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{{todo|use sigma 1.0|inline=1|comment=instead of sigma 1/2}}
{{todo|use sigma 1.0|inline=1|comment=instead of sigma 1/2}}
<s>
 
=== Notable Local Maxima of the Riemann Zeta Function ===
=== Notable Local Maxima of the Riemann Zeta Function ===
{| class="wikitable sortable"
{|class="wikitable sortable"
|+ style="font-size: 105%;" | Notable Local Maxima of the Riemann Zeta Function
|+ style="font-size: 105%;" | Zeta Peak Indexes at sigma = 1, filtered with (height ≥ 2.5 and cents ≥ 40.0) or (height ≥ 2.8 and cents ≥ 12.0)
|- style="white-space: nowrap;"
|-
! colspan="3" |Tuning
!colspan="3"|Tuning
! colspan="3" |Strength
!colspan="1"|Strength
! colspan="2" |Closest EDO
!colspan="2"|Closest EDO
! colspan="2" |Integer limit
!colspan="2"|Integer limit
|-
|-
!ZPI
!ZPI (σ = 1)
!Steps per octave
!Steps per octave
!Cents
!Step size (cents)
!Height
!Height
!Integral
!Gap
!EDO
!EDO
!Octave
!Octave (cents)
!Consistent
!Consistent
!Distinct
!Distinct
|-
|-
|[[34zpi]]
|[[15zpi (σ = 1)]]
|12.0231830072926
|6.95688550773
|99.8071807833375
|172.490980147
|5.193290
|2.55384
|1.269599
|[[7edo]]
|15.899282
|1207.43686103
|6
|5
|-
|[[26zpi (σ = 1)]]
|10.0089746115
|119.892401228
|2.57426
|[[10edo]]
|1198.92401228
|8
|5
|-
|[[34zpi (σ = 1)]]
|12.0220488259
|99.8165967700
|2.85866
|[[12edo]]
|[[12edo]]
|1197.68616940005
|1197.79916124
|10
|10
|6
|6
|-
|-
|[[42zpi]]
|[[42zpi (σ = 1)]]
|13.9002525327005
|13.9020220557
|86.3293668353859
|86.3183783764
|4.592177
|2.50514
|0.984037
|14.097244
|[[14edo]]
|[[14edo]]
|1208.61113569540
|1208.45729727
|7
|7
|5
|5
|-
|-
|[[47zpi]]
|[[47zpi (σ = 1)]]
|15.0534898676781
|15.0534708836
|79.7157343943591
|79.7158349246
|5.050324
|2.69313
|1.104057
|14.918297
|[[15edo]]
|[[15edo]]
|1195.73601591539
|1195.73752387
|8
|8
|7
|7
|-
|-
|[[56zpi]]
|[[56zpi (σ = 1)]]
|17.0445886606675
|17.0432556931
|70.4035764012981
|70.4090827252
|5.056957
|2.65741
|1.032175
|14.269437
|[[17edo]]
|[[17edo]]
|1196.86079882207
|1196.95440633
|4
|4
|4
|4
|-
|-
|[[65zpi]]
|[[65zpi (σ = 1)]]
|18.9480867166984
|18.9489976130
|63.3309324546460
|63.3278880767
|5.980169
|3.02387
|1.313799
|16.699651
|[[19edo]]
|[[19edo]]
|1203.28771663827
|1203.22987346
|10
|10
|7
|7
|-
|-
|[[80zpi]]
|[[80zpi (σ = 1)]]
|22.0251467420146
|22.0251749360
|54.4831784348982
|54.4831086920
|6.062600
|2.99601
|1.258178
|16.213941
|[[22edo]]
|[[22edo]]
|1198.62992556776
|1198.62839122
|12
|12
|8
|8
|-
|-
|[[90zpi]]
|[[90zpi (σ = 1)]]
|24.0057421830853
|24.0053572889
|49.9880399800983
|49.9888414723
|5.721613
|2.82476
|1.092055
|14.821136
|[[24edo]]
|[[24edo]]
|1199.71295952236
|1199.73219533
|6
|6
|6
|6
|-
|-
|[[100zpi]]
|[[100zpi (σ = 1)]]
|25.9356996537225
|25.9356337472
|46.2682717652372
|46.2683893402
|5.545073
|2.71167
|1.031155
|14.793013
|[[26edo]]
|[[26edo]]
|1202.97506589617
|1202.97812285
|14
|14
|9
|9
|-
|-
|[[106zpi]]
|[[106zpi (σ = 1)]]
|27.0866140827635
|27.0853383248
|44.3023257293579
|44.3044124320
|6.069233
|2.90524
|1.185939
|16.215619
|[[27edo]]
|[[27edo]]
|1196.16279469266
|1196.21913566
|10
|10
|8
|8
|-
|-
|[[116zpi]]
|[[116zpi (σ = 1)]]
|28.9399661541990
|28.9431579907
|41.4651487014917
|41.4605759463
|5.566209
|2.68561
|1.000619
|14.904418
|[[29edo]]
|[[29edo]]
|1202.48931234326
|1202.35670244
|8
|8
|7
|7
|-
|-
|[[127zpi]]
|[[127zpi (σ = 1)]]
|30.9783816349790
|30.9779815456
|38.7366910944446
|38.7371913897
|7.003472
|3.23190
|1.403777
|17.739476
|[[31edo]]
|[[31edo]]
|1200.83742392778
|1200.85293308
|12
|12
|9
|9
|-
|-
|[[144zpi]]
|[[144zpi (σ = 1)]]
|34.0448410043159
|34.0437506778
|35.2476312005063
|35.2487600839
|6.685147
|3.07414
|1.241437
|16.236989
|[[34edo]]
|[[34edo]]
|1198.41946081721
|1198.45784285
|6
|6
|6
|6
|-
|-
|[[155zpi]]
|[[155zpi (σ = 1)]]
|35.9823877000425
|35.9827898689
|33.3496490006021
|33.3492762616
|6.027497
|2.80355
|1.028887
|14.706508
|[[36edo]]
|[[36edo]]
|1200.58736402167
|1200.57394542
|8
|8
|8
|8
|-
|-
|[[184zpi]]
|[[184zpi (σ = 1)]]
|40.9880783925993
|40.9880790756
|29.2768055263764
|29.2768050385
|7.570230
|3.32966
|1.423937
|17.722623
|[[41edo]]
|[[41edo]]
|1200.34902658143
|1200.34900658
|16
|16
|10
|10
|-
|-
|[[214zpi]]
|[[214zpi (σ = 1)]]
|46.0089748051542
|46.0106419996
|26.0818678330031
|26.0809227572
|7.495674
|3.25119
|1.356067
|17.747832
|[[46edo]]
|[[46edo]]
|1199.76592031814
|1199.72244683
|14
|14
|11
|11
|-
|-
|[[238zpi]]
|[[238zpi (σ = 1)]]
|49.9385162652878
|49.9382924730
|24.0295485277387
|24.0296562132
|6.655352
|2.90274
|1.111229
|15.942083
|[[50edo]]
|[[50edo]]
|1201.47742638693
|1201.48281066
|10
|10
|9
|9
|-
|-
|[[257zpi]]
|[[257zpi (σ = 1)]]
|52.9968291550147
|52.9969882711
|22.6428640945673
|22.6427961125
|8.249774
|3.46399
|1.486620
|18.069918
|[[53edo]]
|[[53edo]]
|1200.07179701207
|1200.06819396
|10
|10
|10
|10
|-
|-
|[[289zpi]]
|[[289zpi (σ = 1)]]
|58.0667185533159
|58.0645692462
|20.6658827964969
|20.6666477609
|7.814035
|3.25823
|1.358357
|18.056292
|[[58edo]]
|[[58edo]]
|1198.62120219682
|1198.66557013
|16
|16
|12
|12
|-
|-
|[[301zpi]]
|[[301zpi (σ = 1)]]
|59.9201656607655
|59.9223835273
|20.0266469020418
|20.0259056693
|7.046396
|2.98826
|1.131000
|15.932359
|[[60edo]]
|[[60edo]]
|1201.59881412251
|1201.55434016
|10
|10
|10
|10
|-
|-
|[[334zpi]]
|[[321zpi (σ = 1)]]
|65.0158450885860
|63.0197888699
|18.4570391781413
|19.0416378969
|7.813349
|2.87513
|1.269821
|[[63edo]]
|16.514861
|1199.62318750
|8
|8
|-
|[[334zpi (σ = 1)]]
|65.0145858034
|18.4573966776
|3.23462
|[[65edo]]
|[[65edo]]
|1199.70754657919
|1199.73078404
|6
|6
|6
|6
|-
|-
|[[354zpi]]
|[[354zpi (σ = 1)]]
|68.0493056282519
|68.0496579343
|17.6342725163943
|17.6341812204
|7.666604
|3.14200
|1.254592
|17.034505
|[[68edo]]
|[[68edo]]
|1199.13053111481
|1199.12432299
|10
|10
|10
|10
|-
|-
|[[380zpi]]
|[[380zpi (σ = 1)]]
|71.9506065993786
|71.9512656175
|16.6781081733140
|16.6779554147
|9.157547
|3.61665
|1.625363
|19.964746
|[[72edo]]
|[[72edo]]
|1200.82378847861
|1200.81278986
|18
|18
|13
|13
|-
|-
|[[414zpi]]
|[[414zpi (σ = 1)]]
|76.9918536925042
|76.9924672555
|15.5860645308353
|15.5859403235
|8.194847
|3.28825
|1.311364
|17.029289
|[[77edo]]
|[[77edo]]
|1200.12696887432
|1200.11740491
|10
|10
|10
|10
|-
|-
|[[435zpi]]
|[[435zpi (σ = 1)]]
|80.0731374302484
|80.0733926855
|14.9862992572924
|14.9862514845
|7.873146
|3.14833
|1.247325
|17.087322
|[[80edo]]
|[[80edo]]
|1198.90394058339
|1198.90011876
|12
|12
|12
|12
|-
|-
|[[462zpi]]
|[[462zpi (σ = 1)]]
|83.9972142607288
|83.9950884037
|14.2861880666087
|14.2865496400
|8.020965
|3.19687
|1.241945
|16.733121
|[[84edo]]
|[[84edo]]
|1200.03979759513
|1200.07016976
|10
|10
|10
|10
|-
|-
|[[483zpi]]
|[[483zpi (σ = 1)]]
|87.0139255957575
|87.0139579095
|13.7908960178956
|13.7908908965
|8.869041
|3.44872
|1.439474
|18.061741
|[[87edo]]
|[[87edo]]
|1199.80795355692
|1199.80750799
|16
|16
|14
|14
|-
|-
|[[532zpi]]
|[[497zpi (σ = 1)]]
|93.9836761074943
|89.0215260329
|12.7681747480009
|13.4798857476
|8.806201
|3.02681
|1.394050
|[[89edo]]
|17.832744
|1199.70983154
|[[94edo]]
|1200.20842631208
|24
|15
|-
|[[568zpi]]
|99.0473345956631
|12.1154194093028
|9.406495
|1.510412
|18.536483
|[[99edo]]
|1199.42652152097
|12
|12
|12
|12
|-
|-
|[[596zpi]]
|[[532zpi (σ = 1)]]
|102.936629522070
|93.9843698073
|11.6576577800491
|12.7680805059
|8.543510
|3.39762
|1.340775
|[[94edo]]
|18.270998
|1200.19956756
|[[103edo]]
|24
|1200.73875134506
|15
|15
|15
|-
|-
|[[655zpi]]
|[[546zpi (σ = 1)]]
|111.059577998833
|95.9558568688
|10.8050113427643
|12.5057504477
|9.038544
|2.93099
|1.394739
|[[96edo]]
|18.041165
|1200.55204298
|[[111edo]]
|6
|1199.35625904684
|6
|22
|16
|-
|-
|[[706zpi]]
|[[568zpi (σ = 1)]]
|117.969513574257
|99.0456175574
|10.1721195895637
|12.1156294402
|9.850823
|3.56676
|1.544280
|[[99edo]]
|18.861062
|1199.44731458
|[[118edo]]
|1200.31011156852
|12
|12
|12
|12
|-
|[[796zpi]]
|130.003910460506
|9.23049157328654
|10.355108
|1.634018
|19.594551
|[[130edo]]
|1199.96390452725
|16
|16
|-
|[[872zpi]]
|139.990541024216
|8.57200773152536
|10.076688
|1.548424
|19.514765
|[[140edo]]
|1200.08108241355
|10
|10
|-
|[[965zpi]]
|152.052848107925
|7.89199291517551
|10.468420
|1.593855
|19.487224
|[[152edo]]
|1199.58292310668
|15
|15
|-
|[[1114zpi]]
|170.995891689006
|7.01771246166817
|11.076998
|1.652856
|19.091741
|[[171edo]]
|1200.02883094526
|14
|14
|}
|}


Line 1,163: Line 1,073:
|25
|25
|}
|}
</s>
 
=== The α–β–γ family ===
=== The α–β–γ family ===
{| class="wikitable sortable"
{| class="wikitable sortable"
Retrieved from "https://en.xen.wiki/w/User:Contribution/Collection_of_tunings"