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User:Contribution/Collection of tunings: Difference between revisions

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Line 16: Line 16:
=== 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%;" | Zeta Peak Indexes at sigma = 1, filtered with (height ≥ 2.5 and cents ≥ 40.0) or (height ≥ 2.8 and cents ≥ 12.0) or (height ≥ 3.25 and cents ≥ 10.0) or (height ≥ 3.6 and cents ≥ 6.0)
|+ style="font-size: 105%;" |
|-
|-
!colspan="3"|Tuning
!colspan="3"|Tuning
Line 175: Line 175:
|16
|16
|10
|10
|-
|[[196zpi (σ = 1)]]
|43.0234004818
|27.8917981043
|2.78019
|[[43edo]]
|1199.34731849
|8
|8
|-
|-
|[[214zpi (σ = 1)]]
|[[214zpi (σ = 1)]]
Line 310: Line 319:
|24
|24
|15
|15
|-
|[[546zpi (σ = 1)]]
|95.9558568688
|12.5057504477
|2.93099
|[[96edo]]
|1200.55204298
|6
|6
|-
|-
|[[568zpi (σ = 1)]]
|[[568zpi (σ = 1)]]
Line 550: Line 550:


{|class="wikitable sortable"
{|class="wikitable sortable"
|+ style="font-size: 105%;" | Zeta Peak Indexes at sigma = 1, filtered with (height ≥ 1.875 and cents ≥ 6.0)
|+ style="font-size: 105%;" | Zeta Peak Indexes at sigma = 1, filtered with (height ≥ 2.075 and cents ≥ 6.0)
!colspan="3"|Tuning
!colspan="3"|Tuning
!colspan="1"|Strength
!colspan="1"|Strength
Line 564: Line 564:
!Consistent
!Consistent
!Distinct
!Distinct
|-
|[[no-2 19zpi (σ = 1)]]
|8.18712929074
|146.571521883
|1.87661
|[[13edt]]
|1905.42978449
|15
|11
|-
|[[no-2 29zpi (σ = 1)]]
|10.7334869381
|111.799642271
|1.95394
|[[17edt]]
|1900.59391860
|17
|11
|-
|[[no-2 53zpi (σ = 1)]]
|16.4033618519
|73.1557354420
|2.01896
|[[26edt]]
|1902.04912149
|21
|15
|-
|[[no-2 71zpi (σ = 1)]]
|20.2433432017
|59.2787460076
|2.00269
|[[32edt]]
|1896.91987224
|21
|15
|-
|[[no-2 84zpi (σ = 1)]]
|22.7835155508
|52.6696592247
|1.89685
|[[36edt]]
|1896.10773209
|17
|13
|-
|-
|[[no-2 93zpi (σ = 1)]]
|[[no-2 93zpi (σ = 1)]]
Line 617: Line 572:
|1904.39575293
|1904.39575293
|15
|15
|15
|-
|[[no-2 106zpi (σ = 1)]]
|27.1258094838
|44.2383111448
|1.97822
|[[43edt]]
|1902.24737923
|11
|11
|-
|[[no-2 113zpi (σ = 1)]]
|28.4085507996
|42.2408030759
|1.96399
|[[45edt]]
|1900.83613842
|9
|9
|-
|[[no-2 137zpi (σ = 1)]]
|32.7488975372
|36.6424548685
|2.02055
|[[52edt]]
|1905.40765316
|25
|15
|15
|-
|-
Line 654: Line 582:
|15
|15
|15
|15
|-
|[[no-2 166zpi (σ = 1)]]
|37.8594891129
|31.6961487891
|1.97021
|[[60edt]]
|1901.76892734
|15
|15
|-
|[[no-2 173zpi (σ = 1)]]
|39.1519961740
|30.6497782301
|1.99822
|[[62edt]]
|1900.28625027
|9
|9
|-
|[[no-2 199zpi (σ = 1)]]
|43.5167998698
|27.5755571088
|2.05686
|[[69edt]]
|1902.71344050
|9
|9
|-
|-
|[[no-2 207zpi (σ = 1)]]
|[[no-2 207zpi (σ = 1)]]
Line 708: Line 609:
|21
|21
|21
|21
|-
|[[no-2 249zpi (σ = 1)]]
|51.6879877530
|23.2162259002
|2.03774
|[[82edt]]
|1903.73052382
|17
|17
|-
|-
|[[no-2 273zpi (σ = 1)]]
|[[no-2 273zpi (σ = 1)]]
Line 726: Line 618:
|11
|11
|11
|11
|-
|[[no-2 289zpi (σ = 1)]]
|58.0976839265
|20.6548681272
|1.99993
|[[92edt]]
|1900.24786771
|15
|15
|-
|[[no-2 301zpi (σ = 1)]]
|59.8907003349
|20.0364997118
|1.93131
|[[95edt]]
|1903.46747262
|11
|11
|-
|[[no-2 309zpi (σ = 1)]]
|61.2052267978
|19.6061686686
|1.96785
|[[97edt]]
|1901.79836086
|11
|11
|-
|[[no-2 317zpi (σ = 1)]]
|62.4122030931
|19.2270091509
|2.07392
|[[99edt]]
|1903.47390594
|25
|23
|-
|[[no-2 326zpi (σ = 1)]]
|63.7602215687
|18.8205117623
|2.05280
|[[101edt]]
|1900.87168799
|9
|9
|-
|[[no-2 342zpi (σ = 1)]]
|66.2583876236
|18.1109146033
|2.06825
|[[105edt]]
|1901.64603334
|17
|17
|-
|-
|[[no-2 363zpi (σ = 1)]]
|[[no-2 363zpi (σ = 1)]]
Line 798: Line 636:
|17
|17
|17
|17
|-
|[[no-2 397zpi (σ = 1)]]
|74.4867252346
|16.1102531521
|1.92629
|[[118edt]]
|1901.00987195
|15
|15
|-
|[[no-2 409zpi (σ = 1)]]
|76.2807590080
|15.7313589378
|1.97954
|[[121edt]]
|1903.49443147
|25
|23
|-
|[[no-2 418zpi (σ = 1)]]
|77.5713604064
|15.4696268534
|1.90376
|[[123edt]]
|1902.76410297
|9
|9
|-
|[[no-2 435zpi (σ = 1)]]
|80.1032694573
|14.9806619396
|1.99098
|[[127edt]]
|1902.54406634
|11
|11
|-
|-
|[[no-2 453zpi (σ = 1)]]
|[[no-2 453zpi (σ = 1)]]
Line 861: Line 663:
|39
|39
|27
|27
|-
|[[no-2 519zpi (σ = 1)]]
|92.1840749628
|13.0174327885
|1.99259
|[[146edt]]
|1900.54518712
|17
|17
|-
|-
|[[no-2 550zpi (σ = 1)]]
|[[no-2 550zpi (σ = 1)]]
Line 879: Line 672:
|15
|15
|15
|15
|-
|[[no-2 568zpi (σ = 1)]]
|99.0730275901
|12.1122774704
|2.00937
|[[157edt]]
|1901.62756285
|11
|11
|-
|[[no-2 577zpi (σ = 1)]]
|100.316260311
|11.9621684090
|1.98584
|[[159edt]]
|1901.98477703
|11
|11
|-
|[[no-2 596zpi (σ = 1)]]
|102.908364024
|11.6608597502
|1.96654
|[[163edt]]
|1900.72013927
|15
|15
|-
|[[no-2 609zpi (σ = 1)]]
|104.713326539
|11.4598594053
|2.00635
|[[166edt]]
|1902.33666128
|11
|11
|-
|[[no-2 614zpi (σ = 1)]]
|105.436045548
|11.3813069692
|1.92595
|[[167edt]]
|1900.67826385
|23
|23
|-
|-
|[[no-2 627zpi (σ = 1)]]
|[[no-2 627zpi (σ = 1)]]
Line 933: Line 681:
|15
|15
|15
|15
|-
|[[no-2 646zpi (σ = 1)]]
|109.793603482
|10.9295984642
|1.96998
|[[174edt]]
|1901.75013278
|15
|15
|-
|[[no-2 655zpi (σ = 1)]]
|111.085500608
|10.8024899148
|2.00672
|[[176edt]]
|1901.23822501
|21
|21
|-
|[[no-2 659zpi (σ = 1)]]
|111.586744725
|10.7539654729
|1.88303
|[[177edt]]
|1903.45188870
|7
|7
|-
|-
|[[no-2 687zpi (σ = 1)]]
|[[no-2 687zpi (σ = 1)]]
Line 978: Line 699:
|29
|29
|29
|29
|-
|[[no-2 706zpi (σ = 1)]]
|117.949591604
|10.1738376851
|1.91643
|[[187edt]]
|1902.50764711
|11
|11
|-
|[[no-2 725zpi (σ = 1)]]
|120.530724507
|9.95596769960
|1.89765
|[[191edt]]
|1901.58983062
|5
|5
|-
|[[no-2 729zpi (σ = 1)]]
|121.102378223
|9.90897138117
|2.05767
|[[192edt]]
|1902.52250518
|17
|17
|-
|[[no-2 748zpi (σ = 1)]]
|123.601895646
|9.70858896401
|1.91762
|[[196edt]]
|1902.88343695
|11
|11
|-
|[[no-2 753zpi (σ = 1)]]
|124.304838560
|9.65368696748
|1.91680
|[[197edt]]
|1901.77633259
|21
|21
|-
|[[no-2 767zpi (σ = 1)]]
|126.183698594
|9.50994473428
|2.05769
|[[200edt]]
|1901.98894686
|9
|9
|-
|-
|[[no-2 777zpi (σ = 1)]]
|[[no-2 777zpi (σ = 1)]]
Line 1,077: Line 744:
|11
|11
|11
|11
|-
|[[no-2 878zpi (σ = 1)]]
|140.756053126
|8.52538823977
|1.91894
|[[223edt]]
|1901.16157747
|15
|15
|-
|[[no-2 882zpi (σ = 1)]]
|141.320264620
|8.49135121014
|1.94097
|[[224edt]]
|1902.06267107
|17
|17
|-
|-
|[[no-2 902zpi (σ = 1)]]
|[[no-2 902zpi (σ = 1)]]
Line 1,104: Line 753:
|11
|11
|11
|11
|-
|[[no-2 911zpi (σ = 1)]]
|145.102065664
|8.27004077793
|1.96452
|[[230edt]]
|1902.10937892
|23
|23
|-
|[[no-2 921zpi (σ = 1)]]
|146.379932964
|8.19784498941
|1.96989
|[[232edt]]
|1901.90003754
|9
|9
|-
|[[no-2 945zpi (σ = 1)]]
|149.470277594
|8.02835198621
|1.92855
|[[237edt]]
|1902.71942073
|19
|19
|-
|-
|[[no-2 965zpi (σ = 1)]]
|[[no-2 965zpi (σ = 1)]]
Line 1,149: Line 771:
|21
|21
|21
|21
|-
|[[no-2 995zpi (σ = 1)]]
|155.863142206
|7.69906202978
|1.88900
|[[247edt]]
|1901.66832135
|7
|7
|-
|[[no-2 1019zpi (σ = 1)]]
|158.932236585
|7.55038767329
|1.94652
|[[252edt]]
|1902.69769367
|15
|15
|-
|-
|[[no-2 1029zpi (σ = 1)]]
|[[no-2 1029zpi (σ = 1)]]
Line 1,194: Line 798:
|17
|17
|17
|17
|-
|[[no-2 1083zpi (σ = 1)]]
|167.112289634
|7.18080042243
|1.93984
|[[265edt]]
|1902.91211194
|11
|11
|-
|[[no-2 1104zpi (σ = 1)]]
|169.714157484
|7.07071241310
|1.92771
|[[269edt]]
|1902.02163912
|15
|15
|-
|[[no-2 1114zpi (σ = 1)]]
|170.990381058
|7.01793862657
|1.91502
|[[271edt]]
|1901.86136780
|9
|9
|-
|-
|[[no-2 1134zpi (σ = 1)]]
|[[no-2 1134zpi (σ = 1)]]
Line 1,230: Line 807:
|29
|29
|29
|29
|-
|[[no-2 1145zpi (σ = 1)]]
|174.860916353
|6.86259700012
|1.98752
|[[277edt]]
|1900.93936903
|15
|15
|-
|-
|[[no-2 1159zpi (σ = 1)]]
|[[no-2 1159zpi (σ = 1)]]
Line 1,257: Line 825:
|15
|15
|15
|15
|-
|[[no-2 1200zpi (σ = 1)]]
|181.734924328
|6.60302363146
|1.98334
|[[288edt]]
|1901.67080586
|11
|11
|-
|[[no-2 1210zpi (σ = 1)]]
|183.000523023
|6.55735830793
|1.88033
|[[290edt]]
|1901.63390930
|17
|17
|-
|[[no-2 1225zpi (σ = 1)]]
|184.832854856
|6.49235224405
|1.92540
|[[293edt]]
|1902.25920751
|9
|9
|-
|-
|[[no-2 1245zpi (σ = 1)]]
|[[no-2 1245zpi (σ = 1)]]
Line 1,311: Line 852:
|21
|21
|21
|21
|-
|[[no-2 1301zpi (σ = 1)]]
|194.272130007
|6.17690247159
|1.87710
|[[308edt]]
|1902.48596125
|7
|7
|-
|[[no-2 1312zpi (σ = 1)]]
|195.595668163
|6.13510519569
|1.92538
|[[310edt]]
|1901.88261066
|9
|9
|-
|[[no-2 1332zpi (σ = 1)]]
|198.083101013
|6.05806347873
|2.07112
|[[314edt]]
|1902.23193232
|15
|15
|-
|-
|[[no-2 1343zpi (σ = 1)]]
|[[no-2 1343zpi (σ = 1)]]
Line 1,352: Line 866:


{|class="wikitable sortable"
{|class="wikitable sortable"
|+ style="font-size: 105%;" | Zeta Peak Indexes at sigma = 1, filtered with (height ≥ 1.725 and cents ≥ 6.0)
!colspan="3"|Tuning
!colspan="3"|Tuning
!colspan="3"|Strength
!colspan="1"|Strength
!colspan="2"|Closest ED5
!colspan="2"|Closest ED5
!colspan="2"|No-2 No-3 Integer limit
!colspan="2"|No-2 No-3 Integer limit
Line 1,361: Line 876:
!Cents
!Cents
!Height
!Height
!Integral
!Gap
!ED5
!ED5
!Pentave
!Pentave
Line 1,368: Line 881:
!Distinct
!Distinct
|-
|-
|[[no-2 no-3 55zpi analog]]
|[[no-2 no-3 186zpi (σ = 1)]]
|16.7630030425585
|41.3464998527
|71.5862185882446
|29.0230129340
|3.480299
|1.75534
|0.477759
|9.649416
|[[39ed5]]
|2791.86252494154
|13
|13
|-
|[[no-2 no-3 125zpi analog]]
|30.5974484926723
|39.2189564527704
|3.769318
|0.448541
|9.828199
|[[71ed5]]
|2784.54590814670
|19
|19
|-
|[[no-2 no-3 176zpi analog]]
|39.5828667040955
|30.3161468564337
|3.603524
|0.421674
|10.452207
|[[92ed5]]
|2789.08551079190
|11
|11
|-
|[[no-2 no-3 186zpi analog]]
|41.3477989230936
|29.0221010852836
|4.469823
|0.556068
|11.567493
|[[96ed5]]
|[[96ed5]]
|2786.12170418722
|2786.20924167
|35
|35
|23
|23
|-
|-
|[[no-2 no-3 212zpi analog]]
|[[no-2 no-3 565zpi (σ = 1)]]
|45.6783815054539
|98.6253027359
|26.2706330752267
|12.1672630320
|3.818225
|1.74188
|0.433470
|10.611042
|[[106ed5]]
|2784.68710597403
|13
|13
|-
|[[no-2 no-3 235zpi analog]]
|49.4631517377883
|24.2604839732289
|3.853032
|0.428042
|10.508697
|[[115ed5]]
|2789.95565692132
|25
|25
|-
|[[no-2 no-3 284zpi analog]]
|57.2705618247184
|20.9531731794898
|3.913350
|0.465932
|11.922515
|[[133ed5]]
|2786.77203287214
|17
|17
|-
|[[no-2 no-3 298zpi analog]]
|59.4923782274424
|20.1706510271339
|4.083075
|0.465782
|11.463643
|[[138ed5]]
|2783.54984174448
|23
|23
|-
|[[no-2 no-3 312zpi analog]]
|61.6047959566046
|19.4790029147292
|4.416896
|0.501431
|11.339301
|[[143ed5]]
|2785.49741680628
|25
|23
|-
|[[no-2 no-3 340zpi analog]]
|65.8904943328257
|18.2120351676004
|4.092923
|0.526694
|13.998526
|[[153ed5]]
|2786.44138064287
|13
|13
|-
|[[no-2 no-3 368zpi analog]]
|70.2158409653819
|17.0901606176251
|4.382540
|0.518334
|12.481351
|[[163ed5]]
|2785.69618067290
|19
|19
|-
|[[no-2 no-3 423zpi analog]]
|78.3601842342727
|15.3138996765548
|4.270381
|0.502072
|12.963711
|[[182ed5]]
|2787.12974113297
|19
|19
|-
|[[no-2 no-3 438zpi analog]]
|80.4944089071946
|14.9078677176639
|4.243838
|0.450422
|11.371118
|[[187ed5]]
|2787.77126320314
|7
|7
|-
|[[no-2 no-3 465zpi analog]]
|84.4075187897342
|14.2167429774745
|4.301350
|0.486089
|12.332303
|[[196ed5]]
|2786.48162358500
|17
|17
|-
|[[no-2 no-3 477zpi analog]]
|86.1814871554687
|13.9241041157161
|4.459348
|0.505570
|12.446285
|[[200ed5]]
|2784.82082314323
|25
|25
|-
|[[no-2 no-3 565zpi analog]]
|98.6257548378926
|12.1672072570942
|4.883729
|0.545550
|12.639964
|[[229ed5]]
|[[229ed5]]
|2786.29046187457
|2786.30323433
|29
|29
|29
|29
|-
|-
|[[no-2 no-3 581zpi analog]]
|[[no-2 no-3 671zpi (σ = 1)]]
|100.797128599965
|113.258011095
|11.9051010347969
|10.5952769998
|4.579796
|1.77217
|0.536282
|13.693791
|[[234ed5]]
|2785.79364214247
|25
|25
|-
|[[no-2 no-3 671zpi analog]]
|113.256639862217
|10.5954052800778
|5.104294
|0.563708
|12.937931
|[[263ed5]]
|[[263ed5]]
|2786.59158866045
|2786.55785095
|19
|19
|19
|19
|-
|-
|[[no-2 no-3 764zpi analog]]
|[[no-2 no-3 764zpi (σ = 1)]]
|125.745930952370
|125.745000550
|9.54305233506547
|9.54312294522
|5.001815
|1.75634
|0.548008
|12.976730
|[[292ed5]]
|[[292ed5]]
|2786.57128183912
|2786.59190001
|37
|37
|37
|37
|-
|-
|[[no-2 no-3 905zpi analog]]
|[[no-2 no-3 905zpi (σ = 1)]]
|144.300058486204
|144.297529480
|8.31600494545005
|8.31615069448
|5.030210
|1.73926
|0.539592
|13.254432
|[[335ed5]]
|[[335ed5]]
|2785.86165672577
|2785.91048265
|43
|43
|41
|41
|-
|-
|[[no-2 no-3 938zpi analog]]
|[[no-2 no-3 938zpi (σ = 1)]]
|148.561761173834
|148.562870929
|8.07744866861039
|8.07738833059
|5.510552
|1.79949
|0.600083
|13.846076
|[[345ed5]]
|[[345ed5]]
|2786.71979067058
|2786.69897405
|25
|25
|-
|[[no-2 no-3 1046zpi (σ = 1)]]
|162.414291729
|7.38851234841
|1.73251
|[[377ed5]]
|2785.46915535
|23
|23
|-
|[[no-2 no-3 1145zpi (σ = 1)]]
|174.880594782
|6.86182478678
|1.74084
|[[406ed5]]
|2785.90086343
|25
|25
|25
|25
|-
|[[no-2 no-3 1196zpi (σ = 1)]]
|181.292147244
|6.61915046096
|1.77770
|[[421ed5]]
|2786.66234406
|35
|35
|-
|[[no-2 no-3 1280zpi (σ = 1)]]
|191.632570168
|6.26198353937
|1.75036
|[[445ed5]]
|2786.58267502
|29
|29
|}
|}


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