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Line 1: Line 1:
'''186 zeta peak index''' (abbreviated '''186zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 186st [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].
'''186 zeta peak index''' (abbreviated '''186zpi'''), is the [[Equal-step tuning|equal-step]] [[tuning system]] obtained from the 186st [[Zeta peak index|peak]] of the [[The Riemann zeta function and tuning|Riemann zeta function]].


{| class="wikitable"
{{ZPI
! colspan="3" | Tuning
| zpi = 186
! colspan="3" | Strength
| steps = 41.3438354846780
! colspan="2" | Closest EDO
| step size = 29.0248832971658
! colspan="2" | Integer limit
| height = 1.876590
|-
| integral = 0.241233
! ZPI
| gap = 11.567493
! Steps per octave
| edo = 41edo
! Step size (cents)
| octave = 1190.02021518380
! Height
| consistent = 2
! Integral
| distinct = 2
! Gap
}}
! EDO
! Octave (cents)
! Consistent
! Distinct
|-
| [[186zpi]]
| 41.3438354846780
| 29.0248832971658
| 1.876590
| 0.241233
| 11.567493
| [[41edo]]
| 1190.02021518380
| 2
| 2
|}


== Theory ==
== Theory ==
=== Record on the Riemann zeta function with primes 2 and 3 removed ===
=== Record on the Riemann zeta function with primes 2 and 3 removed ===
'''186zpi''' sets a height record on the Riemann zeta function with primes 2 and 3 removed. The previous record is [[125zpi]] and the next one is [[565zpi]]. It is important to highlight that the optimal equal tunings obtained by excluding the prime numbers 2 and 3 from the Riemann zeta function differs very slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.
'''186zpi''' sets a height record on the Riemann zeta function with primes 2 and 3 removed. The previous record is [[125zpi]] and the next one is [[565zpi]]. It is important to highlight that the optimal equal tunings obtained by excluding the prime numbers 2 and 3 from the Riemann zeta function differs very slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.


{| class="wikitable"
{| class="wikitable"
! colspan="6" |Unmodified Riemann zeta function
|-
! colspan="5" |Riemann zeta function with primes 2 and 3 removed
! colspan="6" | Unmodified Riemann zeta function
! colspan="5" | Riemann zeta function with primes 2 and 3 removed
|-
|-
! colspan="3" | Tuning
! colspan="3" | Tuning
Line 61: Line 45:
| 30.6006474885974
| 30.6006474885974
| 39.2148564976330
| 39.2148564976330
|1.468164
| 1.468164
| [[31edo]]
| [[31edo]]
| 1215.66055142662
| 1215.66055142662
| 30.5974484926723
| 30.5974484926723
| 39.2189564527704
| 39.2189564527704
|3.769318
| 3.769318
| [[31edo]]
| [[31edo]]
| 1215.78765003588
| 1215.78765003588
|-
|-
|[[186zpi]]
| [[186zpi]]
|41.3438354846780
| 41.3438354846780
|29.0248832971658
| 29.0248832971658
|1.876590
| 1.876590
|[[41edo]]
| [[41edo]]
|1190.02021518380
| 1190.02021518380
|41.3477989230936
| 41.3477989230936
|29.0221010852836
| 29.0221010852836
|4.469823
| 4.469823
|[[41edo]]
| [[41edo]]
|1189.90614449663
| 1189.90614449663
|-
|-
|[[565zpi]]
| [[565zpi]]
|98.6209462564991
| 98.6209462564991
|12.1678005084130
| 12.1678005084130
|2.305330
| 2.305330
|[[99edo]]
| [[99edo]]
|1204.61225033289
| 1204.61225033289
|98.6257548378926
| 98.6257548378926
|12.1672072570942
| 12.1672072570942
|4.883729
| 4.883729
|[[99edo]]
| [[99edo]]
|1204.55351845233
| 1204.55351845233
|}
|}


Line 107: Line 91:
It is important to note that [[124edo]] provides two possible [[3/2|fifths (3/2)]]. The closest one, from the [[val]] <124 197] (i.e. the [[patent val]]), is the [[3/2|fifth]] mapped to 73 steps of [[124edo]] with a [[relative error]] of +46.465%. The second closest, from the [[val]] <124 196] (i.e. the [[val]] 124b), is mapped to 72 steps of [[124edo]] with a [[relative error]] of -53.535%. This second [[3/2|fifth]], which appears in [[124ed8]], also corresponds to the [[3/2|fifth]] of [[31edo]]. Therefore, we choose to use the [[ups and downs notation]] of the 124b temperament, denoted as <124 196].
It is important to note that [[124edo]] provides two possible [[3/2|fifths (3/2)]]. The closest one, from the [[val]] <124 197] (i.e. the [[patent val]]), is the [[3/2|fifth]] mapped to 73 steps of [[124edo]] with a [[relative error]] of +46.465%. The second closest, from the [[val]] <124 196] (i.e. the [[val]] 124b), is mapped to 72 steps of [[124edo]] with a [[relative error]] of -53.535%. This second [[3/2|fifth]], which appears in [[124ed8]], also corresponds to the [[3/2|fifth]] of [[31edo]]. Therefore, we choose to use the [[ups and downs notation]] of the 124b temperament, denoted as <124 196].


{| class="wikitable center-all left-1 right-2 left-3 center-4 left-5"
{| class="wikitable center-1 right-2 left-3 center-4 center-5"
|+ style="font-size: 105%; white-space: nowrap;" | Intervals in 186zpi
|-
|-
| colspan="3" | 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 116: Line 101:
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small>Small Small:</small></small> relative error < 41.667 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
* <small><small><small>Small Small Small:</small></small></small> relative error < 50 %
| colspan="2" | <center>'''124b at every 3 steps'''</center><br>[[9/8|Whole tone]] = 20 steps<br>[[256/243|Limma]] = 12 steps<br>[[2187/2048|Apotome]] = 8 steps
| colspan="2" style="text-align:right;" | <center>'''⟨124 196] at every 3 steps'''</center><br>[[9/8|Whole tone]] = 20 steps<br>[[256/243|Limma]] = 12 steps<br>[[2187/2048|Apotome]] = 8 steps
|-
|-
! Degree
! Degree
! Cents
! Cents
! Ratios
! Ratios
! Ups and Downs Notation
! Ups and downs notation
! Step
! Step
|-
|-
Line 367: Line 352:
| 1160.995
| 1160.995
|  
|  
| v<sup>4</sup>1 +1oct
| v<sup>4</sup>1 +1 oct
| 120
| 120
|-
|-
Line 373: Line 358:
| 1190.020
| 1190.020
| <small><small>[[2/1]]</small></small>
| <small><small>[[2/1]]</small></small>
| v1 +1oct
| v1 +1 oct
| 123
| 123
|-
|-
Line 379: Line 364:
| 1219.045
| 1219.045
|  
|  
| ^^1 +1oct
| ^^1 +1 oct
| 126
| 126
|-
|-
Line 385: Line 370:
| 1248.070
| 1248.070
| <small>[[31/15]]</small>, <small><small><small>[[29/14]]</small></small></small>
| <small>[[31/15]]</small>, <small><small><small>[[29/14]]</small></small></small>
| vvvA1 +1oct
| vvvA1 +1 oct
| 129
| 129
|-
|-
Line 391: Line 376:
| 1277.095
| 1277.095
| <small><small>[[27/13]]</small></small>, [[25/12]], '''<u>[[23/11]]'''</u>, <small>[[21/10]]</small>
| <small><small>[[27/13]]</small></small>, [[25/12]], '''<u>[[23/11]]'''</u>, <small>[[21/10]]</small>
| v<sup>4</sup>m2 +1oct
| v<sup>4</sup>m2 +1 oct
| 132
| 132
|-
|-
Line 397: Line 382:
| 1306.120
| 1306.120
| <small><small><small>[[19/9]]</small></small></small>, '''<u>[[17/8]]'''</u>, [[32/15]], <small><small><small>[[15/7]]</small></small></small>
| <small><small><small>[[19/9]]</small></small></small>, '''<u>[[17/8]]'''</u>, [[32/15]], <small><small><small>[[15/7]]</small></small></small>
| vm2 +1oct
| vm2 +1 oct
| 135
| 135
|-
|-
Line 403: Line 388:
| 1335.145
| 1335.145
| [[28/13]], '''[[13/6]]'''
| [[28/13]], '''[[13/6]]'''
| ^^m2 +1oct
| ^^m2 +1 oct
| 138
| 138
|-
|-
Line 409: Line 394:
| 1364.170
| 1364.170
| <small><small><small>[[24/11]]</small></small></small>, '''<u>[[11/5]]'''</u>, <small><small>[[31/14]]</small></small>
| <small><small><small>[[24/11]]</small></small></small>, '''<u>[[11/5]]'''</u>, <small><small>[[31/14]]</small></small>
| vvvM2 +1oct
| vvvM2 +1 oct
| 141
| 141
|-
|-
Line 415: Line 400:
| 1393.194
| 1393.194
| <small><small>[[20/9]]</small></small>, '''[[29/13]]''', <small><small>[[9/4]]</small></small>
| <small><small>[[20/9]]</small></small>, '''[[29/13]]''', <small><small>[[9/4]]</small></small>
| M2 +1oct
| M2 +1 oct
| 144
| 144
|-
|-
Line 421: Line 406:
| 1422.219
| 1422.219
| '''<u>[[25/11]]'''</u>, <small>[[16/7]]</small>
| '''<u>[[25/11]]'''</u>, <small>[[16/7]]</small>
| ^^^M2 +1oct
| ^^^M2 +1 oct
| 147
| 147
|-
|-
Line 427: Line 412:
| 1451.244
| 1451.244
| <small>[[23/10]]</small>, '''[[30/13]]'''
| <small>[[23/10]]</small>, '''[[30/13]]'''
| vvA2 +1oct, ^^d3 +1oct
| vvA2 +1 oct, ^^d3 +1 oct
| 150
| 150
|-
|-
Line 433: Line 418:
| 1480.269
| 1480.269
| <small><small><small>[[7/3]]</small></small></small>, <small>[[26/11]]</small>
| <small><small><small>[[7/3]]</small></small></small>, <small>[[26/11]]</small>
| vvvm3 +1oct
| vvvm3 +1 oct
| 153
| 153
|-
|-
Line 439: Line 424:
| 1509.294
| 1509.294
| <small><small>[[19/8]]</small></small>, '''[[31/13]]''', [[12/5]]
| <small><small>[[19/8]]</small></small>, '''[[31/13]]''', [[12/5]]
| m3 +1oct
| m3 +1 oct
| 156
| 156
|-
|-
Line 445: Line 430:
| 1538.319
| 1538.319
| <small><small>[[29/12]]</small></small>, '''<u>[[17/7]]'''</u>, <small>[[22/9]]</small>
| <small><small>[[29/12]]</small></small>, '''<u>[[17/7]]'''</u>, <small>[[22/9]]</small>
| ^^^m3 +1oct
| ^^^m3 +1 oct
| 159
| 159
|-
|-
Line 451: Line 436:
| 1567.344
| 1567.344
| <small><small><small>[[27/11]]</small></small></small>, <small>[[32/13]]</small>
| <small><small><small>[[27/11]]</small></small></small>, <small>[[32/13]]</small>
| vvM3 +1oct
| vvM3 +1 oct
| 162
| 162
|-
|-
Line 457: Line 442:
| 1596.369
| 1596.369
| <small><small>[[5/2]]</small></small>
| <small><small>[[5/2]]</small></small>
| ^M3 +1oct
| ^M3 +1 oct
| 165
| 165
|-
|-
Line 463: Line 448:
| 1625.393
| 1625.393
| <small>[[28/11]]</small>, '''<u>[[23/9]]'''</u>, <small><small>[[18/7]]</small></small>
| <small>[[28/11]]</small>, '''<u>[[23/9]]'''</u>, <small><small>[[18/7]]</small></small>
| ^<sup>4</sup>M3 +1oct
| ^<sup>4</sup>M3 +1 oct
| 168
| 168
|-
|-
Line 469: Line 454:
| 1654.418
| 1654.418
| <small><small>[[31/12]]</small></small>, '''<u>[[13/5]]'''</u>
| <small><small>[[31/12]]</small></small>, '''<u>[[13/5]]'''</u>
| ^^^d4 +1oct
| ^^^d4 +1 oct
| 171
| 171
|-
|-
Line 475: Line 460:
| 1683.443
| 1683.443
| <small><small><small>[[21/8]]</small></small></small>, [[29/11]]
| <small><small><small>[[21/8]]</small></small></small>, [[29/11]]
| vv4 +1oct
| vv4 +1 oct
| 174
| 174
|-
|-
Line 481: Line 466:
| 1712.468
| 1712.468
| <small><small><small>[[8/3]]</small></small></small>, [[27/10]]
| <small><small><small>[[8/3]]</small></small></small>, [[27/10]]
| ^4 +1oct
| ^4 +1 oct
| 177
| 177
|-
|-
Line 487: Line 472:
| 1741.493
| 1741.493
| <small><small><small>[[19/7]]</small></small></small>, '''[[30/11]]''', <small><small>[[11/4]]</small></small>
| <small><small><small>[[19/7]]</small></small></small>, '''[[30/11]]''', <small><small>[[11/4]]</small></small>
| ~4 +1oct
| ~4 +1 oct
| 180
| 180
|-
|-
Line 493: Line 478:
| 1770.518
| 1770.518
| '''<u>[[25/9]]'''</u>, <small><small>[[14/5]]</small></small>
| '''<u>[[25/9]]'''</u>, <small><small>[[14/5]]</small></small>
| vA4 +1oct
| vA4 +1 oct
| 183
| 183
|-
|-
Line 499: Line 484:
| 1799.543
| 1799.543
| [[31/11]], '''[[17/6]]'''
| [[31/11]], '''[[17/6]]'''
| ^^A4 +1oct, vvd5 +1oct
| ^^A4 +1 oct, vvd5 +1 oct
| 186
| 186
|-
|-
Line 505: Line 490:
| 1828.568
| 1828.568
| <small><small>[[20/7]]</small></small>, '''<u>[[23/8]]'''</u>, <small>[[26/9]]</small>
| <small><small>[[20/7]]</small></small>, '''<u>[[23/8]]'''</u>, <small>[[26/9]]</small>
| ^d5 +1oct
| ^d5 +1 oct
| 189
| 189
|-
|-
Line 511: Line 496:
| 1857.593
| 1857.593
| <small><small><small>[[29/10]]</small></small></small>, <small>[[32/11]]</small>
| <small><small><small>[[29/10]]</small></small></small>, <small>[[32/11]]</small>
| ~5 +1oct
| ~5 +1 oct
| 192
| 192
|-
|-
Line 517: Line 502:
| 1886.617
| 1886.617
|  
|  
| v5 +1oct
| v5 +1 oct
| 195
| 195
|-
|-
Line 523: Line 508:
| 1915.642
| 1915.642
| <small><small><small>[[3/1]]</small></small></small>
| <small><small><small>[[3/1]]</small></small></small>
| ^^5 +1oct
| ^^5 +1 oct
| 198
| 198
|-
|-
Line 529: Line 514:
| 1944.667
| 1944.667
| <small><small><small>[[31/10]]</small></small></small>
| <small><small><small>[[31/10]]</small></small></small>
| vvvA5 +1oct
| vvvA5 +1 oct
| 201
| 201
|-
|-
Line 535: Line 520:
| 1973.692
| 1973.692
| <small>[[28/9]]</small>, '''<u>[[25/8]]'''</u>, <small>[[22/7]]</small>
| <small>[[28/9]]</small>, '''<u>[[25/8]]'''</u>, <small>[[22/7]]</small>
| v<sup>4</sup>m6 +1oct
| v<sup>4</sup>m6 +1 oct
| 204
| 204
|-
|-
Line 541: Line 526:
| 2002.717
| 2002.717
| [[19/6]], <small><small>[[16/5]]</small></small>
| [[19/6]], <small><small>[[16/5]]</small></small>
| vm6 +1oct
| vm6 +1 oct
| 207
| 207
|-
|-
Line 547: Line 532:
| 2031.742
| 2031.742
| [[29/9]], <small>[[13/4]]</small>
| [[29/9]], <small>[[13/4]]</small>
| ^^m6 +1oct
| ^^m6 +1 oct
| 210
| 210
|-
|-
Line 553: Line 538:
| 2060.767
| 2060.767
| '''<u>[[23/7]]'''</u>
| '''<u>[[23/7]]'''</u>
| vvvM6 +1oct
| vvvM6 +1 oct
| 213
| 213
|-
|-
Line 559: Line 544:
| 2089.792
| 2089.792
| [[10/3]]
| [[10/3]]
| M6 +1oct
| M6 +1 oct
| 216
| 216
|-
|-
Line 565: Line 550:
| 2118.816
| 2118.816
| <small><small><small>[[27/8]]</small></small></small>, '''<u>[[17/5]]'''</u>, <small><small><small>[[24/7]]</small></small></small>
| <small><small><small>[[27/8]]</small></small></small>, '''<u>[[17/5]]'''</u>, <small><small><small>[[24/7]]</small></small></small>
| ^^^M6 +1oct
| ^^^M6 +1 oct
| 219
| 219
|-
|-
Line 571: Line 556:
| 2147.841
| 2147.841
| [[31/9]]
| [[31/9]]
| vvA6 +1oct, ^^d7 +1oct
| vvA6 +1 oct, ^^d7 +1 oct
| 222
| 222
|-
|-
Line 577: Line 562:
| 2176.866
| 2176.866
| <small>[[7/2]]</small>
| <small>[[7/2]]</small>
| vvvm7 +1oct
| vvvm7 +1 oct
| 225
| 225
|-
|-
Line 583: Line 568:
| 2205.891
| 2205.891
| <small><small>[[32/9]]</small></small>, '''<u>[[25/7]]'''</u>, <small><small>[[18/5]]</small></small>
| <small><small>[[32/9]]</small></small>, '''<u>[[25/7]]'''</u>, <small><small>[[18/5]]</small></small>
| m7 +1oct
| m7 +1 oct
| 228
| 228
|-
|-
Line 589: Line 574:
| 2234.916
| 2234.916
| [[29/8]], <small><small><small>[[11/3]]</small></small></small>
| [[29/8]], <small><small><small>[[11/3]]</small></small></small>
| ^^^m7 +1oct
| ^^^m7 +1 oct
| 231
| 231
|-
|-
Line 595: Line 580:
| 2263.941
| 2263.941
| <small>[[26/7]]</small>
| <small>[[26/7]]</small>
| vvM7 +1oct
| vvM7 +1 oct
| 234
| 234
|-
|-
Line 601: Line 586:
| 2292.966
| 2292.966
| '''[[15/4]]'''
| '''[[15/4]]'''
| ^M7 +1oct
| ^M7 +1 oct
| 237
| 237
|-
|-
Line 607: Line 592:
| 2321.991
| 2321.991
| <small><small>[[19/5]]</small></small>, '''[[23/6]]'''
| <small><small>[[19/5]]</small></small>, '''[[23/6]]'''
| ^<sup>4</sup>M7 +1oct
| ^<sup>4</sup>M7 +1 oct
| 240
| 240
|-
|-
Line 613: Line 598:
| 2351.016
| 2351.016
| <small><small><small>[[27/7]]</small></small></small>, [[31/8]]
| <small><small><small>[[27/7]]</small></small></small>, [[31/8]]
| ^^^d1 +2oct
| ^^^d1 +2 oct
| 243
| 243
|-
|-
Line 619: Line 604:
| 2380.040
| 2380.040
|  
|  
| vv1 +2oct
| vv1 +2 oct
| 246
| 246
|-
|-
Line 625: Line 610:
| 2409.065
| 2409.065
| <small>[[4/1]]</small>
| <small>[[4/1]]</small>
| ^1 +2oct
| ^1 +2 oct
| 249
| 249
|-
|-
Line 631: Line 616:
| 2438.090
| 2438.090
|  
|  
| ^<sup>4</sup>1 +2oct
| ^<sup>4</sup>1 +2 oct
| 252
| 252
|-
|-
Line 637: Line 622:
| 2467.115
| 2467.115
| [[29/7]], '''[[25/6]]'''
| [[29/7]], '''[[25/6]]'''
| ^^^d2 +2oct
| ^^^d2 +2 oct
| 255
| 255
|-
|-
Line 643: Line 628:
| 2496.140
| 2496.140
| <small><small>[[21/5]]</small></small>, <small>[[17/4]]</small>
| <small><small>[[21/5]]</small></small>, <small>[[17/4]]</small>
| vvm2 +2oct
| vvm2 +2 oct
| 258
| 258
|-
|-
Line 649: Line 634:
| 2525.165
| 2525.165
| [[30/7]], <small><small><small>[[13/3]]</small></small></small>
| [[30/7]], <small><small><small>[[13/3]]</small></small></small>
| ^m2 +2oct
| ^m2 +2 oct
| 261
| 261
|-
|-
Line 655: Line 640:
| 2554.190
| 2554.190
| <small><small>[[22/5]]</small></small>
| <small><small>[[22/5]]</small></small>
| ~2 +2oct
| ~2 +2 oct
| 264
| 264
|-
|-
Line 661: Line 646:
| 2583.215
| 2583.215
| [[31/7]]
| [[31/7]]
| vM2 +2oct
| vM2 +2 oct
| 267
| 267
|-
|-
Line 667: Line 652:
| 2612.239
| 2612.239
| <small>[[9/2]]</small>
| <small>[[9/2]]</small>
| ^^M2 +2oct
| ^^M2 +2 oct
| 270
| 270
|-
|-
Line 673: Line 658:
| 2641.264
| 2641.264
| <small><small>[[32/7]]</small></small>, '''<u>[[23/5]]'''</u>
| <small><small>[[32/7]]</small></small>, '''<u>[[23/5]]'''</u>
| vvvA2 +2oct
| vvvA2 +2 oct
| 273
| 273
|-
|-
Line 679: Line 664:
| 2670.289
| 2670.289
| '''[[14/3]]'''
| '''[[14/3]]'''
| v<sup>4</sup>m3 +2oct
| v<sup>4</sup>m3 +2 oct
| 276
| 276
|-
|-
Line 685: Line 670:
| 2699.314
| 2699.314
| '''<u>[[19/4]]'''</u>
| '''<u>[[19/4]]'''</u>
| vm3 +2oct
| vm3 +2 oct
| 279
| 279
|-
|-
Line 691: Line 676:
| 2728.339
| 2728.339
| <small><small><small>[[24/5]]</small></small></small>, '''<u>[[29/6]]'''</u>
| <small><small><small>[[24/5]]</small></small></small>, '''<u>[[29/6]]'''</u>
| ^^m3 +2oct
| ^^m3 +2 oct
| 282
| 282
|-
|-
Line 697: Line 682:
| 2757.364
| 2757.364
|  
|  
| vvvM3 +2oct
| vvvM3 +2 oct
| 285
| 285
|-
|-
Line 703: Line 688:
| 2786.389
| 2786.389
| '''<u>[[5/1]]'''</u>
| '''<u>[[5/1]]'''</u>
| M3 +2oct
| M3 +2 oct
| 288
| 288
|-
|-
Line 709: Line 694:
| 2815.414
| 2815.414
|  
|  
| ^^^M3 +2oct
| ^^^M3 +2 oct
| 291
| 291
|-
|-
Line 715: Line 700:
| 2844.439
| 2844.439
| '''<u>[[31/6]]'''</u>, <small><small>[[26/5]]</small></small>
| '''<u>[[31/6]]'''</u>, <small><small>[[26/5]]</small></small>
| vvA3 +2oct, ^^d4 +2oct
| vvA3 +2 oct, ^^d4 +2 oct
| 294
| 294
|-
|-
Line 721: Line 706:
| 2873.463
| 2873.463
| '''[[21/4]]'''
| '''[[21/4]]'''
| vvv4 +2oct
| vvv4 +2 oct
| 297
| 297
|-
|-
Line 727: Line 712:
| 2902.488
| 2902.488
| '''[[16/3]]'''
| '''[[16/3]]'''
| P4 +2oct
| P4 +2 oct
| 300
| 300
|-
|-
Line 733: Line 718:
| 2931.513
| 2931.513
| <small><small>[[27/5]]</small></small>
| <small><small>[[27/5]]</small></small>
| ^^^4 +2oct
| ^^^4 +2 oct
| 303
| 303
|-
|-
Line 739: Line 724:
| 2960.538
| 2960.538
| <small>[[11/2]]</small>
| <small>[[11/2]]</small>
| vvA4 +2oct
| vvA4 +2 oct
| 306
| 306
|-
|-
Line 745: Line 730:
| 2989.563
| 2989.563
| [[28/5]], <small><small><small>[[17/3]]</small></small></small>
| [[28/5]], <small><small><small>[[17/3]]</small></small></small>
| ^A4 +2oct
| ^A4 +2 oct
| 309
| 309
|-
|-
Line 751: Line 736:
| 3018.588
| 3018.588
| <small><small>[[23/4]]</small></small>
| <small><small>[[23/4]]</small></small>
| d5 +2oct
| d5 +2 oct
| 312
| 312
|-
|-
Line 757: Line 742:
| 3047.613
| 3047.613
| '''[[29/5]]'''
| '''[[29/5]]'''
| ^^^d5 +2oct
| ^^^d5 +2 oct
| 315
| 315
|-
|-
Line 763: Line 748:
| 3076.638
| 3076.638
|  
|  
| vv5 +2oct
| vv5 +2 oct
| 318
| 318
|-
|-
Line 769: Line 754:
| 3105.663
| 3105.663
| '''[[6/1]]'''
| '''[[6/1]]'''
| ^5 +2oct
| ^5 +2 oct
| 321
| 321
|-
|-
Line 775: Line 760:
| 3134.687
| 3134.687
|  
|  
| ^<sup>4</sup>5 +2oct
| ^<sup>4</sup>5 +2 oct
| 324
| 324
|-
|-
Line 781: Line 766:
| 3163.712
| 3163.712
| [[31/5]], <small>[[25/4]]</small>
| [[31/5]], <small>[[25/4]]</small>
| ^^^d6 +2oct
| ^^^d6 +2 oct
| 327
| 327
|-
|-
Line 787: Line 772:
| 3192.737
| 3192.737
| '''[[19/3]]'''
| '''[[19/3]]'''
| vvm6 +2oct
| vvm6 +2 oct
| 330
| 330
|-
|-
Line 793: Line 778:
| 3221.762
| 3221.762
| <small>[[32/5]]</small>
| <small>[[32/5]]</small>
| ^m6 +2oct
| ^m6 +2 oct
| 333
| 333
|-
|-
Line 799: Line 784:
| 3250.787
| 3250.787
| <small><small>[[13/2]]</small></small>
| <small><small>[[13/2]]</small></small>
| ~6 +2oct
| ~6 +2 oct
| 336
| 336
|-
|-
Line 805: Line 790:
| 3279.812
| 3279.812
| '''[[20/3]]'''
| '''[[20/3]]'''
| vM6 +2oct
| vM6 +2 oct
| 339
| 339
|-
|-
Line 811: Line 796:
| 3308.837
| 3308.837
| '''[[27/4]]'''
| '''[[27/4]]'''
| ^^M6 +2oct
| ^^M6 +2 oct
| 342
| 342
|-
|-
Line 817: Line 802:
| 3337.862
| 3337.862
|  
|  
| vvvA6 +2oct
| vvvA6 +2 oct
| 345
| 345
|-
|-
Line 823: Line 808:
| 3366.886
| 3366.886
| '''<u>[[7/1]]'''</u>
| '''<u>[[7/1]]'''</u>
| v<sup>4</sup>m7 +2oct
| v<sup>4</sup>m7 +2 oct
| 348
| 348
|-
|-
Line 829: Line 814:
| 3395.911
| 3395.911
|  
|  
| vm7 +2oct
| vm7 +2 oct
| 351
| 351
|-
|-
Line 835: Line 820:
| 3424.936
| 3424.936
| '''[[29/4]]'''
| '''[[29/4]]'''
| ^^m7 +2oct
| ^^m7 +2 oct
| 354
| 354
|-
|-
Line 841: Line 826:
| 3453.961
| 3453.961
| '''[[22/3]]'''
| '''[[22/3]]'''
| vvvM7 +2oct
| vvvM7 +2 oct
| 357
| 357
|-
|-
Line 847: Line 832:
| 3482.986
| 3482.986
| [[15/2]]
| [[15/2]]
| M7 +2oct
| M7 +2 oct
| 360
| 360
|-
|-
Line 853: Line 838:
| 3512.011
| 3512.011
| <small><small><small>[[23/3]]</small></small></small>
| <small><small><small>[[23/3]]</small></small></small>
| ^^^M7 +2oct
| ^^^M7 +2 oct
| 363
| 363
|-
|-
Line 859: Line 844:
| 3541.036
| 3541.036
| '''[[31/4]]'''
| '''[[31/4]]'''
| vvA7 +2oct, ^^d1 +3oct
| vvA7 +2 oct, ^^d1 +3 oct
| 366
| 366
|-
|-
Line 865: Line 850:
| 3570.061
| 3570.061
|  
|  
| vvv1 +3oct
| vvv1 +3 oct
| 369
| 369
|-
|-
Line 871: Line 856:
| 3599.086
| 3599.086
| '''<u>[[8/1]]'''</u>
| '''<u>[[8/1]]'''</u>
| P1 +3oct
| P1 +3 oct
| 372
| 372
|-
|-
Line 877: Line 862:
| 3628.110
| 3628.110
|  
|  
| ^^^1 +3oct
| ^^^1 +3 oct
| 375
| 375
|-
|-
Line 883: Line 868:
| 3657.135
| 3657.135
| <small><small><small>[[25/3]]</small></small></small>
| <small><small><small>[[25/3]]</small></small></small>
| vvA1 +3oct, ^^d2 +3oct
| vvA1 +3 oct, ^^d2 +3 oct
| 378
| 378
|-
|-
Line 889: Line 874:
| 3686.160
| 3686.160
|  
|  
| vvvm2 +3oct
| vvvm2 +3 oct
| 381
| 381
|-
|-
Line 895: Line 880:
| 3715.185
| 3715.185
| <small><small>[[17/2]]</small></small>
| <small><small>[[17/2]]</small></small>
| m2 +3oct
| m2 +3 oct
| 384
| 384
|-
|-
Line 901: Line 886:
| 3744.210
| 3744.210
| [[26/3]]
| [[26/3]]
| ^^^m2 +3oct
| ^^^m2 +3 oct
| 387
| 387
|-
|-
Line 907: Line 892:
| 3773.235
| 3773.235
|  
|  
| vvM2 +3oct
| vvM2 +3 oct
| 390
| 390
|-
|-
Line 913: Line 898:
| 3802.260
| 3802.260
| '''<u>[[9/1]]'''</u>
| '''<u>[[9/1]]'''</u>
| ^M2 +3oct
| ^M2 +3 oct
| 393
| 393
|-
|-
Line 919: Line 904:
| 3831.285
| 3831.285
|  
|  
| ^<sup>4</sup>M2 +3oct
| ^<sup>4</sup>M2 +3 oct
| 396
| 396
|-
|-
Line 925: Line 910:
| 3860.309
| 3860.309
| [[28/3]]
| [[28/3]]
| ^^^d3 +3oct
| ^^^d3 +3 oct
| 399
| 399
|-
|-
Line 931: Line 916:
| 3889.334
| 3889.334
| <small>[[19/2]]</small>
| <small>[[19/2]]</small>
| vvm3 +3oct
| vvm3 +3 oct
| 402
| 402
|-
|-
Line 937: Line 922:
| 3918.359
| 3918.359
| <small>[[29/3]]</small>
| <small>[[29/3]]</small>
| ^m3 +3oct
| ^m3 +3 oct
| 405
| 405
|-
|-
Line 943: Line 928:
| 3947.384
| 3947.384
|  
|  
| ~3 +3oct
| ~3 +3 oct
| 408
| 408
|-
|-
Line 949: Line 934:
| 3976.409
| 3976.409
| <small><small>[[10/1]]</small></small>
| <small><small>[[10/1]]</small></small>
| vM3 +3oct
| vM3 +3 oct
| 411
| 411
|-
|-
Line 955: Line 940:
| 4005.434
| 4005.434
|  
|  
| ^^M3 +3oct
| ^^M3 +3 oct
| 414
| 414
|-
|-
Line 961: Line 946:
| 4034.459
| 4034.459
| <small>[[31/3]]</small>
| <small>[[31/3]]</small>
| vvvA3 +3oct
| vvvA3 +3 oct
| 417
| 417
|-
|-
Line 967: Line 952:
| 4063.484
| 4063.484
| <small>[[21/2]]</small>
| <small>[[21/2]]</small>
| v<sup>4</sup>4 +3oct
| v<sup>4</sup>4 +3 oct
| 420
| 420
|-
|-
Line 973: Line 958:
| 4092.509
| 4092.509
| [[32/3]]
| [[32/3]]
| v4 +3oct
| v4 +3 oct
| 423
| 423
|-
|-
Line 979: Line 964:
| 4121.533
| 4121.533
|  
|  
| ^^4 +3oct
| ^^4 +3 oct
| 426
| 426
|-
|-
Line 985: Line 970:
| 4150.558
| 4150.558
| '''<u>[[11/1]]'''</u>
| '''<u>[[11/1]]'''</u>
| vvvA4 +3oct
| vvvA4 +3 oct
| 429
| 429
|-
|-
Line 991: Line 976:
| 4179.583
| 4179.583
|  
|  
| A4 +3oct
| A4 +3 oct
| 432
| 432
|-
|-
Line 997: Line 982:
| 4208.608
| 4208.608
|  
|  
| vd5 +3oct
| vd5 +3 oct
| 435
| 435
|-
|-
Line 1,003: Line 988:
| 4237.633
| 4237.633
| <small>[[23/2]]</small>
| <small>[[23/2]]</small>
| ^^d5 +3oct
| ^^d5 +3 oct
| 438
| 438
|-
|-
Line 1,009: Line 994:
| 4266.658
| 4266.658
|  
|  
| vvv5 +3oct
| vvv5 +3 oct
| 441
| 441
|-
|-
Line 1,015: Line 1,000:
| 4295.683
| 4295.683
| [[12/1]]
| [[12/1]]
| P5 +3oct
| P5 +3 oct
| 444
| 444
|-
|-
Line 1,021: Line 1,006:
| 4324.708
| 4324.708
|  
|  
| ^^^5 +3oct
| ^^^5 +3 oct
| 447
| 447
|-
|-
Line 1,027: Line 1,012:
| 4353.732
| 4353.732
|  
|  
| vvA5 +3oct, ^^d6 +3oct
| vvA5 +3 oct, ^^d6 +3 oct
| 450
| 450
|-
|-
Line 1,033: Line 1,018:
| 4382.757
| 4382.757
| <small><small>[[25/2]]</small></small>
| <small><small>[[25/2]]</small></small>
| vvvm6 +3oct
| vvvm6 +3 oct
| 453
| 453
|-
|-
Line 1,039: Line 1,024:
| 4411.782
| 4411.782
|  
|  
| m6 +3oct
| m6 +3 oct
| 456
| 456
|-
|-
Line 1,045: Line 1,030:
| 4440.807
| 4440.807
| '''<u>[[13/1]]'''</u>
| '''<u>[[13/1]]'''</u>
| ^^^m6 +3oct
| ^^^m6 +3 oct
| 459
| 459
|-
|-
Line 1,051: Line 1,036:
| 4469.832
| 4469.832
|  
|  
| vvM6 +3oct
| vvM6 +3 oct
| 462
| 462
|-
|-
Line 1,057: Line 1,042:
| 4498.857
| 4498.857
| [[27/2]]
| [[27/2]]
| ^M6 +3oct
| ^M6 +3 oct
| 465
| 465
|-
|-
Line 1,063: Line 1,048:
| 4527.882
| 4527.882
|  
|  
| ^<sup>4</sup>M6 +3oct
| ^<sup>4</sup>M6 +3 oct
| 468
| 468
|-
|-
Line 1,069: Line 1,054:
| 4556.907
| 4556.907
| <small><small>[[14/1]]</small></small>
| <small><small>[[14/1]]</small></small>
| ^^^d7 +3oct
| ^^^d7 +3 oct
| 471
| 471
|-
|-
Line 1,075: Line 1,060:
| 4585.932
| 4585.932
|  
|  
| vvm7 +3oct
| vvm7 +3 oct
| 474
| 474
|-
|-
Line 1,081: Line 1,066:
| 4614.956
| 4614.956
|  
|  
| ^m7 +3oct
| ^m7 +3 oct
| 477
| 477
|-
|-
Line 1,087: Line 1,072:
| 4643.981
| 4643.981
| <small><small><small>[[29/2]]</small></small></small>
| <small><small><small>[[29/2]]</small></small></small>
| ~7 +3oct
| ~7 +3 oct
| 480
| 480
|-
|-
Line 1,093: Line 1,078:
| 4673.006
| 4673.006
|  
|  
| vM7 +3oct
| vM7 +3 oct
| 483
| 483
|-
|-
Line 1,099: Line 1,084:
| 4702.031
| 4702.031
| <small><small><small>[[15/1]]</small></small></small>
| <small><small><small>[[15/1]]</small></small></small>
| ^^M7 +3oct
| ^^M7 +3 oct
| 486
| 486
|-
|-
Line 1,105: Line 1,090:
| 4731.056
| 4731.056
| <small><small><small>[[31/2]]</small></small></small>
| <small><small><small>[[31/2]]</small></small></small>
| vvvA7 +3oct
| vvvA7 +3 oct
| 489
| 489
|-
|-
Line 1,111: Line 1,096:
| 4760.081
| 4760.081
|  
|  
| v<sup>4</sup>1 +4oct
| v<sup>4</sup>1 +4 oct
| 492
| 492
|-
|-
Line 1,117: Line 1,102:
| 4789.106
| 4789.106
| <small><small>[[16/1]]</small></small>
| <small><small>[[16/1]]</small></small>
| v1 +4oct
| v1 +4 oct
| 495
| 495
|-
|-
Line 1,123: Line 1,108:
| 4818.131
| 4818.131
|  
|  
| ^^1 +4oct
| ^^1 +4 oct
| 498
| 498
|-
|-
Line 1,129: Line 1,114:
| 4847.156
| 4847.156
|  
|  
| vvvA1 +4oct
| vvvA1 +4 oct
| 501
| 501
|-
|-
Line 1,135: Line 1,120:
| 4876.180
| 4876.180
|  
|  
| v<sup>4</sup>m2 +4oct
| v<sup>4</sup>m2 +4 oct
| 504
| 504
|-
|-
Line 1,141: Line 1,126:
| 4905.205
| 4905.205
| '''<u>[[17/1]]'''</u>
| '''<u>[[17/1]]'''</u>
| vm2 +4oct
| vm2 +4 oct
| 507
| 507
|-
|-
Line 1,147: Line 1,132:
| 4934.230
| 4934.230
|  
|  
| ^^m2 +4oct
| ^^m2 +4 oct
| 510
| 510
|-
|-
Line 1,153: Line 1,138:
| 4963.255
| 4963.255
|  
|  
| vvvM2 +4oct
| vvvM2 +4 oct
| 513
| 513
|-
|-
Line 1,159: Line 1,144:
| 4992.280
| 4992.280
| <small><small>[[18/1]]</small></small>
| <small><small>[[18/1]]</small></small>
| M2 +4oct
| M2 +4 oct
| 516
| 516
|-
|-
Line 1,165: Line 1,150:
| 5021.305
| 5021.305
|  
|  
| ^^^M2 +4oct
| ^^^M2 +4 oct
| 519
| 519
|-
|-
Line 1,171: Line 1,156:
| 5050.330
| 5050.330
|  
|  
| vvA2 +4oct, ^^d3 +4oct
| vvA2 +4 oct, ^^d3 +4 oct
| 522
| 522
|-
|-
Line 1,177: Line 1,162:
| 5079.355
| 5079.355
|  
|  
| vvvm3 +4oct
| vvvm3 +4 oct
| 525
| 525
|-
|-
Line 1,183: Line 1,168:
| 5108.379
| 5108.379
| <small><small>[[19/1]]</small></small>
| <small><small>[[19/1]]</small></small>
| m3 +4oct
| m3 +4 oct
| 528
| 528
|-
|-
Line 1,189: Line 1,174:
| 5137.404
| 5137.404
|  
|  
| ^^^m3 +4oct
| ^^^m3 +4 oct
| 531
| 531
|-
|-
Line 1,195: Line 1,180:
| 5166.429
| 5166.429
|  
|  
| vvM3 +4oct
| vvM3 +4 oct
| 534
| 534
|-
|-
Line 1,201: Line 1,186:
| 5195.454
| 5195.454
| <small>[[20/1]]</small>
| <small>[[20/1]]</small>
| ^M3 +4oct
| ^M3 +4 oct
| 537
| 537
|-
|-
Line 1,207: Line 1,192:
| 5224.479
| 5224.479
|  
|  
| ^<sup>4</sup>M3 +4oct
| ^<sup>4</sup>M3 +4 oct
| 540
| 540
|-
|-
Line 1,213: Line 1,198:
| 5253.504
| 5253.504
|  
|  
| ^^^d4 +4oct
| ^^^d4 +4 oct
| 543
| 543
|-
|-
Line 1,219: Line 1,204:
| 5282.529
| 5282.529
| <small><small>[[21/1]]</small></small>
| <small><small>[[21/1]]</small></small>
| vv4 +4oct
| vv4 +4 oct
| 546
| 546
|-
|-
Line 1,225: Line 1,210:
| 5311.554
| 5311.554
|  
|  
| ^4 +4oct
| ^4 +4 oct
| 549
| 549
|-
|-
Line 1,231: Line 1,216:
| 5340.579
| 5340.579
| <small><small>[[22/1]]</small></small>
| <small><small>[[22/1]]</small></small>
| ~4 +4oct
| ~4 +4 oct
| 552
| 552
|-
|-
Line 1,237: Line 1,222:
| 5369.603
| 5369.603
|  
|  
| vA4 +4oct
| vA4 +4 oct
| 555
| 555
|-
|-
Line 1,243: Line 1,228:
| 5398.628
| 5398.628
|  
|  
| ^^A4 +4oct, vvd5 +4oct
| ^^A4 +4 oct, vvd5 +4 oct
| 558
| 558
|-
|-
Line 1,249: Line 1,234:
| 5427.653
| 5427.653
| '''<u>[[23/1]]'''</u>
| '''<u>[[23/1]]'''</u>
| ^d5 +4oct
| ^d5 +4 oct
| 561
| 561
|-
|-
Line 1,255: Line 1,240:
| 5456.678
| 5456.678
|  
|  
| ~5 +4oct
| ~5 +4 oct
| 564
| 564
|-
|-
Line 1,261: Line 1,246:
| 5485.703
| 5485.703
|  
|  
| v5 +4oct
| v5 +4 oct
| 567
| 567
|-
|-
Line 1,267: Line 1,252:
| 5514.728
| 5514.728
| <small><small><small>[[24/1]]</small></small></small>
| <small><small><small>[[24/1]]</small></small></small>
| ^^5 +4oct
| ^^5 +4 oct
| 570
| 570
|-
|-
Line 1,273: Line 1,258:
| 5543.753
| 5543.753
|  
|  
| vvvA5 +4oct
| vvvA5 +4 oct
| 573
| 573
|-
|-
Line 1,279: Line 1,264:
| 5572.778
| 5572.778
| '''<u>[[25/1]]'''</u>
| '''<u>[[25/1]]'''</u>
| v<sup>4</sup>m6 +4oct
| v<sup>4</sup>m6 +4 oct
| 576
| 576
|-
|-
Line 1,285: Line 1,270:
| 5601.802
| 5601.802
|  
|  
| vm6 +4oct
| vm6 +4 oct
| 579
| 579
|-
|-
Line 1,291: Line 1,276:
| 5630.827
| 5630.827
| <small><small>[[26/1]]</small></small>
| <small><small>[[26/1]]</small></small>
| ^^m6 +4oct
| ^^m6 +4 oct
| 582
| 582
|-
|-
Line 1,297: Line 1,282:
| 5659.852
| 5659.852
|  
|  
| vvvM6 +4oct
| vvvM6 +4 oct
| 585
| 585
|-
|-
Line 1,303: Line 1,288:
| 5688.877
| 5688.877
|  
|  
| M6 +4oct
| M6 +4 oct
| 588
| 588
|-
|-
Line 1,309: Line 1,294:
| 5717.902
| 5717.902
| <small><small>[[27/1]]</small></small>
| <small><small>[[27/1]]</small></small>
| ^^^M6 +4oct
| ^^^M6 +4 oct
| 591
| 591
|-
|-
Line 1,315: Line 1,300:
| 5746.927
| 5746.927
|  
|  
| vvA6 +4oct, ^^d7 +4oct
| vvA6 +4 oct, ^^d7 +4 oct
| 594
| 594
|-
|-
Line 1,321: Line 1,306:
| 5775.952
| 5775.952
| [[28/1]]
| [[28/1]]
| vvvm7 +4oct
| vvvm7 +4 oct
| 597
| 597
|-
|-
Line 1,327: Line 1,312:
| 5804.977
| 5804.977
|  
|  
| m7 +4oct
| m7 +4 oct
| 600
| 600
|-
|-
Line 1,333: Line 1,318:
| 5834.002
| 5834.002
| '''[[29/1]]'''
| '''[[29/1]]'''
| ^^^m7 +4oct
| ^^^m7 +4 oct
| 603
| 603
|-
|-
Line 1,339: Line 1,324:
| 5863.026
| 5863.026
|  
|  
| vvM7 +4oct
| vvM7 +4 oct
| 606
| 606
|-
|-
Line 1,345: Line 1,330:
| 5892.051
| 5892.051
| '''[[30/1]]'''
| '''[[30/1]]'''
| ^M7 +4oct
| ^M7 +4 oct
| 609
| 609
|-
|-
Line 1,351: Line 1,336:
| 5921.076
| 5921.076
|  
|  
| ^<sup>4</sup>M7 +4oct
| ^<sup>4</sup>M7 +4 oct
| 612
| 612
|-
|-
Line 1,357: Line 1,342:
| 5950.101
| 5950.101
| [[31/1]]
| [[31/1]]
| ^^^d1 +5oct
| ^^^d1 +5 oct
| 615
| 615
|-
|-
Line 1,363: Line 1,348:
| 5979.126
| 5979.126
|  
|  
| vv1 +5oct
| vv1 +5 oct
| 618
| 618
|-
|-
Line 1,369: Line 1,354:
| 6008.151
| 6008.151
| <small>[[32/1]]</small>
| <small>[[32/1]]</small>
| ^1 +5oct
| ^1 +5 oct
| 621
| 621
|}
|}


===Approximation to JI===
== Approximation to JI ==


The following table illustrates the representation of the 32-[[integer limit]] intervals in [[186zpi]]. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
=== Interval mappings ===


{| class="wikitable center-all mw-collapsible mw-collapsed"
The following tables show how [[32-integer-limit]] intervals are represented in 186zpi. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italics''.
|+ style="white-space: nowrap;" | Intervals by direct approximation (even if inconsistent)
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 186zpi (by direct approximation)
|-
|-
! Ratio
! Ratio
Line 1,385: Line 1,372:
|-
|-
| [[17/13]]
| [[17/13]]
| 0.030
| -0.030
| 0.102
| -0.102
|-
|-
| '''[[5/1]]'''
| '''[[5/1]]'''
| '''0.075'''
| '''+0.075'''
| '''0.259'''
| '''+0.259'''
|-
|-
| [[25/17]]
| [[25/17]]
| 0.100
| -0.100
| 0.344
| -0.344
|-
|-
| [[25/13]]
| [[25/13]]
| 0.129
| -0.129
| 0.446
| -0.446
|-
|-
| [[23/11]]
| [[23/11]]
| 0.138
| +0.138
| 0.477
| +0.477
|-
|-
| [[25/1]]
| [[25/1]]
| 0.150
| +0.150
| 0.517
| +0.517
|-
|- style="background-color: #cccccc;"
| ''[[11/8]]''
| ''[[11/8]]''
| ''0.155''
| ''+0.155''
| ''0.533''
| ''+0.533''
|-
|-
| [[17/5]]
| [[17/5]]
| 0.175
| +0.175
| 0.602
| +0.602
|-
|-
| [[13/5]]
| [[13/5]]
| 0.204
| +0.204
| 0.704
| +0.704
|-
|-
| '''[[17/1]]'''
| '''[[17/1]]'''
| '''0.250'''
| '''+0.250'''
| '''0.861'''
| '''+0.861'''
|-
|-
| '''[[13/1]]'''
| '''[[13/1]]'''
| '''0.279'''
| '''+0.279'''
| '''0.963'''
| '''+0.963'''
|-
|- style="background-color: #cccccc;"
| ''[[9/7]]''
| ''[[9/7]]''
| ''0.289''
| ''+0.289''
| ''0.996''
| ''+0.996''
|-
|- style="background-color: #cccccc;"
| ''[[23/8]]''
| ''[[23/8]]''
| ''0.293''
| ''+0.293''
| ''1.011''
| ''+1.011''
|-
|-
| '''[[23/1]]'''
| '''[[23/1]]'''
| '''0.621'''
| '''-0.621'''
| '''2.140'''
| '''-2.140'''
|-
|-
| [[31/29]]
| [[31/29]]
| 0.641
| +0.641
| 2.209
| +2.209
|-
|-
| [[30/29]]
| [[30/29]]
| 0.642
| -0.642
| 2.211
| -2.211
|-
|-
| [[23/5]]
| [[23/5]]
| 0.696
| -0.696
| 2.399
| -2.399
|-
|-
| [[29/6]]
| [[29/6]]
| 0.717
| +0.717
| 2.470
| +2.470
|-
|- style="background-color: #cccccc;"
| ''[[9/8]]''
| ''[[9/8]]''
| ''0.736''
| ''-0.736''
| ''2.535''
| ''-2.535''
|-
|-
| '''[[11/1]]'''
| '''[[11/1]]'''
| '''0.760'''
| '''-0.760'''
| '''2.617'''
| '''-2.617'''
|-
|-
| [[25/23]]
| [[25/23]]
| 0.771
| +0.771
| 2.657
| +2.657
|-
|-
| [[11/5]]
| [[11/5]]
| 0.835
| -0.835
| 2.876
| -2.876
|-
|-
| [[23/17]]
| [[23/17]]
| 0.871
| -0.871
| 3.001
| -3.001
|-
|-
| [[21/19]]
| [[21/19]]
| 0.881
| +0.881
| 3.037
| +3.037
|-
|- style="background-color: #cccccc;"
| ''[[11/9]]''
| ''[[11/9]]''
| ''0.891''
| ''+0.891''
| ''3.069''
| ''+3.069''
|-
|-
| [[23/13]]
| [[23/13]]
| 0.901
| -0.901
| 3.103
| -3.103
|-
|-
| [[25/11]]
| [[25/11]]
| 0.910
| +0.910
| 3.135
| +3.135
|-
|- style="background-color: #cccccc;"
| ''[[8/1]]''
| ''[[8/1]]''
| ''0.914''
| ''-0.914''
| ''3.151''
| ''-3.151''
|-
|- style="background-color: #cccccc;"
| ''[[8/5]]''
| ''[[8/5]]''
| ''0.990''
| ''-0.990''
| ''3.409''
| ''-3.409''
|-
|-
| [[17/11]]
| [[17/11]]
| 1.009
| +1.009
| 3.478
| +3.478
|-
|- style="background-color: #cccccc;"
| ''[[8/7]]''
| ''[[8/7]]''
| ''1.025''
| ''+1.025''
| ''3.531''
| ''+3.531''
|-
|- style="background-color: #cccccc;"
| ''[[23/9]]''
| ''[[23/9]]''
| ''1.029''
| ''+1.029''
| ''3.546''
| ''+3.546''
|-
|-
| [[13/11]]
| [[13/11]]
| 1.039
| +1.039
| 3.580
| +3.580
|-
|- style="background-color: #cccccc;"
| ''[[25/8]]''
| ''[[25/8]]''
| ''1.065''
| ''+1.065''
| ''3.668''
| ''+3.668''
|-
|- style="background-color: #cccccc;"
| ''[[17/8]]''
| ''[[17/8]]''
| ''1.164''
| ''+1.164''
| ''4.012''
| ''+4.012''
|-
|- style="background-color: #cccccc;"
| ''[[27/19]]''
| ''[[27/19]]''
| ''1.171''
| ''+1.171''
| ''4.033''
| ''+4.033''
|-
|-
| [[11/7]]
| [[11/7]]
| 1.180
| +1.180
| 4.065
| +4.065
|-
|- style="background-color: #cccccc;"
| ''[[13/8]]''
| ''[[13/8]]''
| ''1.194''
| ''+1.194''
| ''4.114''
| ''+4.114''
|-
|-
| [[31/30]]
| [[31/30]]
| 1.283
| +1.283
| 4.420
| +4.420
|-
|-
| [[23/7]]
| [[23/7]]
| 1.318
| +1.318
| 4.542
| +4.542
|-
|-
| [[31/6]]
| [[31/6]]
| 1.358
| +1.358
| 4.679
| +4.679
|-
|- style="background-color: #cccccc;"
| ''[[9/1]]''
| ''[[9/1]]''
| ''1.650''
| ''-1.650''
| ''5.686''
| ''-5.686''
|-
|- style="background-color: #cccccc;"
| ''[[9/5]]''
| ''[[9/5]]''
| ''1.725''
| ''-1.725''
| ''5.944''
| ''-5.944''
|-
|- style="background-color: #cccccc;"
| ''[[20/19]]''
| ''[[20/19]]''
| ''1.726''
| ''-1.726''
| ''5.947''
| ''-5.947''
|-
|- style="background-color: #cccccc;"
| ''[[25/9]]''
| ''[[25/9]]''
| ''1.800''
| ''+1.800''
| ''6.203''
| ''+6.203''
|-
|- style="background-color: #cccccc;"
| ''[[19/4]]''
| ''[[19/4]]''
| ''1.801''
| ''+1.801''
| ''6.205''
| ''+6.205''
|-
|- style="background-color: #cccccc;"
| ''[[17/9]]''
| ''[[17/9]]''
| ''1.900''
| ''+1.900''
| ''6.547''
| ''+6.547''
|-
|- style="background-color: #cccccc;"
| ''[[24/19]]''
| ''[[24/19]]''
| ''1.906''
| ''+1.906''
| ''6.568''
| ''+6.568''
|-
|- style="background-color: #cccccc;"
| ''[[13/9]]''
| ''[[13/9]]''
| ''1.930''
| ''+1.930''
| ''6.649''
| ''+6.649''
|-
|-
| '''[[7/1]]'''
| '''[[7/1]]'''
| '''1.939'''
| '''-1.939'''
| '''6.682'''
| '''-6.682'''
|-
|-
| [[7/5]]
| [[7/5]]
| 2.015
| -2.015
| 6.941
| -6.941
|-
|- style="background-color: #cccccc;"
| ''[[31/28]]''
| ''[[31/28]]''
| ''2.060''
| ''-2.060''
| ''7.099''
| ''-7.099''
|-
|-
| [[25/7]]
| [[25/7]]
| 2.090
| +2.090
| 7.199
| +7.199
|-
|-
| [[17/7]]
| [[17/7]]
| 2.189
| +2.189
| 7.543
| +7.543
|-
|-
| [[13/7]]
| [[13/7]]
| 2.219
| +2.219
| 7.645
| +7.645
|-
|- style="background-color: #cccccc;"
| ''[[21/20]]''
| ''[[21/20]]''
| ''2.607''
| ''+2.607''
| ''8.984''
| ''+8.984''
|-
|- style="background-color: #cccccc;"
| ''[[21/4]]''
| ''[[21/4]]''
| ''2.683''
| ''+2.683''
| ''9.242''
| ''+9.242''
|-
|- style="background-color: #cccccc;"
| ''[[29/28]]''
| ''[[29/28]]''
| ''2.702''
| ''-2.702''
| ''9.308''
| ''-9.308''
|-
|- style="background-color: #cccccc;"
| ''[[32/19]]''
| ''[[32/19]]''
| ''2.716''
| ''-2.716''
| ''9.356''
| ''-9.356''
|-
|-
| [[19/3]]
| [[19/3]]
| 2.821
| -2.821
| 9.719
| -9.719
|-
|-
| [[19/15]]
| [[19/15]]
| 2.896
| -2.896
| 9.977
| -9.977
|-
|- style="background-color: #cccccc;"
| ''[[27/20]]''
| ''[[27/20]]''
| ''2.897''
| ''+2.897''
| ''9.980''
| ''+9.980''
|-
|- style="background-color: #cccccc;"
| ''[[27/4]]''
| ''[[27/4]]''
| ''2.972''
| ''+2.972''
| ''10.238''
| ''+10.238''
|-
|- style="background-color: #cccccc;"
| ''[[32/31]]''
| ''[[32/31]]''
| ''3.085''
| ''+3.085''
| ''10.630''
| ''+10.630''
|-
|- style="background-color: #cccccc;"
| ''[[15/14]]''
| ''[[15/14]]''
| ''3.343''
| ''-3.343''
| ''11.519''
| ''-11.519''
|-
|- style="background-color: #cccccc;"
| ''[[14/3]]''
| ''[[14/3]]''
| ''3.418''
| ''+3.418''
| ''11.777''
| ''+11.777''
|-
|-
| [[13/6]]
| [[13/6]]
| 3.428
| -3.428
| 11.811
| -11.811
|-
|-
| [[17/6]]
| [[17/6]]
| 3.458
| -3.458
| 11.913
| -11.913
|-
|-
| [[30/13]]
| [[30/13]]
| 3.503
| +3.503
| 12.069
| +12.069
|-
|-
| [[30/17]]
| [[30/17]]
| 3.533
| +3.533
| 12.171
| +12.171
|-
|-
| [[25/6]]
| [[25/6]]
| 3.557
| -3.557
| 12.256
| -12.256
|-
|- style="background-color: #cccccc;"
| ''[[32/21]]''
| ''[[32/21]]''
| ''3.597''
| ''-3.597''
| ''12.393''
| ''-12.393''
|-
|-
| [[6/5]]
| [[6/5]]
| 3.632
| +3.632
| 12.515
| +12.515
|-
|-
| [[6/1]]
| [[6/1]]
| 3.708
| +3.708
| 12.774
| +12.774
|-
|- style="background-color: #cccccc;"
| ''[[32/29]]''
| ''[[32/29]]''
| ''3.726''
| ''+3.726''
| ''12.839''
| ''+12.839''
|-
|- style="background-color: #cccccc;"
| ''[[28/19]]''
| ''[[28/19]]''
| ''3.741''
| ''-3.741''
| ''12.887''
| ''-12.887''
|-
|-
| [[30/1]]
| [[30/1]]
| 3.783
| +3.783
| 13.032
| +13.032
|-
|- style="background-color: #cccccc;"
| ''[[32/27]]''
| ''[[32/27]]''
| ''3.886''
| ''-3.886''
| ''13.389''
| ''-13.389''
|-
|- style="background-color: #cccccc;"
| ''[[31/4]]''
| ''[[31/4]]''
| ''4.000''
| ''-4.000''
| ''13.781''
| ''-13.781''
|-
|- style="background-color: #cccccc;"
| ''[[31/20]]''
| ''[[31/20]]''
| ''4.075''
| ''-4.075''
| ''14.039''
| ''-14.039''
|-
|-
| [[29/13]]
| [[29/13]]
| 4.145
| +4.145
| 14.280
| +14.280
|-
|-
| [[29/17]]
| [[29/17]]
| 4.174
| +4.174
| 14.382
| +14.382
|-
|-
| [[29/25]]
| [[29/25]]
| 4.274
| +4.274
| 14.726
| +14.726
|-
|-
| [[23/6]]
| [[23/6]]
| 4.329
| -4.329
| 14.914
| -14.914
|-
|-
| [[12/7]]
| [[12/7]]
| 4.333
| -4.333
| 14.928
| -14.928
|-
|-
| [[29/5]]
| [[29/5]]
| 4.349
| +4.349
| 14.985
| +14.985
|-
|- style="background-color: #cccccc;"
| ''[[16/15]]''
| ''[[16/15]]''
| ''4.368''
| ''+4.368''
| ''15.050''
| ''+15.050''
|-
|-
| [[30/23]]
| [[30/23]]
| 4.404
| +4.404
| 15.172
| +15.172
|-
|-
| '''[[29/1]]'''
| '''[[29/1]]'''
| '''4.424'''
| '''+4.424'''
| '''15.243'''
| '''+15.243'''
|-
|- style="background-color: #cccccc;"
| ''[[16/3]]''
| ''[[16/3]]''
| ''4.443''
| ''+4.443''
| ''15.309''
| ''+15.309''
|-
|-
| [[11/6]]
| [[11/6]]
| 4.467
| -4.467
| 15.391
| -15.391
|-
|- style="background-color: #cccccc;"
| ''[[22/15]]''
| ''[[22/15]]''
| ''4.523''
| ''+4.523''
| ''15.583''
| ''+15.583''
|-
|-
| [[30/11]]
| [[30/11]]
| 4.542
| +4.542
| 15.649
| +15.649
|-
|- style="background-color: #cccccc;"
| ''[[20/3]]''
| ''[[20/3]]''
| ''4.547''
| ''-4.547''
| ''15.666''
| ''-15.666''
|-
|- style="background-color: #cccccc;"
| ''[[22/3]]''
| ''[[22/3]]''
| ''4.598''
| ''+4.598''
| ''15.842''
| ''+15.842''
|-
|- style="background-color: #cccccc;"
| ''[[4/3]]''
| ''[[4/3]]''
| ''4.622''
| ''-4.622''
| ''15.924''
| ''-15.924''
|-
|- style="background-color: #cccccc;"
| ''[[29/4]]''
| ''[[29/4]]''
| ''4.641''
| ''-4.641''
| ''15.990''
| ''-15.990''
|-
|- style="background-color: #cccccc;"
| ''[[15/4]]''
| ''[[15/4]]''
| ''4.697''
| ''+4.697''
| ''16.183''
| ''+16.183''
|-
|- style="background-color: #cccccc;"
| ''[[29/20]]''
| ''[[29/20]]''
| ''4.716''
| ''-4.716''
| ''16.248''
| ''-16.248''
|-
|-
| [[31/13]]
| [[31/13]]
| 4.786
| +4.786
| 16.489
| +16.489
|-
|-
| [[31/17]]
| [[31/17]]
| 4.816
| +4.816
| 16.591
| +16.591
|-
|- style="background-color: #cccccc;"
| ''[[28/27]]''
| ''[[28/27]]''
| ''4.911''
| ''-4.911''
| ''16.920''
| ''-16.920''
|-
|-
| [[31/25]]
| [[31/25]]
| 4.915
| +4.915
| 16.935
| +16.935
|-
|-
| [[31/5]]
| [[31/5]]
| 4.990
| +4.990
| 17.194
| +17.194
|-
|-
| [[29/23]]
| [[29/23]]
| 5.046
| +5.046
| 17.383
| +17.383
|-
|-
| '''[[31/1]]'''
| '''[[31/1]]'''
| '''5.066'''
| '''+5.066'''
| '''17.452'''
| '''+17.452'''
|-
|- style="background-color: #cccccc;"
| ''[[27/14]]''
| ''[[27/14]]''
| ''5.069''
| ''-5.069''
| ''17.463''
| ''-17.463''
|-
|-
| [[29/11]]
| [[29/11]]
| 5.184
| +5.184
| 17.860
| +17.860
|-
|- style="background-color: #cccccc;"
| ''[[15/2]]''
| ''[[15/2]]''
| ''5.283''
| ''-5.283''
| ''18.201''
| ''-18.201''
|-
|- style="background-color: #cccccc;"
| ''[[29/8]]''
| ''[[29/8]]''
| ''5.339''
| ''+5.339''
| ''18.394''
| ''+18.394''
|-
|- style="background-color: #cccccc;"
| ''[[3/2]]''
| ''[[3/2]]''
| ''5.358''
| ''-5.358''
| ''18.459''
| ''-18.459''
|-
|- style="background-color: #cccccc;"
| ''[[10/3]]''
| ''[[10/3]]''
| ''5.433''
| ''+5.433''
| ''18.718''
| ''+18.718''
|-
|-
| [[12/11]]
| [[12/11]]
| 5.513
| -5.513
| 18.993
| -18.993
|-
|- style="background-color: #cccccc;"
| ''[[32/3]]''
| ''[[32/3]]''
| ''5.536''
| ''-5.536''
| ''19.075''
| ''-19.075''
|-
|- style="background-color: #cccccc;"
| ''[[26/15]]''
| ''[[26/15]]''
| ''5.562''
| ''+5.562''
| ''19.164''
| ''+19.164''
|-
|- style="background-color: #cccccc;"
| ''[[32/15]]''
| ''[[32/15]]''
| ''5.612''
| ''-5.612''
| ''19.334''
| ''-19.334''
|-
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| ''[[26/3]]''
| ''[[26/3]]''
| ''5.637''
| ''+5.637''
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| ''+19.422''
|-
|-
| [[7/6]]
| [[7/6]]
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| -5.647
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| -19.456
|-
|-
| [[23/12]]
| [[23/12]]
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| +5.651
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| +19.470
|-
|-
| [[31/23]]
| [[31/23]]
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| +5.687
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| +19.592
|-
|-
| [[30/7]]
| [[30/7]]
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| +5.722
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| +19.714
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|-
| [[31/19]]
| [[31/19]]
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| -5.801
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| -19.986
|-
|-
| [[31/11]]
| [[31/11]]
| 5.825
| +5.825
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| +20.069
|-
|- style="background-color: #cccccc;"
| ''[[31/8]]''
| ''[[31/8]]''
| ''5.980''
| ''+5.980''
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| ''+20.603''
|-
|- style="background-color: #cccccc;"
| ''[[29/9]]''
| ''[[29/9]]''
| ''6.075''
| ''+6.075''
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| ''+20.929''
|-
|- style="background-color: #cccccc;"
| ''[[27/16]]''
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| ''6.094''
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| ''-20.994''
|-
|- style="background-color: #cccccc;"
| ''[[19/14]]''
| ''[[19/14]]''
| ''6.239''
| ''-6.239''
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| ''-21.496''
|-
|- style="background-color: #cccccc;"
| ''[[27/22]]''
| ''[[27/22]]''
| ''6.248''
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| ''-21.528''
|-
|-
| [[12/1]]
| [[12/1]]
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| -6.272
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| -21.610
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|-
| [[12/5]]
| [[12/5]]
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| -21.869
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|-
| [[29/7]]
| [[29/7]]
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| +6.364
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| +21.925
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| ''[[21/16]]''
| ''[[21/16]]''
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|-
|-
| [[25/12]]
| [[25/12]]
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| +6.422
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| +22.127
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|-
| [[29/19]]
| [[29/19]]
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| -6.442
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| -22.195
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|-
| [[17/12]]
| [[17/12]]
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| +6.522
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| +22.471
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|-
| [[19/18]]
| [[19/18]]
| 6.528
| -6.528
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| -22.492
|-
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| ''[[22/21]]''
| ''[[22/21]]''
| ''6.538''
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| ''+22.524''
|-
|-
| [[13/12]]
| [[13/12]]
| 6.552
| +6.552
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| +22.573
|-
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| ''[[28/3]]''
| ''[[28/3]]''
| ''6.561''
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|-
|- style="background-color: #cccccc;"
| ''[[28/15]]''
| ''[[28/15]]''
| ''6.637''
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| ''-22.865''
|-
|-
| [[31/21]]
| [[31/21]]
| 6.682
| -6.682
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| -23.023
|-
|- style="background-color: #cccccc;"
| ''[[31/9]]''
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| ''+6.716''
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| ''+23.138''
|-
|- style="background-color: #cccccc;"
| ''[[28/13]]''
| ''[[28/13]]''
| ''6.846''
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| ''+23.588''
|-
|- style="background-color: #cccccc;"
| ''[[28/17]]''
| ''[[28/17]]''
| ''6.876''
| ''+6.876''
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| ''+23.690''
|-
|- style="background-color: #cccccc;"
| ''[[31/27]]''
| ''[[31/27]]''
| ''6.972''
| ''-6.972''
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| ''-24.019''
|-
|- style="background-color: #cccccc;"
| ''[[28/25]]''
| ''[[28/25]]''
| ''6.976''
| ''+6.976''
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| ''+24.034''
|-
|-
| [[31/7]]
| [[31/7]]
| 7.005
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| +24.134
|-
|- style="background-color: #cccccc;"
| ''[[27/2]]''
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|-
|- style="background-color: #cccccc;"
| ''[[28/5]]''
| ''[[28/5]]''
| ''7.051''
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| ''+24.292''
|-
|- style="background-color: #cccccc;"
| ''[[27/10]]''
| ''[[27/10]]''
| ''7.083''
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|-
|-
| [[30/19]]
| [[30/19]]
| 7.084
| -7.084
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| -24.406
|-
|- style="background-color: #cccccc;"
| ''[[28/1]]''
| ''[[28/1]]''
| ''7.126''
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| ''+24.551''
|-
|-
| [[19/6]]
| [[19/6]]
| 7.159
| +7.159
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| +24.665
|-
|- style="background-color: #cccccc;"
| ''[[19/16]]''
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|-
|- style="background-color: #cccccc;"
| ''[[27/26]]''
| ''[[27/26]]''
| ''7.288''
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|-
|- style="background-color: #cccccc;"
| ''[[21/2]]''
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|-
|-
| [[29/21]]
| [[29/21]]
| 7.324
| -7.324
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| -25.232
|-
|- style="background-color: #cccccc;"
| ''[[21/10]]''
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| ''7.372''
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|-
|- style="background-color: #cccccc;"
| ''[[22/19]]''
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| ''+25.561''
|-
|- style="background-color: #cccccc;"
| ''[[26/21]]''
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| ''7.577''
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| ''+26.104''
|-
|- style="background-color: #cccccc;"
| ''[[29/27]]''
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| ''7.613''
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|-
|- style="background-color: #cccccc;"
| ''[[31/24]]''
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| ''7.707''
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| ''-26.554''
|-
|- style="background-color: #cccccc;"
| ''[[28/23]]''
| ''[[28/23]]''
| ''7.747''
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| ''+26.691''
|-
|-
| [[26/7]]
| [[26/7]]
| 7.761
| -7.761
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| -26.739
|-
|- style="background-color: #cccccc;"
| ''[[32/13]]''
| ''[[32/13]]''
| ''7.871''
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| ''+27.119''
|-
|- style="background-color: #cccccc;"
| ''[[28/11]]''
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| ''7.886''
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| ''+27.168''
|-
|- style="background-color: #cccccc;"
| ''[[32/17]]''
| ''[[32/17]]''
| ''7.901''
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| ''+27.221''
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|-
| [[10/7]]
| [[10/7]]
| 7.965
| -7.965
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| -27.443
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|- style="background-color: #cccccc;"
| ''[[32/25]]''
| ''[[32/25]]''
| ''8.001''
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| ''+27.565''
|-
|-
| [[7/2]]
| [[7/2]]
| 8.040
| +8.040
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| +27.702
|-
|- style="background-color: #cccccc;"
| ''[[26/9]]''
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|-
|- style="background-color: #cccccc;"
| ''[[32/5]]''
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| ''+27.824''
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|- style="background-color: #cccccc;"
| ''[[32/1]]''
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|- style="background-color: #cccccc;"
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|- style="background-color: #cccccc;"
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|-
|- style="background-color: #cccccc;"
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|-
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|-
|- style="background-color: #cccccc;"
| ''[[29/24]]''
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|-
|- style="background-color: #cccccc;"
| ''[[26/19]]''
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| ''+29.141''
|-
|-
| [[31/3]]
| [[31/3]]
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| -29.705
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|-
| [[31/15]]
| [[31/15]]
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| -8.697
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| -29.964
|-
|- style="background-color: #cccccc;"
| ''[[32/23]]''
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| ''8.772''
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| ''+30.222''
|-
|- style="background-color: #cccccc;"
| ''[[28/9]]''
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| ''+30.237''
|-
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| ''[[13/4]]''
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|-
| [[22/7]]
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| -30.319
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| ''+30.529''
|-
|- style="background-color: #cccccc;"
| ''[[20/17]]''
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|- style="background-color: #cccccc;"
| ''[[32/11]]''
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| ''[[25/4]]''
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| -30.803
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| ''+31.233''
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|-
| [[26/23]]
| [[26/23]]
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| -31.281
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|-
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| ''+31.492''
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|-
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| +31.508
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|-
| [[11/2]]
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| +9.220
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| +31.766
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|- style="background-color: #cccccc;"
| ''[[16/9]]''
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| ''-31.848''
|-
|-
| [[29/3]]
| [[29/3]]
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| -9.263
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| -31.914
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|-
| [[23/10]]
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| +31.985
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|-
| [[29/15]]
| [[29/15]]
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| -32.173
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|-
| [[23/2]]
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| +32.243
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|-
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| ''[[18/7]]''
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| ''-33.387''
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|-
| [[26/1]]
| [[26/1]]
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| -9.700
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| -33.421
|-
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| ''[[23/20]]''
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| ''-33.632''
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|-
| [[26/5]]
| [[26/5]]
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| -9.775
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| -33.679
|-
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| ''[[32/9]]''
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| ''9.801''
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| ''[[11/4]]''
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|-
| [[26/25]]
| [[26/25]]
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| -33.938
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| ''[[20/11]]''
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| ''9.900''
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| ''+34.109''
|-
|-
| [[10/1]]
| [[10/1]]
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| -9.905
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| -34.125
|-
|-
| [[26/17]]
| [[26/17]]
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| -34.282
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|-
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| '''[[2/1]]'''
| '''9.980'''
| '''-9.980'''
| '''34.384'''
| '''-34.384'''
|-
|-
| [[5/2]]
| [[5/2]]
| 10.055
| +10.055
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| +34.642
|-
|- style="background-color: #cccccc;"
| ''[[32/7]]''
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| ''10.090''
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| ''+34.764''
|-
|-
| [[23/22]]
| [[23/22]]
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| +10.118
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| +34.861
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|-
| [[25/2]]
| [[25/2]]
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| +10.130
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| +34.901
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| ''[[16/11]]''
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| ''10.135''
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| ''-34.917''
|-
|-
| [[17/10]]
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| +34.986
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|-
| [[13/10]]
| [[13/10]]
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| +10.184
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| +35.088
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|-
| [[17/2]]
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| +35.244
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|-
| [[13/2]]
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| +10.259
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| +35.346
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| ''[[14/9]]''
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| ''10.269''
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| ''-35.380''
|-
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| ''[[23/16]]''
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| ''10.273''
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| ''+35.394''
|-
|-
| [[19/13]]
| [[19/13]]
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| +10.587
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| +36.475
|-
|-
| [[19/17]]
| [[19/17]]
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| +10.617
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| +36.577
|-
|-
| [[29/12]]
| [[29/12]]
| 10.697
| +10.697
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| +36.853
|-
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| ''[[9/4]]''
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| ''10.716''
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| ''-36.919''
|-
|-
| [[25/19]]
| [[25/19]]
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| -10.716
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| -36.921
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|-
| [[22/1]]
| [[22/1]]
| 10.739
| -10.739
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| -37.001
|-
|- style="background-color: #cccccc;"
| ''[[20/9]]''
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| ''10.791''
| ''+10.791''
| ''37.177''
| ''+37.177''
|-
|-
| [[19/5]]
| [[19/5]]
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| +10.791
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| +37.180
|-
|-
| [[22/5]]
| [[22/5]]
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| -10.814
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| -37.259
|-
|-
| '''[[19/1]]'''
| '''[[19/1]]'''
| '''10.866'''
| '''+10.866'''
| '''37.438'''
| '''+37.438'''
|-
|- style="background-color: #cccccc;"
| ''[[18/11]]''
| ''[[18/11]]''
| ''10.870''
| ''-10.870''
| ''37.452''
| ''-37.452''
|-
|-
| [[25/22]]
| [[25/22]]
| 10.890
| +10.890
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| +37.518
|-
|- style="background-color: #cccccc;"
| ''[[16/1]]''
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| ''10.894''
| ''-10.894''
| ''37.534''
| ''-37.534''
|-
|- style="background-color: #cccccc;"
| ''[[16/5]]''
| ''[[16/5]]''
| ''10.969''
| ''-10.969''
| ''37.793''
| ''-37.793''
|-
|-
| [[22/17]]
| [[22/17]]
| 10.989
| -10.989
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| -37.862
|-
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| ''[[7/4]]''
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| ''11.005''
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| ''-37.915''
|-
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| ''[[23/18]]''
| ''[[23/18]]''
| ''11.009''
| ''+11.009''
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| ''+37.929''
|-
|-
| [[22/13]]
| [[22/13]]
| 11.019
| -11.019
| 37.964
| -37.964
|-
|- style="background-color: #cccccc;"
| ''[[25/16]]''
| ''[[25/16]]''
| ''11.044''
| ''+11.044''
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| ''+38.052''
|-
|- style="background-color: #cccccc;"
| ''[[20/7]]''
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| ''11.080''
| ''+11.080''
| ''38.174''
| ''+38.174''
|-
|- style="background-color: #cccccc;"
| ''[[17/16]]''
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| ''11.144''
| ''+11.144''
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| ''+38.395''
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|-
| [[14/11]]
| [[14/11]]
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| -11.160
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| -38.448
|-
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| ''[[16/13]]''
| ''[[16/13]]''
| ''11.174''
| ''-11.174''
| ''38.497''
| ''-38.497''
|-
|-
| [[23/14]]
| [[23/14]]
| 11.298
| +11.298
| 38.925
| +38.925
|-
|-
| [[31/12]]
| [[31/12]]
| 11.338
| +11.338
| 39.062
| +39.062
|-
|-
| [[21/13]]
| [[21/13]]
| 11.468
| +11.468
| 39.512
| +39.512
|-
|-
| [[23/19]]
| [[23/19]]
| 11.488
| -11.488
| 39.579
| -39.579
|-
|-
| [[21/17]]
| [[21/17]]
| 11.498
| +11.498
| 39.614
| +39.614
|-
|-
| [[25/21]]
| [[25/21]]
| 11.598
| -11.598
| 39.958
| -39.958
|-
|-
| [[19/11]]
| [[19/11]]
| 11.626
| +11.626
| 40.056
| +40.056
|-
|- style="background-color: #cccccc;"
| ''[[18/1]]''
| ''[[18/1]]''
| ''11.630''
| ''-11.630''
| ''40.069''
| ''-40.069''
|-
|-
| [[21/5]]
| [[21/5]]
| 11.673
| +11.673
| 40.216
| +40.216
|-
|- style="background-color: #cccccc;"
| ''[[18/5]]''
| ''[[18/5]]''
| ''11.705''
| ''-11.705''
| ''40.328''
| ''-40.328''
|-
|-
| [[21/1]]
| [[21/1]]
| 11.748
| +11.748
| 40.475
| +40.475
|-
|- style="background-color: #cccccc;"
| ''[[27/13]]''
| ''[[27/13]]''
| ''11.758''
| ''+11.758''
| ''40.508''
| ''+40.508''
|-
|- style="background-color: #cccccc;"
| ''[[25/18]]''
| ''[[25/18]]''
| ''11.780''
| ''+11.780''
| ''40.587''
| ''+40.587''
|-
|- style="background-color: #cccccc;"
| ''[[19/8]]''
| ''[[19/8]]''
| ''11.781''
| ''+11.781''
| ''40.589''
| ''+40.589''
|-
|- style="background-color: #cccccc;"
| ''[[27/17]]''
| ''[[27/17]]''
| ''11.787''
| ''+11.787''
| ''40.610''
| ''+40.610''
|-
|- style="background-color: #cccccc;"
| ''[[18/17]]''
| ''[[18/17]]''
| ''11.880''
| ''-11.880''
| ''40.930''
| ''-40.930''
|-
|- style="background-color: #cccccc;"
| ''[[19/12]]''
| ''[[19/12]]''
| ''11.886''
| ''-11.886''
| ''40.952''
| ''-40.952''
|-
|- style="background-color: #cccccc;"
| ''[[27/25]]''
| ''[[27/25]]''
| ''11.887''
| ''+11.887''
| ''40.954''
| ''+40.954''
|-
|- style="background-color: #cccccc;"
| ''[[18/13]]''
| ''[[18/13]]''
| ''11.910''
| ''-11.910''
| ''41.032''
| ''-41.032''
|-
|-
| [[14/1]]
| [[14/1]]
| 11.919
| -11.919
| 41.066
| -41.066
|-
|- style="background-color: #cccccc;"
| ''[[27/5]]''
| ''[[27/5]]''
| ''11.962''
| ''+11.962''
| ''41.213''
| ''+41.213''
|-
|-
| [[14/5]]
| [[14/5]]
| 11.994
| -11.994
| 41.324
| -41.324
|-
|- style="background-color: #cccccc;"
| ''[[27/1]]''
| ''[[27/1]]''
| ''12.037''
| ''+12.037''
| ''41.471''
| ''+41.471''
|-
|- style="background-color: #cccccc;"
| ''[[31/14]]''
| ''[[31/14]]''
| ''12.040''
| ''-12.040''
| ''41.482''
| ''-41.482''
|-
|-
| [[25/14]]
| [[25/14]]
| 12.069
| +12.069
| 41.583
| +41.583
|-
|-
| [[17/14]]
| [[17/14]]
| 12.169
| +12.169
| 41.926
| +41.926
|-
|-
| [[14/13]]
| [[14/13]]
| 12.199
| -12.199
| 42.028
| -42.028
|-
|-
| [[31/18]]
| [[31/18]]
| 12.329
| -12.329
| 42.478
| -42.478
|-
|-
| [[23/21]]
| [[23/21]]
| 12.369
| -12.369
| 42.615
| -42.615
|-
|- style="background-color: #cccccc;"
| ''[[24/13]]''
| ''[[24/13]]''
| ''12.493''
| ''+12.493''
| ''43.044''
| ''+43.044''
|-
|-
| [[21/11]]
| [[21/11]]
| 12.507
| +12.507
| 43.092
| +43.092
|-
|- style="background-color: #cccccc;"
| ''[[19/9]]''
| ''[[19/9]]''
| ''12.517''
| ''+12.517''
| ''43.124''
| ''+43.124''
|-
|- style="background-color: #cccccc;"
| ''[[24/17]]''
| ''[[24/17]]''
| ''12.523''
| ''+12.523''
| ''43.146''
| ''+43.146''
|-
|- style="background-color: #cccccc;"
| ''[[25/24]]''
| ''[[25/24]]''
| ''12.623''
| ''-12.623''
| ''43.489''
| ''-43.489''
|-
|- style="background-color: #cccccc;"
| ''[[27/23]]''
| ''[[27/23]]''
| ''12.658''
| ''+12.658''
| ''43.611''
| ''+43.611''
|-
|- style="background-color: #cccccc;"
| ''[[21/8]]''
| ''[[21/8]]''
| ''12.662''
| ''+12.662''
| ''43.626''
| ''+43.626''
|-
|- style="background-color: #cccccc;"
| ''[[29/14]]''
| ''[[29/14]]''
| ''12.681''
| ''-12.681''
| ''43.691''
| ''-43.691''
|-
|- style="background-color: #cccccc;"
| ''[[24/5]]''
| ''[[24/5]]''
| ''12.698''
| ''+12.698''
| ''43.748''
| ''+43.748''
|-
|- style="background-color: #cccccc;"
| ''[[24/1]]''
| ''[[24/1]]''
| ''12.773''
| ''+12.773''
| ''44.006''
| ''+44.006''
|-
|- style="background-color: #cccccc;"
| ''[[27/11]]''
| ''[[27/11]]''
| ''12.797''
| ''+12.797''
| ''44.089''
| ''+44.089''
|-
|-
| [[19/7]]
| [[19/7]]
| 12.806
| +12.806
| 44.120
| +44.120
|-
|- style="background-color: #cccccc;"
| ''[[27/8]]''
| ''[[27/8]]''
| ''12.951''
| ''+12.951''
| ''44.622''
| ''+44.622''
|-
|-
| [[29/18]]
| [[29/18]]
| 12.970
| -12.970
| 44.687
| -44.687
|-
|- style="background-color: #cccccc;"
| ''[[31/16]]''
| ''[[31/16]]''
| ''13.065''
| ''-13.065''
| ''45.014''
| ''-45.014''
|-
|- style="background-color: #cccccc;"
| ''[[31/22]]''
| ''[[31/22]]''
| ''13.220''
| ''-13.220''
| ''45.547''
| ''-45.547''
|-
|- style="background-color: #cccccc;"
| ''[[15/7]]''
| ''[[15/7]]''
| ''13.323''
| ''-13.323''
| ''45.902''
| ''-45.902''
|-
|- style="background-color: #cccccc;"
| ''[[24/23]]''
| ''[[24/23]]''
| ''13.394''
| ''+13.394''
| ''46.147''
| ''+46.147''
|-
|- style="background-color: #cccccc;"
| ''[[7/3]]''
| ''[[7/3]]''
| ''13.398''
| ''+13.398''
| ''46.161''
| ''+46.161''
|-
|-
| [[13/3]]
| [[13/3]]
| 13.408
| -13.408
| 46.194
| -46.194
|-
|-
| [[17/3]]
| [[17/3]]
| 13.437
| -13.437
| 46.296
| -46.296
|-
|-
| [[15/13]]
| [[15/13]]
| 13.483
| +13.483
| 46.453
| +46.453
|-
|-
| [[17/15]]
| [[17/15]]
| 13.513
| -13.513
| 46.555
| -46.555
|-
|- style="background-color: #cccccc;"
| ''[[24/11]]''
| ''[[24/11]]''
| ''13.532''
| ''+13.532''
| ''46.624''
| ''+46.624''
|-
|-
| [[25/3]]
| [[25/3]]
| 13.537
| -13.537
| 46.640
| -46.640
|-
|-
| [[5/3]]
| [[5/3]]
| 13.612
| -13.612
| 46.898
| -46.898
|-
|-
| '''[[3/1]]'''
| '''[[3/1]]'''
| '''13.687'''
| '''+13.687'''
| '''47.157'''
| '''+47.157'''
|-
|- style="background-color: #cccccc;"
| ''[[29/16]]''
| ''[[29/16]]''
| ''13.706''
| ''-13.706''
| ''47.223''
| ''-47.223''
|-
|-
| [[15/1]]
| [[15/1]]
| 13.762
| +13.762
| 47.416
| +47.416
|-
|- style="background-color: #cccccc;"
| ''[[29/22]]''
| ''[[29/22]]''
| ''13.861''
| ''-13.861''
| ''47.756''
| ''-47.756''
|-
|- style="background-color: #cccccc;"
| ''[[27/7]]''
| ''[[27/7]]''
| ''13.976''
| ''+13.976''
| ''48.153''
| ''+48.153''
|-
|- style="background-color: #cccccc;"
| ''[[31/2]]''
| ''[[31/2]]''
| ''13.980''
| ''-13.980''
| ''48.164''
| ''-48.164''
|-
|- style="background-color: #cccccc;"
| ''[[31/10]]''
| ''[[31/10]]''
| ''14.055''
| ''-14.055''
| ''48.423''
| ''-48.423''
|-
|-
| [[29/26]]
| [[29/26]]
| 14.125
| +14.125
| 48.664
| +48.664
|-
|- style="background-color: #cccccc;"
| ''[[31/26]]''
| ''[[31/26]]''
| ''14.259''
| ''-14.259''
| ''49.127''
| ''-49.127''
|-
|-
| [[23/3]]
| [[23/3]]
| 14.308
| -14.308
| 49.297
| -49.297
|-
|-
| [[24/7]]
| [[24/7]]
| 14.313
| -14.313
| 49.312
| -49.312
|-
|-
| [[29/10]]
| [[29/10]]
| 14.329
| +14.329
| 49.368
| +49.368
|-
|- style="background-color: #cccccc;"
| ''[[15/8]]''
| ''[[15/8]]''
| ''14.348''
| ''-14.348''
| ''49.434''
| ''-49.434''
|-
|-
| [[23/15]]
| [[23/15]]
| 14.384
| -14.384
| 49.556
| -49.556
|-
|-
| [[29/2]]
| [[29/2]]
| 14.404
| +14.404
| 49.627
| +49.627
|-
|- style="background-color: #cccccc;"
| ''[[8/3]]''
| ''[[8/3]]''
| ''14.423''
| ''+14.423''
| ''49.692''
| ''+49.692''
|-
|-
| [[11/3]]
| [[11/3]]
| 14.447
| -14.447
| 49.774
| -49.774
|- style="background-color: #cccccc;"
| ''[[15/11]]''
| ''-14.503''
| ''-49.967''
|}
 
{| class="wikitable center-1 right-2 right-3 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | 32-integer-limit intervals in 186zpi (by patent val mapping)
|-
|-
! Ratio
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[17/13]]
| -0.030
| -0.102
|-
| '''[[5/1]]'''
| '''+0.075'''
| '''+0.259'''
|-
| [[25/17]]
| -0.100
| -0.344
|-
| [[25/13]]
| -0.129
| -0.446
|-
| [[23/11]]
| +0.138
| +0.477
|-
| [[25/1]]
| +0.150
| +0.517
|-
| [[17/5]]
| +0.175
| +0.602
|-
| [[13/5]]
| +0.204
| +0.704
|-
| '''[[17/1]]'''
| '''+0.250'''
| '''+0.861'''
|-
| '''[[13/1]]'''
| '''+0.279'''
| '''+0.963'''
|-
| '''[[23/1]]'''
| '''-0.621'''
| '''-2.140'''
|-
| [[31/29]]
| +0.641
| +2.209
|-
| [[30/29]]
| -0.642
| -2.211
|-
| [[23/5]]
| -0.696
| -2.399
|-
| [[29/6]]
| +0.717
| +2.470
|-
| '''[[11/1]]'''
| '''-0.760'''
| '''-2.617'''
|-
| [[25/23]]
| +0.771
| +2.657
|-
| [[11/5]]
| -0.835
| -2.876
|-
| [[23/17]]
| -0.871
| -3.001
|-
| [[21/19]]
| +0.881
| +3.037
|-
| [[23/13]]
| -0.901
| -3.103
|-
| [[25/11]]
| +0.910
| +3.135
|-
| [[17/11]]
| +1.009
| +3.478
|-
| [[13/11]]
| +1.039
| +3.580
|-
| [[11/7]]
| +1.180
| +4.065
|-
| [[31/30]]
| +1.283
| +4.420
|-
| [[23/7]]
| +1.318
| +4.542
|-
| [[31/6]]
| +1.358
| +4.679
|-
| '''[[7/1]]'''
| '''-1.939'''
| '''-6.682'''
|-
| [[7/5]]
| -2.015
| -6.941
|-
| [[25/7]]
| +2.090
| +7.199
|-
| [[17/7]]
| +2.189
| +7.543
|-
| [[13/7]]
| +2.219
| +7.645
|-
| [[19/3]]
| -2.821
| -9.719
|-
| [[19/15]]
| -2.896
| -9.977
|-
| [[13/6]]
| -3.428
| -11.811
|-
| [[17/6]]
| -3.458
| -11.913
|-
| [[30/13]]
| +3.503
| +12.069
|-
| [[30/17]]
| +3.533
| +12.171
|-
| [[25/6]]
| -3.557
| -12.256
|-
| [[6/5]]
| +3.632
| +12.515
|-
| [[6/1]]
| +3.708
| +12.774
|-
| [[30/1]]
| +3.783
| +13.032
|-
| [[29/13]]
| +4.145
| +14.280
|-
| [[29/17]]
| +4.174
| +14.382
|-
| [[29/25]]
| +4.274
| +14.726
|-
| [[23/6]]
| -4.329
| -14.914
|-
| [[12/7]]
| -4.333
| -14.928
|-
| [[29/5]]
| +4.349
| +14.985
|-
| [[30/23]]
| +4.404
| +15.172
|-
| '''[[29/1]]'''
| '''+4.424'''
| '''+15.243'''
|-
| [[11/6]]
| -4.467
| -15.391
|-
| [[30/11]]
| +4.542
| +15.649
|-
| [[31/13]]
| +4.786
| +16.489
|-
| [[31/17]]
| +4.816
| +16.591
|-
| [[31/25]]
| +4.915
| +16.935
|-
| [[31/5]]
| +4.990
| +17.194
|-
| [[29/23]]
| +5.046
| +17.383
|-
| '''[[31/1]]'''
| '''+5.066'''
| '''+17.452'''
|-
| [[29/11]]
| +5.184
| +17.860
|-
| [[12/11]]
| -5.513
| -18.993
|-
| [[7/6]]
| -5.647
| -19.456
|-
| [[23/12]]
| +5.651
| +19.470
|-
| [[31/23]]
| +5.687
| +19.592
|-
| [[30/7]]
| +5.722
| +19.714
|-
| [[31/19]]
| -5.801
| -19.986
|-
| [[31/11]]
| +5.825
| +20.069
|-
| [[12/1]]
| -6.272
| -21.610
|-
| [[12/5]]
| -6.347
| -21.869
|-
| [[29/7]]
| +6.364
| +21.925
|-
| [[25/12]]
| +6.422
| +22.127
|-
| [[29/19]]
| -6.442
| -22.195
|-
| [[17/12]]
| +6.522
| +22.471
|-
| [[19/18]]
| -6.528
| -22.492
|-
| [[13/12]]
| +6.552
| +22.573
|-
| [[31/21]]
| -6.682
| -23.023
|-
| [[31/7]]
| +7.005
| +24.134
|-
| [[30/19]]
| -7.084
| -24.406
|-
| [[19/6]]
| +7.159
| +24.665
|-
| [[29/21]]
| -7.324
| -25.232
|-
| [[26/7]]
| -7.761
| -26.739
|-
| [[10/7]]
| -7.965
| -27.443
|-
| [[7/2]]
| +8.040
| +27.702
|-
| [[31/3]]
| -8.622
| -29.705
|-
| [[31/15]]
| -8.697
| -29.964
|-
| [[22/7]]
| -8.800
| -30.319
|-
| [[26/11]]
| -8.941
| -30.803
|-
| [[26/23]]
| -9.079
| -31.281
|-
| [[11/10]]
| +9.145
| +31.508
|-
| [[11/2]]
| +9.220
| +31.766
|-
| [[29/3]]
| -9.263
| -31.914
|-
| [[23/10]]
| +9.284
| +31.985
|-
| [[29/15]]
| -9.338
| -32.173
|-
| [[23/2]]
| +9.359
| +32.243
|-
| [[26/1]]
| -9.700
| -33.421
|-
| [[26/5]]
| -9.775
| -33.679
|-
| [[26/25]]
| -9.850
| -33.938
|-
| [[10/1]]
| -9.905
| -34.125
|-
| [[26/17]]
| -9.950
| -34.282
|-
| '''[[2/1]]'''
| '''-9.980'''
| '''-34.384'''
|-
| [[5/2]]
| +10.055
| +34.642
|-
| [[23/22]]
| +10.118
| +34.861
|-
| [[25/2]]
| +10.130
| +34.901
|-
| [[17/10]]
| +10.155
| +34.986
|-
| [[13/10]]
| +10.184
| +35.088
|-
| [[17/2]]
| +10.230
| +35.244
|-
| [[13/2]]
| +10.259
| +35.346
|-
| [[19/13]]
| +10.587
| +36.475
|-
| [[19/17]]
| +10.617
| +36.577
|-
| [[29/12]]
| +10.697
| +36.853
|-
| [[25/19]]
| -10.716
| -36.921
|-
| [[22/1]]
| -10.739
| -37.001
|-
| [[19/5]]
| +10.791
| +37.180
|-
| [[22/5]]
| -10.814
| -37.259
|-
| '''[[19/1]]'''
| '''+10.866'''
| '''+37.438'''
|-
| [[25/22]]
| +10.890
| +37.518
|-
| [[22/17]]
| -10.989
| -37.862
|-
| [[22/13]]
| -11.019
| -37.964
|-
| [[14/11]]
| -11.160
| -38.448
|-
| [[23/14]]
| +11.298
| +38.925
|-
| [[31/12]]
| +11.338
| +39.062
|-
| [[21/13]]
| +11.468
| +39.512
|-
| [[23/19]]
| -11.488
| -39.579
|-
| [[21/17]]
| +11.498
| +39.614
|-
| [[25/21]]
| -11.598
| -39.958
|-
| [[19/11]]
| +11.626
| +40.056
|-
| [[21/5]]
| +11.673
| +40.216
|-
| [[21/1]]
| +11.748
| +40.475
|-
| [[14/1]]
| -11.919
| -41.066
|-
| [[14/5]]
| -11.994
| -41.324
|-
| [[25/14]]
| +12.069
| +41.583
|-
| [[17/14]]
| +12.169
| +41.926
|-
| [[14/13]]
| -12.199
| -42.028
|-
| [[31/18]]
| -12.329
| -42.478
|-
| [[23/21]]
| -12.369
| -42.615
|-
| [[21/11]]
| +12.507
| +43.092
|-
| [[19/7]]
| +12.806
| +44.120
|-
| [[29/18]]
| -12.970
| -44.687
|-
| [[13/3]]
| -13.408
| -46.194
|-
| [[17/3]]
| -13.437
| -46.296
|-
| [[15/13]]
| +13.483
| +46.453
|-
| [[17/15]]
| -13.513
| -46.555
|-
| [[25/3]]
| -13.537
| -46.640
|-
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|}


[[Category:Zeta peak indexes]]
[[Category:Zeta peak indexes]]
Retrieved from "https://en.xen.wiki/w/186zpi"