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'''45 zeta peak index''' (abbreviated '''45zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 45th peak of the [[The Riemann zeta function and tuning|Riemann zeta function]].
'''45 zeta peak index''' (abbreviated '''45zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 45th [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].


{|class="wikitable"
{{ZPI
!colspan="3"|Tuning
| zpi = 45
!colspan="3"|Strength
| steps = 14.5944346577250
!colspan="2"|Closest EDO
| step size = 82.2231232756126
!colspan="2"|Integer limit
| height = 2.097730
|-
| integral = 0.344839
!ZPI
| gap = 10.594800
!Steps per octave
| edo = 15edo
!Step size (cents)
| octave = 1233.34684913419
!Height
| consistent = 2
!Integral
| distinct = 2
!Gap
}}
!EDO
!Octave (cents)
!Consistent
!Distinct
|-
|[[45zpi]]
|14.5944346577250
|82.2231232756126
|2.097730
|0.344839
|10.594800
|[[15edo]]
|1233.34684913419
|2
|2
|}


== Theory ==
== Theory ==
45zpi is characterized by a very broad octave error, yet it maintains a quite decent zeta strength. This combination makes it an ideal candidate for no-octave tuning applications.  
45zpi is characterized by a very broad octave error, yet it maintains a quite decent zeta strength. This combination makes it an ideal candidate for no-octave tuning applications.  
No other [[Zeta peak index|zeta peak indexes]] exhibit both a larger octave error and greater zeta height than 45zpi.


45zpi supports a complex chord structure with ratios of 1:3:4:5:7:9:13:15:18:19:20:21:22:23:24:25, which further exemplifies its capabilities.
45zpi supports a complex chord structure with ratios of 1:3:4:5:7:9:13:15:18:19:20:21:22:23:24:25, which further exemplifies its capabilities.


[[File:45zpi chord 1-3-4-5-7-9-13-15-18-19-20-21-22-23-24-25.mp3|45zpi chord 1:3:4:5:7:9:13:15:18:19:20:21:22:23:24:25]]
[[File:45zpi chord 1-3-4-5-7-9-13-15-18-19-20-21-22-23-24-25.mp3|45zpi chord 1:3:4:5:7:9:13:15:18:19:20:21:22:23:24:25]]
The closest [[Zeta peak index|zeta peak indexes]] to 45zpi that exceed its strength are [[42zpi]] and [[47zpi]], though [[43zpi]] is nearly as strong as 45zpi.


=== Harmonic series ===
=== Harmonic series ===
{{Harmonics in cet|82.2231232756126|columns=15|title=Approximation of harmonics in 45zpi}}
{{Harmonics in cet|82.2231232756126|columns=15|title=Approximation of harmonics in 45zpi}}
{{Harmonics in cet|82.2231232756126|columns=16|start=16|title=Approximation of harmonics in 45zpi}}
{{Harmonics in cet|82.2231232756126|columns=16|start=16|title=Approximation of harmonics in 45zpi}}
== Intervals ==
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ style="white-space:nowrap" | Intervals in 45zpi
|-
| colspan="3" style="text-align:left;" | JI ratios are comprised of 25-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>'''⟨73 116] at every 5 steps'''</center><br>[[9/8|Whole tone]] = 13 steps<br>[[256/243|Limma]] = 4 steps<br>[[2187/2048|Apotome]] = 9 steps
|-
! Degree
! Cents
! Ratios
! Ups and downs notation
! Step
|-
| 0
| 0.000
|
| P1
| 0
|-
| 1
| 82.223
| '''[[25/24]]''', '''[[24/23]]''', '''<u>[[23/22]]'''</u>, '''<u>[[22/21]]'''</u>, '''<u>[[21/20]]'''</u>, '''<u>[[20/19]]'''</u>, '''[[19/18]]''', [[18/17]], <small>[[17/16]]</small>, <small><small>[[16/15]]</small></small>, <small><small><small>[[15/14]]</small></small></small>
| ^m2
| 5
|-
| 2
| 164.446
| <small><small><small>[[14/13]]</small></small></small>, <small>[[13/12]]</small>, [[25/23]], [[12/11]], '''[[23/21]]''', '''<u>[[11/10]]'''</u>, '''[[21/19]]''', [[10/9]], <small><small>[[19/17]]</small></small>, <small><small><small>[[9/8]]</small></small></small>
| vvvM2
| 10
|-
| 3
| 246.669
| <small><small>[[17/15]]</small></small>, <small>[[25/22]]</small>, [[8/7]], '''<u>[[23/20]]'''</u>, '''<u>[[15/13]]'''</u>, '''[[22/19]]''', [[7/6]], <small><small><small>[[20/17]]</small></small></small>
| ^^M2, vvm3
| 15
|-
| 4
| 328.892
| <small><small><small>[[13/11]]</small></small></small>, <small><small>[[19/16]]</small></small>, <small>[[25/21]]</small>, '''[[6/5]]''', '''<u>[[23/19]]'''</u>, '''[[17/14]]''', [[11/9]], <small><small>[[16/13]]</small></small>, <small><small><small>[[21/17]]</small></small></small>
| ^^^m3
| 20
|-
| 5
| 411.116
| <small>[[5/4]]</small>, '''<u>[[24/19]]'''</u>, '''<u>[[19/15]]'''</u>, '''<u>[[14/11]]'''</u>, '''[[23/18]]''', <small>[[9/7]]</small>, <small><small><small>[[22/17]]</small></small></small>
| vM3
| 25
|-
| 6
| 493.339
| <small><small><small>[[13/10]]</small></small></small>, <small><small>[[17/13]]</small></small>, <small>[[21/16]]</small>, [[25/19]], '''<u>[[4/3]]'''</u>, <small><small>[[23/17]]</small></small>, <small><small><small>[[19/14]]</small></small></small>
| P4
| 30
|-
| 7
| 575.562
| <small><small><small>[[15/11]]</small></small></small>, <small>[[11/8]]</small>, '''[[18/13]]''', '''<u>[[25/18]]'''</u>, '''[[7/5]]''', <small>[[24/17]]</small>, <small><small>[[17/12]]</small></small>
| v<sup>4</sup>A4
| 35
|-
| 8
| 657.785
| <small><small><small>[[10/7]]</small></small></small>, <small><small>[[23/16]]</small></small>, <small>[[13/9]]</small>, '''[[16/11]]''', '''<u>[[19/13]]'''</u>, '''<u>[[22/15]]'''</u>, '''[[25/17]]'''
| vvv5
| 40
|-
| 9
| 740.008
| <small><small><small>[[3/2]]</small></small></small>, '''<u>[[23/15]]'''</u>, '''<u>[[20/13]]'''</u>, '''[[17/11]]''', <small>[[14/9]]</small>, <small><small>[[25/16]]</small></small>
| ^^5, vvm6
| 45
|-
| 10
| 822.231
| <small><small><small>[[11/7]]</small></small></small>, <small>[[19/12]]</small>, '''[[8/5]]''', '''[[21/13]]''', [[13/8]], <small><small>[[18/11]]</small></small>, <small><small><small>[[23/14]]</small></small></small>
| ^^^m6
| 50
|-
| 11
| 904.454
| [[5/3]], '''<u>[[22/13]]'''</u>, [[17/10]], <small><small>[[12/7]]</small></small>
| vM6
| 55
|-
| 12
| 986.677
| <small><small><small>[[19/11]]</small></small></small>, [[7/4]], '''<u>[[23/13]]'''</u>, '''[[16/9]]''', [[25/14]], <small><small>[[9/5]]</small></small>
| m7
| 60
|-
| 13
| 1068.901
| <small><small>[[20/11]]</small></small>, [[11/6]], '''[[24/13]]''', '''<u>[[13/7]]'''</u>, [[15/8]], <small><small>[[17/9]]</small></small>
| v<sup>4</sup>M7
| 65
|-
| 14
| 1151.124
| <small><small><small>[[19/10]]</small></small></small>, <small><small>[[21/11]]</small></small>, <small>[[23/12]]</small>, [[25/13]]
| ^M7
| 70
|-
| 15
| 1233.347
| <small><small>[[2/1]]</small></small>, <small><small><small>[[25/12]]</small></small></small>
| ^^1 +1 oct, vvm2 +1 oct
| 75
|-
| 16
| 1315.570
| <small><small><small>[[23/11]]</small></small></small>, <small><small>[[21/10]]</small></small>, <small>[[19/9]]</small>, '''[[17/8]]''', '''<u>[[15/7]]'''</u>, <small>[[13/6]]</small>, <small><small><small>[[24/11]]</small></small></small>
| ^^^m2 +1 oct
| 80
|-
| 17
| 1397.793
| <small><small>[[11/5]]</small></small>, [[20/9]], '''<u>[[9/4]]'''</u>, <small>[[25/11]]</small>, <small><small>[[16/7]]</small></small>
| vM2 +1 oct
| 85
|-
| 18
| 1480.016
| <small><small><small>[[23/10]]</small></small></small>, '''[[7/3]]''', [[19/8]], <small><small><small>[[12/5]]</small></small></small>
| m3 +1 oct
| 90
|-
| 19
| 1562.239
| <small>[[17/7]]</small>, [[22/9]], <small>[[5/2]]</small>
| v<sup>4</sup>M3 +1 oct
| 95
|-
| 20
| 1644.462
| [[23/9]], '''[[18/7]]''', '''[[13/5]]''', <small>[[21/8]]</small>
| ^M3 +1 oct
| 100
|-
| 21
| 1726.686
| <small><small>[[8/3]]</small></small>, '''<u>[[19/7]]'''</u>, <small>[[11/4]]</small>
| ^^4 +1 oct
| 105
|-
| 22
| 1808.909
| <small><small><small>[[25/9]]</small></small></small>, <small>[[14/5]]</small>, '''<u>[[17/6]]'''</u>, '''[[20/7]]''', [[23/8]]
| ^^^d5 +1 oct
| 110
|-
| 23
| 1891.132
| '''[[3/1]]'''
| v5 +1 oct
| 115
|-
| 24
| 1973.355
| '''<u>[[25/8]]'''</u>, '''[[22/7]]''', <small>[[19/6]]</small>, <small><small><small>[[16/5]]</small></small></small>
| m6 +1 oct
| 120
|-
| 25
| 2055.578
| [[13/4]], '''<u>[[23/7]]'''</u>, <small><small>[[10/3]]</small></small>
| v<sup>4</sup>M6 +1 oct
| 125
|-
| 26
| 2137.801
| [[17/5]], '''<u>[[24/7]]'''</u>, <small><small>[[7/2]]</small></small>
| ^M6 +1 oct
| 130
|-
| 27
| 2220.024
| [[25/7]], '''<u>[[18/5]]'''</u>, <small><small>[[11/3]]</small></small>
| ^^m7 +1 oct
| 135
|-
| 28
| 2302.247
| [[15/4]], '''[[19/5]]''', <small>[[23/6]]</small>
| vvM7 +1 oct
| 140
|-
| 29
| 2384.471
| [[4/1]]
| v1 +2 oct
| 145
|-
| 30
| 2466.694
| '''<u>[[25/6]]'''</u>, [[21/5]], <small><small><small>[[17/4]]</small></small></small>
| m2 +2 oct
| 150
|-
| 31
| 2548.917
| '''[[13/3]]''', [[22/5]]
| v<sup>4</sup>M2 +2 oct
| 155
|-
| 32
| 2631.140
| <small>[[9/2]]</small>, '''[[23/5]]''', <small><small><small>[[14/3]]</small></small></small>
| ^M2 +2 oct
| 160
|-
| 33
| 2713.363
| [[19/4]], '''<u>[[24/5]]'''</u>
| ^^m3 +2 oct
| 165
|-
| 34
| 2795.586
| '''[[5/1]]'''
| vvM3 +2 oct
| 170
|-
| 35
| 2877.809
| '''[[21/4]]''', [[16/3]]
| v4 +2 oct
| 175
|-
| 36
| 2960.032
| '''[[11/2]]'''
| ^<sup>4</sup>4 +2 oct
| 180
|-
| 37
| 3042.256
| <small><small><small>[[17/3]]</small></small></small>, [[23/4]]
| v<sup>4</sup>5 +2 oct
| 185
|-
| 38
| 3124.479
| <small>[[6/1]]</small>
| ^5 +2 oct
| 190
|-
| 39
| 3206.702
| <small><small>[[25/4]]</small></small>, '''[[19/3]]''', <small><small>[[13/2]]</small></small>
| ^^m6 +2 oct
| 195
|-
| 40
| 3288.925
| '''<u>[[20/3]]'''</u>
| vvM6 +2 oct
| 200
|-
| 41
| 3371.148
| '''<u>[[7/1]]'''</u>
| vm7 +2 oct
| 205
|-
| 42
| 3453.371
| '''<u>[[22/3]]'''</u>, <small><small><small>[[15/2]]</small></small></small>
| ^<sup>4</sup>m7 +2 oct
| 210
|-
| 43
| 3535.594
| '''[[23/3]]'''
| M7 +2 oct
| 215
|-
| 44
| 3617.817
| [[8/1]]
| ^1 +3 oct
| 220
|-
| 45
| 3700.041
| <small><small>[[25/3]]</small></small>, '''<u>[[17/2]]'''</u>
| ^^m2 +3 oct
| 225
|-
| 46
| 3782.264
| <small>[[9/1]]</small>
| vvM2 +3 oct
| 230
|-
| 47
| 3864.487
| <small><small>[[19/2]]</small></small>
| vm3 +3 oct
| 235
|-
| 48
| 3946.710
| <small><small><small>[[10/1]]</small></small></small>
| ^<sup>4</sup>m3 +3 oct
| 240
|-
| 49
| 4028.933
|
| M3 +3 oct
| 245
|-
| 50
| 4111.156
| <small><small><small>[[21/2]]</small></small></small>, <small><small><small>[[11/1]]</small></small></small>
| ^4 +3 oct
| 250
|-
| 51
| 4193.379
| <small><small><small>[[23/2]]</small></small></small>
| vvvA4 +3 oct
| 255
|-
| 52
| 4275.602
| <small>[[12/1]]</small>
| vv5 +3 oct
| 260
|-
| 53
| 4357.826
| [[25/2]]
| vm6 +3 oct
| 265
|-
| 54
| 4440.049
| '''<u>[[13/1]]'''</u>
| ^<sup>4</sup>m6 +3 oct
| 270
|-
| 55
| 4522.272
|
| M6 +3 oct
| 275
|-
| 56
| 4604.495
| <small><small><small>[[14/1]]</small></small></small>
| ^m7 +3 oct
| 280
|-
| 57
| 4686.718
| '''<u>[[15/1]]'''</u>
| vvvM7 +3 oct
| 285
|-
| 58
| 4768.941
| <small><small>[[16/1]]</small></small>
| ^^M7 +3 oct, vv1 +4 oct
| 290
|-
| 59
| 4851.164
|
| vm2 +4 oct
| 295
|-
| 60
| 4933.387
| <small><small>[[17/1]]</small></small>
| ^<sup>4</sup>m2 +4 oct
| 300
|-
| 61
| 5015.611
| '''[[18/1]]'''
| M2 +4 oct
| 305
|-
| 62
| 5097.834
| '''<u>[[19/1]]'''</u>
| ^m3 +4 oct
| 310
|-
| 63
| 5180.057
| '''<u>[[20/1]]'''</u>
| vvvM3 +4 oct
| 315
|-
| 64
| 5262.280
| '''[[21/1]]'''
| ^^M3 +4 oct, vv4 +4 oct
| 320
|-
| 65
| 5344.503
| '''<u>[[22/1]]'''</u>
| ^^^4 +4 oct
| 325
|-
| 66
| 5426.726
| '''<u>[[23/1]]'''</u>
| ^<sup>4</sup>d5 +4 oct
| 330
|-
| 67
| 5508.949
| '''[[24/1]]'''
| P5 +4 oct
| 335
|-
| 68
| 5591.172
| [[25/1]]
| ^m6 +4 oct
| 340
|}
== Approximation to JI ==
=== Interval mappings ===
The following tables show how 25-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"
|+ style="white-space: nowrap;" | 25-integer-limit intervals in 45zpi (by direct approximation)
|-
! 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'''
|- style="background-color: #cccccc;"
| ''[[11/10]]''
| ''-0.558''
| ''-0.679''
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''+0.728''
| ''+0.885''
|-
| [[19/13]]
| +0.800
| +0.973
|-
| [[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
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''-2.244''
| ''-2.729''
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''-2.278''
| ''-2.771''
|-
| '''[[7/1]]'''
| '''+2.322'''
| '''+2.824'''
|-
| [[18/5]]
| +2.428
| +2.953
|-
| [[13/7]]
| -2.801
| -3.407
|-
| [[23/7]]
| -3.870
| -4.707
|-
| [[15/7]]
| -3.873
| -4.710
|-
| [[25/6]]
| -3.979
| -4.839
|-
| [[22/3]]
| +4.008
| +4.875
|- style="background-color: #cccccc;"
| ''[[20/3]]''
| ''+4.566''
| ''+5.553''
|- style="background-color: #cccccc;"
| ''[[24/7]]''
| ''+4.672''
| ''+5.682''
|- style="background-color: #cccccc;"
| ''[[4/3]]''
| ''-4.706''
| ''-5.724''
|- style="background-color: #cccccc;"
| ''[[23/20]]''
| ''+4.709''
| ''+5.727''
|-
| [[17/2]]
| -4.915
| -5.977
|-
| [[22/15]]
| -5.264
| -6.402
|-
| [[23/22]]
| +5.267
| +6.405
|- style="background-color: #cccccc;"
| ''[[20/13]]''
| ''-5.778''
| ''-7.027''
|-
| [[17/6]]
| +5.908
| +7.186
|- style="background-color: #cccccc;"
| ''[[9/4]]''
| ''-6.117''
| ''-7.439''
|- style="background-color: #cccccc;"
| ''[[20/1]]''
| ''-6.257''
| ''-7.610''
|-
| [[22/13]]
| -6.336
| -7.706
|- style="background-color: #cccccc;"
| ''[[14/11]]''
| ''-6.392''
| ''-7.774''
|- style="background-color: #cccccc;"
| ''[[20/19]]''
| ''-6.578''
| ''-8.000''
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''+6.674''
| ''+8.116''
|-
| [[22/1]]
| -6.815
| -8.288
|-
| [[25/18]]
| +6.844
| +8.324
|-
| [[7/5]]
| -6.950
| -8.453
|-
| [[23/21]]
| +6.953
| +8.456
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''+6.994''
| ''+8.506''
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''+7.028''
| ''+8.548''
|-
| [[22/19]]
| -7.136
| -8.678
|-
| [[17/14]]
| -7.237
| -8.802
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''+7.473''
| ''+9.089''
|-
| [[21/13]]
| -8.022
| -9.756
|-
| [[21/1]]
| -8.501
| -10.339
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''+8.542''
| ''+10.389''
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''+8.545''
| ''+10.392''
|- style="background-color: #cccccc;"
| ''[[20/7]]''
| ''-8.579''
| ''-10.434''
|- style="background-color: #cccccc;"
| ''[[11/2]]''
| ''+8.714''
| ''+10.599''
|-
| [[21/19]]
| -8.822
| -10.729
|-
| [[19/5]]
| -8.952
| -10.887
|- style="background-color: #cccccc;"
| ''[[16/11]]''
| ''+9.103''
| ''+11.071''
|-
| [[22/7]]
| -9.137
| -11.113
|-
| '''[[5/1]]'''
| '''+9.272'''
| '''+11.277'''
|-
| [[23/3]]
| +9.275
| +11.280
|-
| [[18/7]]
| +9.378
| +11.406
|- style="background-color: #cccccc;"
| ''[[16/9]]''
| ''-9.413''
| ''-11.448''
|-
| [[13/5]]
| -9.751
| -11.860
|-
| [[25/17]]
| -9.887
| -12.025
|-
| [[13/3]]
| +10.344
| +12.581
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''+10.615''
| ''+12.909''
|-
| [[23/5]]
| -10.821
| -13.160
|-
| '''[[3/1]]'''
| '''-10.823'''
| '''-13.163'''
|-
| [[19/3]]
| +11.144
| +13.553
|-
| [[19/18]]
| -11.380
| -13.840
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''+11.551''
| ''+14.048''
|-
| [[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
|- style="background-color: #cccccc;"
| ''[[17/11]]''
| ''-13.629''
| ''-16.576''
|- style="background-color: #cccccc;"
| ''[[12/11]]''
| ''+13.809''
| ''+16.795''
|- style="background-color: #cccccc;"
| ''[[15/4]]''
| ''+13.979''
| ''+17.001''
|- style="background-color: #cccccc;"
| ''[[23/4]]''
| ''+13.981''
| ''+17.004''
|-
| [[17/10]]
| -14.187
| -17.255
|-
| [[25/2]]
| -14.802
| -18.002
|-
| [[22/9]]
| +14.831
| +18.038
|- style="background-color: #cccccc;"
| ''[[13/4]]''
| ''+15.050''
| ''+18.304''
|- style="background-color: #cccccc;"
| ''[[20/9]]''
| ''+15.389''
| ''+18.717''
|- style="background-color: #cccccc;"
| ''[[8/7]]''
| ''+15.495''
| ''+18.845''
|- style="background-color: #cccccc;"
| ''[[4/1]]''
| ''-15.529''
| ''-18.887''
|- style="background-color: #cccccc;"
| ''[[19/4]]''
| ''+15.850''
| ''+19.277''
|-
| [[22/5]]
| -16.087
| -19.566
|-
| [[25/7]]
| +16.223
| +19.730
|-
| [[18/17]]
| -16.731
| -20.349
|-
| [[25/14]]
| -17.124
| -20.826
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''-17.497''
| ''-21.280''
|-
| [[21/5]]
| -17.773
| -21.616
|- style="background-color: #cccccc;"
| ''[[8/1]]''
| ''+17.817''
| ''+21.670''
|- style="background-color: #cccccc;"
| ''[[7/4]]''
| ''+17.852''
| ''+21.711''
|- style="background-color: #cccccc;"
| ''[[10/9]]''
| ''-17.957''
| ''-21.840''
|-
| [[25/19]]
| +18.224
| +22.164
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''-18.296''
| ''-22.252''
|-
| [[11/9]]
| -18.515
| -22.519
|-
| [[25/1]]
| +18.545
| +22.554
|-
| [[25/13]]
| +19.024
| +23.137
|-
| [[17/5]]
| +19.160
| +23.302
|- style="background-color: #cccccc;"
| ''[[23/8]]''
| ''-19.366''
| ''-23.553''
|- style="background-color: #cccccc;"
| ''[[15/8]]''
| ''-19.368''
| ''-23.556''
|- style="background-color: #cccccc;"
| ''[[11/6]]''
| ''+19.538''
| ''+23.762''
|-
| [[25/23]]
| +20.093
| +24.437
|-
| [[5/3]]
| +20.096
| +24.440
|-
| [[23/9]]
| +20.098
| +24.443
|-
| [[7/6]]
| -20.202
| -24.569
|- style="background-color: #cccccc;"
| ''[[16/3]]''
| ''-20.236''
| ''-24.611''
|-
| [[13/9]]
| +21.167
| +25.744
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''-21.438''
| ''-26.073''
|-
| [[9/1]]
| -21.646
| -26.326
|-
| [[19/9]]
| +21.967
| +26.716
|-
| [[19/6]]
| -22.203
| -27.003
|-
| [[6/1]]
| +22.524
| +27.393
|- style="background-color: #cccccc;"
| ''[[21/16]]''
| ''+22.558''
| ''+27.435''
|- style="background-color: #cccccc;"
| ''[[17/16]]''
| ''-22.732''
| ''-27.647''
|-
| [[13/6]]
| -23.003
| -27.976
|- style="background-color: #cccccc;"
| ''[[25/11]]''
| ''-23.516''
| ''-28.601''
|-
| [[9/7]]
| -23.968
| -29.151
|-
| [[23/6]]
| -24.072
| -29.276
|-
| [[5/2]]
| -24.074
| -29.279
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''+24.244''
| ''+29.486''
|- style="background-color: #cccccc;"
| ''[[11/4]]''
| ''-24.632''
| ''-29.958''
|- style="background-color: #cccccc;"
| ''[[5/4]]''
| ''+24.802''
| ''+30.164''
|- style="background-color: #cccccc;"
| ''[[23/12]]''
| ''+24.804''
| ''+30.167''
|- style="background-color: #cccccc;"
| ''[[14/9]]''
| ''-24.908''
| ''-30.293''
|-
| [[25/22]]
| +25.360
| +30.843
|- style="background-color: #cccccc;"
| ''[[13/12]]''
| ''+25.874''
| ''+31.468''
|-
| [[17/7]]
| +26.110
| +31.755
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''-26.318''
| ''-32.009''
|- style="background-color: #cccccc;"
| ''[[12/1]]''
| ''-26.353''
| ''-32.050''
|-
| [[14/5]]
| +26.397
| +32.104
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''+26.673''
| ''+32.440''
|-
| [[25/21]]
| +27.046
| +32.893
|- style="background-color: #cccccc;"
| ''[[9/2]]''
| ''+27.230''
| ''+33.117''
|-
| [[17/12]]
| -27.439
| -33.371
|-
| [[19/17]]
| -28.111
| -34.189
|-
| '''[[17/1]]'''
| '''+28.432'''
| '''+34.579'''
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''+28.641''
| ''+34.833''
|- style="background-color: #cccccc;"
| ''[[12/7]]''
| ''-28.675''
| ''-34.874''
|- style="background-color: #cccccc;"
| ''[[10/3]]''
| ''-28.781''
| ''-35.003''
|-
| [[17/13]]
| +28.911
| +35.162
|-
| [[11/3]]
| -29.339
| -35.682
|-
| [[25/3]]
| +29.368
| +35.718
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''-29.508''
| ''-35.888''
|- style="background-color: #cccccc;"
| ''[[23/16]]''
| ''+29.511''
| ''+35.891''
|-
| [[23/17]]
| -29.980
| -36.462
|-
| [[17/15]]
| +29.983
| +36.465
|- style="background-color: #cccccc;"
| ''[[18/11]]''
| ''-30.361''
| ''-36.925''
|- style="background-color: #cccccc;"
| ''[[16/13]]''
| ''-30.580''
| ''-37.191''
|-
| [[9/5]]
| -30.919
| -37.604
|-
| [[7/2]]
| -31.025
| -37.732
|- style="background-color: #cccccc;"
| ''[[16/1]]''
| ''-31.059''
| ''-37.774''
|- style="background-color: #cccccc;"
| ''[[21/10]]''
| ''+31.103''
| ''+37.827''
|- style="background-color: #cccccc;"
| ''[[19/16]]''
| ''+31.379''
| ''+38.164''
|-
| [[21/11]]
| +31.661
| +38.506
|- style="background-color: #cccccc;"
| ''[[17/9]]''
| ''-32.145''
| ''-39.095''
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''-32.619''
| ''-39.672''
|- style="background-color: #cccccc;"
| ''[[11/5]]''
| ''+32.789''
| ''+39.878''
|-
| [[19/2]]
| -33.026
| -40.167
|-
| '''[[2/1]]'''
| '''+33.347'''
| '''+40.557'''
|- style="background-color: #cccccc;"
| ''[[16/7]]''
| ''-33.381''
| ''-40.598''
|-
| [[13/2]]
| -33.826
| -41.139
|- style="background-color: #cccccc;"
| ''[[20/11]]''
| ''+33.905''
| ''+41.235''
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''+34.074''
| ''+41.441''
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''-34.689''
| ''-42.189''
|-
| [[23/2]]
| -34.895
| -42.439
|-
| [[15/2]]
| -34.898
| -42.442
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''-35.067''
| ''-42.649''
|-
| [[22/17]]
| -35.247
| -42.867
|-
| [[19/14]]
| -35.348
| -42.991
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''-35.625''
| ''-43.327''
|-
| [[14/1]]
| +35.669
| +43.381
|- style="background-color: #cccccc;"
| ''[[14/3]]''
| ''-35.731''
| ''-43.456''
|-
| [[14/13]]
| +36.148
| +43.963
|-
| [[21/17]]
| -36.933
| -44.918
|-
| [[23/14]]
| -37.217
| -45.264
|-
| [[15/14]]
| -37.220
| -45.267
|-
| [[25/12]]
| -37.326
| -45.395
|- style="background-color: #cccccc;"
| ''[[3/2]]''
| ''+38.053''
| ''+46.280''
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''+38.056''
| ''+46.283''
|-
| [[17/4]]
| -38.262
| -46.534
|-
| [[15/11]]
| +38.611
| +46.959
|-
| [[23/11]]
| +38.614
| +46.962
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''+39.125''
| ''+47.584''
|-
| [[17/3]]
| +39.255
| +47.742
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''-39.464''
| ''-47.996''
|- style="background-color: #cccccc;"
| ''[[10/1]]''
| ''-39.604''
| ''-48.166''
|-
| [[13/11]]
| +39.683
| +48.262
|- style="background-color: #cccccc;"
| ''[[11/7]]''
| ''+39.739''
| ''+48.331''
|- style="background-color: #cccccc;"
| ''[[19/10]]''
| ''+39.924''
| ''+48.556''
|-
| '''[[11/1]]'''
| '''-40.162'''
| '''-48.845'''
|-
| [[25/9]]
| +40.191
| +48.881
|-
| [[10/7]]
| +40.297
| +49.010
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''-40.331''
| ''-49.051''
|- style="background-color: #cccccc;"
| ''[[21/2]]''
| ''+40.375''
| ''+49.105''
|-
| [[19/11]]
| +40.482
| +49.235
|}
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 25-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
|-
| [[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
|-
| [[23/7]]
| -3.870
| -4.707
|-
| [[15/7]]
| -3.873
| -4.710
|-
| [[25/6]]
| -3.979
| -4.839
|-
| [[22/3]]
| +4.008
| +4.875
|-
| [[17/2]]
| -4.915
| -5.977
|-
| [[22/15]]
| -5.264
| -6.402
|-
| [[23/22]]
| +5.267
| +6.405
|-
| [[17/6]]
| +5.908
| +7.186
|-
| [[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
|-
| [[21/13]]
| -8.022
| -9.756
|-
| [[21/1]]
| -8.501
| -10.339
|-
| [[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
|-
| [[25/17]]
| -9.887
| -12.025
|-
| [[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
|-
| [[17/10]]
| -14.187
| -17.255
|-
| [[25/2]]
| -14.802
| -18.002
|-
| [[22/9]]
| +14.831
| +18.038
|-
| [[22/5]]
| -16.087
| -19.566
|-
| [[25/7]]
| +16.223
| +19.730
|-
| [[18/17]]
| -16.731
| -20.349
|-
| [[25/14]]
| -17.124
| -20.826
|-
| [[21/5]]
| -17.773
| -21.616
|-
| [[25/19]]
| +18.224
| +22.164
|-
| [[11/9]]
| -18.515
| -22.519
|-
| [[25/1]]
| +18.545
| +22.554
|-
| [[25/13]]
| +19.024
| +23.137
|-
| [[17/5]]
| +19.160
| +23.302
|-
| [[25/23]]
| +20.093
| +24.437
|-
| [[5/3]]
| +20.096
| +24.440
|-
| [[23/9]]
| +20.098
| +24.443
|-
| [[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
|-
| [[9/7]]
| -23.968
| -29.151
|-
| [[23/6]]
| -24.072
| -29.276
|-
| [[5/2]]
| -24.074
| -29.279
|-
| [[25/22]]
| +25.360
| +30.843
|-
| [[17/7]]
| +26.110
| +31.755
|-
| [[14/5]]
| +26.397
| +32.104
|-
| [[25/21]]
| +27.046
| +32.893
|-
| [[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
|-
| [[23/17]]
| -29.980
| -36.462
|-
| [[17/15]]
| +29.983
| +36.465
|-
| [[9/5]]
| -30.919
| -37.604
|-
| [[7/2]]
| -31.025
| -37.732
|-
| [[21/11]]
| +31.661
| +38.506
|-
| [[19/2]]
| -33.026
| -40.167
|-
| '''[[2/1]]'''
| '''+33.347'''
| '''+40.557'''
|-
| [[13/2]]
| -33.826
| -41.139
|-
| [[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
|-
| [[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]]
| +38.611
| +46.959
|-
| [[23/11]]
| +38.614
| +46.962
|-
| [[17/3]]
| +39.255
| +47.742
|-
| [[13/11]]
| +39.683
| +48.262
|-
| '''[[11/1]]'''
| '''-40.162'''
| '''-48.845'''
|-
| [[25/9]]
| +40.191
| +48.881
|-
| [[10/7]]
| +40.297
| +49.010
|-
| [[19/11]]
| +40.482
| +49.235
|- style="background-color: #cccccc;"
| ''[[21/2]]''
| ''-41.848''
| ''-50.895''
|- style="background-color: #cccccc;"
| ''[[19/10]]''
| ''-42.299''
| ''-51.444''
|- style="background-color: #cccccc;"
| ''[[11/7]]''
| ''-42.484''
| ''-51.669''
|- style="background-color: #cccccc;"
| ''[[10/1]]''
| ''+42.619''
| ''+51.834''
|- style="background-color: #cccccc;"
| ''[[13/10]]''
| ''-43.098''
| ''-52.416''
|- style="background-color: #cccccc;"
| ''[[23/10]]''
| ''-44.168''
| ''-53.717''
|- style="background-color: #cccccc;"
| ''[[3/2]]''
| ''-44.170''
| ''-53.720''
|- style="background-color: #cccccc;"
| ''[[14/3]]''
| ''+46.492''
| ''+56.544''
|- style="background-color: #cccccc;"
| ''[[12/5]]''
| ''+46.598''
| ''+56.673''
|- style="background-color: #cccccc;"
| ''[[20/17]]''
| ''+47.534''
| ''+57.811''
|- style="background-color: #cccccc;"
| ''[[25/4]]''
| ''-48.149''
| ''-58.559''
|- style="background-color: #cccccc;"
| ''[[11/5]]''
| ''-49.434''
| ''-60.122''
|- style="background-color: #cccccc;"
| ''[[17/9]]''
| ''+50.078''
| ''+60.905''
|- style="background-color: #cccccc;"
| ''[[21/10]]''
| ''-51.120''
| ''-62.173''
|- style="background-color: #cccccc;"
| ''[[18/11]]''
| ''+51.862''
| ''+63.075''
|- style="background-color: #cccccc;"
| ''[[10/3]]''
| ''+53.442''
| ''+64.997''
|- style="background-color: #cccccc;"
| ''[[12/7]]''
| ''+53.548''
| ''+65.126''
|- style="background-color: #cccccc;"
| ''[[9/2]]''
| ''-54.993''
| ''-66.883''
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''-55.550''
| ''-67.560''
|- style="background-color: #cccccc;"
| ''[[12/1]]''
| ''+55.871''
| ''+67.950''
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{{Stub}}
[[Category:Zeta peak indexes]]
Retrieved from "https://en.xen.wiki/w/45zpi"