
| [[26/25]]
| -14.323
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| -32.275
| +32.275
| -39.253
| +39.253
|-
|-
| [[27/1]]
| [[27/1]]
| +32.469
| -32.469
| +39.489
| -39.489
|-
|-
| [[26/19]]
| [[26/19]]
| -32.547
| +32.547
| -39.584
| +39.584
|-
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''[[25/16]]''
| ''+32.619''
| ''-32.619''
| ''+39.672''
| ''-39.672''
|-
|- style="background-color: #cccccc;"
| ''[[11/5]]''
| ''[[11/5]]''
| ''-32.789''
| ''+32.789''
| ''-39.878''
| ''+39.878''
|-
|-
| [[27/19]]
| [[27/19]]
| +32.790
| -32.790
| +39.879
| -39.879
|-
|-
| [[26/1]]
| [[26/1]]
| -32.868
| +32.868
| -39.974
| +39.974
|-
|-
| [[19/2]]
| [[19/2]]
| +33.026
| -33.026
| +40.167
| -40.167
|-
|-
| [[31/29]]
| [[31/29]]
| +33.235
| -33.235
| +40.421
| -40.421
|-
|-
| [[30/23]]
| [[30/23]]
| -33.344
| +33.344
| -40.554
| +40.554
|-
|-
| '''[[2/1]]'''
| '''[[2/1]]'''
| '''-33.347'''
| '''+33.347'''
| '''-40.557'''
| '''+40.557'''
|-
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''[[16/7]]''
| ''+33.381''
| ''-33.381''
| ''+40.598''
| ''-40.598''
|-
|- style="background-color: #cccccc;"
| ''[[29/11]]''
| ''[[29/11]]''
| ''+33.797''
| ''-33.797''
| ''+41.104''
| ''-41.104''
|-
|-
| [[13/2]]
| [[13/2]]
| +33.826
| -33.826
| +41.139
| -41.139
|-
|- style="background-color: #cccccc;"
| ''[[20/11]]''
| ''[[20/11]]''
| ''-33.905''
| ''+33.905''
| ''-41.235''
| ''+41.235''
|-
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''[[25/4]]''
| ''-34.074''
| ''+34.074''
| ''-41.441''
| ''+41.441''
|-
|-
| [[31/5]]
| [[31/5]]
| +34.243
| -34.243
| +41.647
| -41.647
|-
|-
| [[29/10]]
| [[29/10]]
| +34.355
| -34.355
| +41.782
| -41.782
|-
|-
| [[26/23]]
| [[26/23]]
| -34.416
| +34.416
| -41.857
| +41.857
|-
|-
| [[26/15]]
| [[26/15]]
| -34.419
| +34.419
| -41.860
| +41.860
|-
|- style="background-color: #cccccc;"
| ''[[29/12]]''
| ''[[29/12]]''
| ''-34.617''
| ''+34.617''
| ''-42.101''
| ''+42.101''
|-
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''[[20/17]]''
| ''+34.689''
| ''-34.689''
| ''+42.189''
| ''-42.189''
|-
|- style="background-color: #cccccc;"
| ''[[31/6]]''
| ''[[31/6]]''
| ''-34.729''
| ''+34.729''
| ''-42.237''
| ''+42.237''
|-
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''[[32/27]]''
| ''-34.757''
| ''+34.757''
| ''-42.272''
| ''+42.272''
|-
|-
| [[27/7]]
| [[27/7]]
| +34.792
| -34.792
| +42.314
| -42.314
|-
|-
| [[23/2]]
| [[23/2]]
| +34.895
| -34.895
| +42.439
| -42.439
|-
|-
| [[15/2]]
| [[15/2]]
| +34.898
| -34.898
| +42.442
| -42.442
|-
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''[[24/11]]''
| ''+35.067''
| ''-35.067''
| ''+42.649''
| ''-42.649''
|-
|-
| [[22/17]]
| [[22/17]]
| +35.247
| -35.247
| +42.867
| -42.867
|-
|-
| [[19/14]]
| [[19/14]]
| +35.348
| -35.348
| +42.991
| -42.991
|-
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''[[12/5]]''
| ''+35.625''
| ''-35.625''
| ''+43.327''
| ''-43.327''
|-
|-
| [[14/1]]
| [[14/1]]
| -35.669
| +35.669
| -43.381
| +43.381
|-
|- style="background-color: #cccccc;"
| ''[[14/3]]''
| ''[[14/3]]''
| ''+35.731''
| ''-35.731''
| ''+43.456''
| ''-43.456''
|-
|-
| [[14/13]]
| [[14/13]]
| -36.148
| +36.148
| -43.963
| +43.963
|-
|-
| [[31/18]]
| [[31/18]]
| +36.671
| -36.671
| +44.600
| -44.600
|-
|-
| [[21/17]]
| [[21/17]]
| +36.933
| -36.933
| +44.918
| -44.918
|-
|-
| [[23/14]]
| [[23/14]]
| +37.217
| -37.217
| +45.264
| -45.264
|-
|-
| [[15/14]]
| [[15/14]]
| +37.220
| -37.220
| +45.267
| -45.267
|-
|-
| [[25/12]]
| [[25/12]]
| +37.326
| -37.326
| +45.395
| -45.395
|-
|- style="background-color: #cccccc;"
| ''[[3/2]]''
| ''[[3/2]]''
| ''-38.053''
| ''+38.053''
| ''-46.280''
| ''+46.280''
|-
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''[[23/10]]''
| ''-38.056''
| ''+38.056''
| ''-46.283''
| ''+46.283''
|-
|-
| [[17/4]]
| [[17/4]]
| +38.262
| -38.262
| +46.534
| -46.534
|-
|- style="background-color: #cccccc;"
| ''[[26/3]]''
| ''[[26/3]]''
| ''+38.532''
| ''-38.532''
| ''+46.863''
| ''-46.863''
|-
|-
| [[15/11]]
| [[15/11]]
| -38.611
| +38.611
| -46.959
| +46.959
|-
|-
| [[23/11]]
| [[23/11]]
| -38.614
| +38.614
| -46.962
| +46.962
|-
|- style="background-color: #cccccc;"
| ''[[31/25]]''
| ''[[31/25]]''
| ''-38.707''
| ''+38.707''
| ''-47.076''
| ''+47.076''
|-
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''[[13/10]]''
| ''-39.125''
| ''+39.125''
| ''-47.584''
| ''+47.584''
|-
|-
| [[17/3]]
| [[17/3]]
| -39.255
| +39.255
| -47.742
| +47.742
|-
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''[[29/16]]''
| ''-39.323''
| ''+39.323''
| ''-47.825''
| ''+47.825''
|-
|- style="background-color: #cccccc;"
| ''[[31/8]]''
| ''[[31/8]]''
| ''-39.435''
| ''+39.435''
| ''-47.961''
| ''+47.961''
|-
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''[[9/8]]''
| ''+39.464''
| ''-39.464''
| ''+47.996''
| ''-47.996''
|-
|- style="background-color: #cccccc;"
| ''[[10/1]]''
| ''[[10/1]]''
| ''+39.604''
| ''-39.604''
| ''+48.166''
| ''-48.166''
|-
|-
| [[13/11]]
| [[13/11]]
| -39.683
| +39.683
| -48.262
| +48.262
|-
|- style="background-color: #cccccc;"
| ''[[11/7]]''
| ''[[11/7]]''
| ''-39.739''
| ''+39.739''
| ''-48.331''
| ''+48.331''
|-
|- style="background-color: #cccccc;"
| ''[[32/11]]''
| ''[[32/11]]''
| ''+39.773''
| ''-39.773''
| ''+48.372''
| ''-48.372''
|-
|- style="background-color: #cccccc;"
| ''[[19/10]]''
| ''[[19/10]]''
| ''-39.924''
| ''+39.924''
| ''-48.556''
| ''+48.556''
|-
|-
| '''[[11/1]]'''
| '''[[11/1]]'''
| '''+40.162'''
| '''-40.162'''
| '''+48.845'''
| '''-48.845'''
|-
|-
| [[25/9]]
| [[25/9]]
| -40.191
| +40.191
| -48.881
| +48.881
|-
|-
| [[10/7]]
| [[10/7]]
| -40.297
| +40.297
| -49.010
| +49.010
|-
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''[[16/5]]''
| ''+40.331''
| ''-40.331''
| ''+49.051''
| ''-49.051''
|-
|- style="background-color: #cccccc;"
| ''[[21/2]]''
| ''[[21/2]]''
| ''-40.375''
| ''+40.375''
| ''-49.105''
| ''+49.105''
|-
|- style="background-color: #cccccc;"
| ''[[27/5]]''
| ''[[27/5]]''
| ''-40.481''
| ''+40.481''
| ''-49.233''
| ''+49.233''
|-
|-
| [[19/11]]
| [[19/11]]
| -40.482
| +40.482
| -49.235
| +49.235
|-
|-
| [[28/17]]
| [[28/17]]
| -40.584
| +40.584
| -49.358
| +49.358
|-
|-
| [[29/27]]
| [[29/27]]
| -40.734
| +40.734
| -49.541
| +49.541
|- style="background-color: #cccccc;"
| ''[[26/21]]''
| ''-40.854''
| ''-49.687''
|}
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 45zpi (by patent val mapping)
|-
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[23/15]]
| +0.002
| +0.003
|-
| '''[[19/1]]'''
| '''+0.321'''
| '''+0.390'''
|-
| '''[[13/1]]'''
| '''-0.479'''
| '''-0.583'''
|-
| [[19/13]]
| +0.800
| +0.973
|-
| [[29/5]]
| -1.008
| -1.226
|-
| [[23/13]]
| -1.069
| -1.300
|-
| [[15/13]]
| -1.072
| -1.303
|-
| '''[[23/1]]'''
| '''-1.548'''
| '''-1.883'''
|-
| [[15/1]]
| -1.551
| -1.886
|-
| [[22/21]]
| +1.686
| +2.051
|-
| [[23/19]]
| -1.869
| -2.273
|-
| [[19/15]]
| +1.871
| +2.276
|-
| [[19/7]]
| -2.002
| -2.434
|-
| '''[[7/1]]'''
| '''+2.322'''
| '''+2.824'''
|-
| [[18/5]]
| +2.428
| +2.953
|-
| [[13/7]]
| -2.801
| -3.407
|-
| [[31/9]]
| -3.324
| -4.043
|-
| [[30/17]]
| +3.364
| +4.092
|-
| [[29/18]]
| -3.436
| -4.179
|-
| [[23/7]]
| -3.870
| -4.707
|-
| [[15/7]]
| -3.873
| -4.710
|-
| [[25/6]]
| -3.979
| -4.839
|-
| [[22/3]]
| +4.008
| +4.875
|-
| [[26/17]]
| +4.436
| +5.395
|-
| [[17/2]]
| -4.915
| -5.977
|-
| [[22/15]]
| -5.264
| -6.402
|-
| [[23/22]]
| +5.267
| +6.405
|-
| [[17/6]]
| +5.908
| +7.186
|-
| [[29/7]]
| +5.942
| +7.227
|-
| [[22/13]]
| -6.336
| -7.706
|-
| [[22/1]]
| -6.815
| -8.288
|-
| [[25/18]]
| +6.844
| +8.324
|-
| [[7/5]]
| -6.950
| -8.453
|-
| [[23/21]]
| +6.953
| +8.456
|-
| [[22/19]]
| -7.136
| -8.678
|-
| [[17/14]]
| -7.237
| -8.802
|-
| [[31/27]]
| +7.499
| +9.120
|-
| [[27/11]]
| +7.692
| +9.355
|-
| [[29/19]]
| +7.944
| +9.661
|-
| [[21/13]]
| -8.022
| -9.756
|-
| '''[[29/1]]'''
| '''+8.265'''
| '''+10.051'''
|-
| [[21/1]]
| -8.501
| -10.339
|-
| [[29/13]]
| +8.744
| +10.634
|-
| [[21/19]]
| -8.822
| -10.729
|-
| [[19/5]]
| -8.952
| -10.887
|-
| [[22/7]]
| -9.137
| -11.113
|-
| '''[[5/1]]'''
| '''+9.272'''
| '''+11.277'''
|-
| [[23/3]]
| +9.275
| +11.280
|-
| [[18/7]]
| +9.378
| +11.406
|-
| [[13/5]]
| -9.751
| -11.860
|-
| [[29/23]]
| +9.813
| +11.934
|-
| [[29/15]]
| +9.815
| +11.937
|-
| [[25/17]]
| -9.887
| -12.025
|-
| [[29/25]]
| -10.280
| -12.503
|-
| [[13/3]]
| +10.344
| +12.581
|-
| [[23/5]]
| -10.821
| -13.160
|-
| '''[[3/1]]'''
| '''-10.823'''
| '''-13.163'''
|-
| [[19/3]]
| +11.144
| +13.553
|-
| [[19/18]]
| -11.380
| -13.840
|-
| [[18/1]]
| +11.701
| +14.230
|-
| [[18/13]]
| +12.180
| +14.813
|-
| [[7/3]]
| +13.145
| +15.987
|-
| [[23/18]]
| -13.249
| -16.113
|-
| [[6/5]]
| +13.251
| +16.116
|-
| [[31/3]]
| -14.148
| -17.206
|-
| [[17/10]]
| -14.187
| -17.255
|-
| [[29/6]]
| -14.259
| -17.342
|-
| [[26/25]]
| +14.323
| +17.420
|-
| [[25/2]]
| -14.802
| -18.002
|-
| [[22/9]]
| +14.831
| +18.038
|-
| [[29/22]]
| +15.079
| +18.340
|-
| [[31/11]]
| +15.191
| +18.475
|-
| [[22/5]]
| -16.087
| -19.566
|-
| [[25/7]]
| +16.223
| +19.730
|-
| [[31/21]]
| -16.470
| -20.030
|-
| [[18/17]]
| -16.731
| -20.349
|-
| [[29/21]]
| +16.766
| +20.390
|-
| [[25/14]]
| -17.124
| -20.826
|-
| [[21/5]]
| -17.773
| -21.616
|-
| [[31/22]]
| -18.156
| -22.081
|-
| [[25/19]]
| +18.224
| +22.164
|-
| [[11/9]]
| -18.515
| -22.519
|-
| [[25/1]]
| +18.545
| +22.554
|-
| [[25/13]]
| +19.024
| +23.137
|-
| [[29/3]]
| +19.088
| +23.215
|-
| [[17/5]]
| +19.160
| +23.302
|-
| [[25/23]]
| +20.093
| +24.437
|-
| [[5/3]]
| +20.096
| +24.440
|-
| [[23/9]]
| +20.098
| +24.443
|-
| [[29/17]]
| -20.167
| -24.528
|-
| [[7/6]]
| -20.202
| -24.569
|-
| [[13/9]]
| +21.167
| +25.744
|-
| [[9/1]]
| -21.646
| -26.326
|-
| [[19/9]]
| +21.967
| +26.716
|-
| [[19/6]]
| -22.203
| -27.003
|-
| [[6/1]]
| +22.524
| +27.393
|-
| [[13/6]]
| -23.003
| -27.976
|-
| [[31/15]]
| -23.420
| -28.483
|-
| [[31/23]]
| -23.422
| -28.486
|-
| [[30/29]]
| +23.532
| +28.619
|-
| [[26/5]]
| +23.595
| +28.697
|-
| [[9/7]]
| -23.968
| -29.151
|-
| [[23/6]]
| -24.072
| -29.276
|-
| [[5/2]]
| -24.074
| -29.279
|-
| [[31/13]]
| -24.492
| -29.787
|-
| [[29/26]]
| -24.603
| -29.923
|-
| '''[[31/1]]'''
| '''-24.971'''
| '''-30.369'''
|-
| [[29/2]]
| -25.082
| -30.505
|-
| [[31/19]]
| -25.291
| -30.759
|-
| [[25/22]]
| +25.360
| +30.843
|-
| [[27/22]]
| -25.655
| -31.201
|-
| [[17/7]]
| +26.110
| +31.755
|-
| [[14/5]]
| +26.397
| +32.104
|-
| [[25/21]]
| +27.046
| +32.893
|-
| [[31/7]]
| -27.293
| -33.194
|-
| [[29/14]]
| -27.404
| -33.329
|-
| [[17/12]]
| -27.439
| -33.371
|-
| [[19/17]]
| -28.111
| -34.189
|-
| '''[[17/1]]'''
| '''+28.432'''
| '''+34.579'''
|-
| [[17/13]]
| +28.911
| +35.162
|-
| [[11/3]]
| -29.339
| -35.682
|-
| [[25/3]]
| +29.368
| +35.718
|-
| [[30/7]]
| +29.474
| +35.846
|-
| [[29/9]]
| +29.911
| +36.378
|-
| [[23/17]]
| -29.980
| -36.462
|-
| [[17/15]]
| +29.983
| +36.465
|-
| [[26/7]]
| +30.546
| +37.150
|-
| [[9/5]]
| -30.919
| -37.604
|-
| [[27/23]]
| -30.921
| -37.607
|-
| [[7/2]]
| -31.025
| -37.732
|-
| [[30/19]]
| +31.476
| +38.281
|-
| [[21/11]]
| +31.661
| +38.506
|-
| [[30/1]]
| +31.796
| +38.671
|-
| [[27/13]]
| -31.990
| -38.907
|-
| [[30/13]]
| +32.275
| +39.253
|-
| [[27/1]]
| -32.469
| -39.489
|-
| [[26/19]]
| +32.547
| +39.584
|-
| [[27/19]]
| -32.790
| -39.879
|-
| [[26/1]]
| +32.868
| +39.974
|-
| [[19/2]]
| -33.026
| -40.167
|-
| [[31/29]]
| -33.235
| -40.421
|-
| [[30/23]]
| +33.344
| +40.554
|-
| '''[[2/1]]'''
| '''+33.347'''
| '''+40.557'''
|-
| [[13/2]]
| -33.826
| -41.139
|-
| [[31/5]]
| -34.243
| -41.647
|-
| [[29/10]]
| -34.355
| -41.782
|-
| [[26/23]]
| +34.416
| +41.857
|-
| [[26/15]]
| +34.419
| +41.860
|-
| [[27/7]]
| -34.792
| -42.314
|-
| [[23/2]]
| -34.895
| -42.439
|-
| [[15/2]]
| -34.898
| -42.442
|-
| [[22/17]]
| -35.247
| -42.867
|-
| [[19/14]]
| -35.348
| -42.991
|-
| [[14/1]]
| +35.669
| +43.381
|-
| [[14/13]]
| +36.148
| +43.963
|-
| [[31/18]]
| -36.671
| -44.600
|-
| [[21/17]]
| -36.933
| -44.918
|-
| [[23/14]]
| -37.217
| -45.264
|-
| [[15/14]]
| -37.220
| -45.267
|-
| [[25/12]]
| -37.326
| -45.395
|-
| [[17/4]]
| -38.262
| -46.534
|-
| [[15/11]]
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{{Stub}}
{{Stub}}


[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]
Retrieved from "https://en.xen.wiki/w/45zpi"