Xenharmonic Wiki

User:Contribution/Collection of tunings: Difference between revisions

← Older edit
VisualWikitext
Contribution (talk | contribs)
3,348 edits
Contribution (talk | contribs)
3,348 edits
No edit summary
 
(17 intermediate revisions by the same user not shown)
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 400: Line 400:
|18
|18
|18
|18
|}
{{todo|use sigma 1.0|inline=1|comment=instead of sigma 1/2}}
=== Notable Local Maxima of the Riemann Zeta Function after removing the prime 2 from the zeta product ===
{|class="wikitable sortable"
!colspan="3"|Tuning
!colspan="3"|Strength
!colspan="2"|Closest EDT
!colspan="2"|No-2 Integer limit
|-
!No-2 ZPI analog
!Steps per octave
!Cents
!Height
!Integral
!Gap
!EDT
!Tritave
!Consistent
!Distinct
|-
|[[no-2 93zpi analog]]
|24.5738316304204
|48.8324335434323
|4.665720
|0.766618
|13.261693
|[[39edt]]
|1904.46490819386
|15
|15
|-
|[[no-2 151zpi analog]]
|35.3059427335609
|33.9886123153798
|4.738265
|0.709543
|13.081926
|[[56edt]]
|1903.36228966127
|15
|15
|-
|[[no-2 199zpi analog]]
|43.5176229677494
|27.5750355411028
|4.824506
|0.678480
|12.871286
|[[69edt]]
|1902.67745233609
|9
|9
|-
|[[no-2 207zpi analog]]
|44.8152489207676
|26.7766001282638
|4.819120
|0.732965
|14.719415
|[[71edt]]
|1901.13860910673
|17
|17
|-
|[[no-2 222zpi analog]]
|47.3521317910583
|25.3420480686067
|5.059485
|0.721113
|13.412098
|[[75edt]]
|1900.65360514550
|15
|15
|-
|[[no-2 233zpi analog]]
|49.1685275266548
|24.4058559481869
|4.790248
|0.736865
|15.624024
|[[78edt]]
|1903.65676395858
|21
|21
|-
|[[no-2 249zpi analog]]
|51.6860577447882
|23.2170928168922
|4.848916
|0.664134
|13.043858
|[[82edt]]
|1903.80161098516
|17
|17
|-
|[[no-2 273zpi analog]]
|55.5353711835277
|21.6078505360910
|5.441186
|0.771944
|14.061502
|[[88edt]]
|1901.49084717601
|11
|11
|-
|[[no-2 317zpi analog]]
|62.4092182976906
|19.2279287055965
|5.154539
|0.705887
|14.235540
|[[99edt]]
|1903.56494185405
|25
|23
|-
|[[no-2 326zpi analog]]
|63.7619933650274
|18.8199887843874
|4.961196
|0.662970
|13.437518
|[[101edt]]
|1900.81886722313
|9
|9
|-
|[[no-2 342zpi analog]]
|66.2581615380500
|18.1109764011620
|5.073625
|0.677884
|13.529076
|[[105edt]]
|1901.65252212201
|17
|17
|-
|[[no-2 363zpi analog]]
|69.4221749409126
|17.2855431426825
|5.247825
|0.705262
|14.276498
|[[110edt]]
|1901.40974569508
|23
|23
|-
|[[no-2 453zpi analog]]
|82.6705208991009
|14.5154522670130
|6.410342
|0.925687
|16.646686
|[[131edt]]
|1901.52424697870
|27
|27
|-
|[[no-2 492zpi analog]]
|88.3242305963095
|13.5863057271867
|5.480169
|0.696272
|13.636687
|[[140edt]]
|1902.08280180614
|9
|9
|-
|[[no-2 510zpi analog]]
|90.8297848520406
|13.2115252937654
|5.712975
|0.810755
|16.378662
|[[144edt]]
|1902.45964230221
|39
|27
|-
|[[no-2 550zpi analog]]
|96.5193707902430
|12.4327374927449
|6.047703
|0.795582
|14.790729
|[[153edt]]
|1902.20883638997
|15
|15
|-
|[[no-2 627zpi analog]]
|107.244707551072
|11.1893633485693
|6.217266
|0.828658
|15.375247
|[[170edt]]
|1902.19176925679
|15
|15
|-
|[[no-2 687zpi analog]]
|115.410497106759
|10.3976677172610
|5.985004
|0.754232
|14.631506
|[[183edt]]
|1902.77319225877
|15
|15
|-
|[[no-2 697zpi analog]]
|116.733331758968
|10.2798402300191
|5.835644
|0.746180
|15.041001
|[[185edt]]
|1901.77044255353
|29
|29
|-
|[[no-2 777zpi analog]]
|127.487421022497
|9.41269334947362
|6.134922
|0.758067
|14.474624
|[[202edt]]
|1901.36405659367
|17
|17
|-
|[[no-2 810zpi analog]]
|131.820548689719
|9.10328482112888
|6.140639
|0.820704
|16.484428
|[[209edt]]
|1902.58652761594
|21
|21
|-
|[[no-2 829zpi analog]]
|134.375301622234
|8.93021251311149
|5.870928
|0.707721
|14.252150
|[[213edt]]
|1902.13526529275
|29
|29
|-
|[[no-2 839zpi analog]]
|135.657235331861
|8.84582379306507
|5.733350
|0.672634
|13.637550
|[[215edt]]
|1901.85211550899
|15
|15
|-
|[[no-2 858zpi analog]]
|138.196733558228
|8.68327325185579
|5.998270
|0.762777
|15.383590
|[[219edt]]
|1901.63684215642
|11
|11
|-
|[[no-2 985zpi analog]]
|154.604938100947
|7.76171844664157
|7.104335
|0.924588
|16.674411
|[[245edt]]
|1901.62101942718
|21
|21
|}
|}


Line 844: Line 547:
|}
|}


=== Notable Local Maxima of the Riemann Zeta Function after removing the primes 2 and 3 from the zeta product ===
=== Notable Local Maxima of the Riemann Zeta Function after removing the prime 2 from the zeta product ===


{|class="wikitable sortable"
{|class="wikitable sortable"
|+ 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="3"|Strength
!colspan="1"|Strength
!colspan="2"|Closest ED5
!colspan="2"|Closest EDT
!colspan="2"|No-2 No-3 Integer limit
!colspan="2"|No-2 Integer limit
|-
|-
!No-2 No-3 ZPI analog
!No-2 ZPI (σ = 1)
!Steps per octave
!Steps per octave
!Cents
!Cents
!Height
!Height
!Integral
!EDT
!Gap
!Tritave
!ED5
!Pentave
!Consistent
!Consistent
!Distinct
!Distinct
|-
|-
|[[no-2 no-3 55zpi analog]]
|[[no-2 93zpi (σ = 1)]]
|16.7630030425585
|24.5747239922
|71.5862185882446
|48.8306603314
|3.480299
|2.12985
|0.477759
|[[39edt]]
|9.649416
|1904.39575293
|[[39ed5]]
|15
|2791.86252494154
|15
|13
|-
|13
|[[no-2 151zpi (σ = 1)]]
|35.3061077059
|33.9884534992
|2.08576
|[[56edt]]
|1903.35339595
|15
|15
|-
|[[no-2 207zpi (σ = 1)]]
|44.8164999984
|26.7758526445
|2.10342
|[[71edt]]
|1901.08553776
|17
|17
|-
|[[no-2 222zpi (σ = 1)]]
|47.3516876312
|25.3422857776
|2.11876
|[[75edt]]
|1900.67143332
|15
|15
|-
|-
|[[no-2 no-3 125zpi analog]]
|[[no-2 233zpi (σ = 1)]]
|30.5974484926723
|49.1657210129
|39.2189564527704
|24.4072491012
|3.769318
|2.07714
|0.448541
|[[78edt]]
|9.828199
|1903.76542989
|[[71ed5]]
|21
|2784.54590814670
|21
|19
|19
|-
|-
|[[no-2 no-3 176zpi analog]]
|[[no-2 273zpi (σ = 1)]]
|39.5828667040955
|55.5359583782
|30.3161468564337
|21.6076220712
|3.603524
|2.19450
|0.421674
|[[88edt]]
|10.452207
|1901.47074227
|[[92ed5]]
|2789.08551079190
|11
|11
|11
|11
|-
|-
|[[no-2 no-3 186zpi analog]]
|[[no-2 363zpi (σ = 1)]]
|41.3477989230936
|69.4191721809
|29.0221010852836
|17.2862908372
|4.469823
|2.08043
|0.556068
|[[110edt]]
|11.567493
|1901.49199210
|[[96ed5]]
|23
|2786.12170418722
|35
|23
|23
|-
|-
|[[no-2 no-3 212zpi analog]]
|[[no-2 380zpi (σ = 1)]]
|45.6783815054539
|71.9200195089
|26.2706330752267
|16.6852012582
|3.818225
|2.07565
|0.433470
|[[114edt]]
|10.611042
|1902.11294344
|[[106ed5]]
|17
|2784.68710597403
|17
|13
|-
|13
|[[no-2 453zpi (σ = 1)]]
|82.6700405439
|14.5155366092
|2.38406
|[[131edt]]
|1901.53529581
|27
|27
|-
|[[no-2 492zpi (σ = 1)]]
|88.3238806401
|13.5863595587
|2.12238
|[[140edt]]
|1902.09033822
|9
|9
|-
|[[no-2 510zpi (σ = 1)]]
|90.8334979880
|13.2109852266
|2.23067
|[[144edt]]
|1902.38187263
|39
|27
|-
|[[no-2 550zpi (σ = 1)]]
|96.5187261015
|12.4328205362
|2.24293
|[[153edt]]
|1902.22154203
|15
|15
|-
|[[no-2 627zpi (σ = 1)]]
|107.244021785
|11.1894348983
|2.29774
|[[170edt]]
|1902.20393272
|15
|15
|-
|[[no-2 687zpi (σ = 1)]]
|115.412802617
|10.3974600113
|2.18983
|[[183edt]]
|1902.73518207
|15
|15
|-
|-
|[[no-2 no-3 235zpi analog]]
|[[no-2 697zpi (σ = 1)]]
|49.4631517377883
|116.734850378
|24.2604839732289
|10.2797064983
|3.853032
|2.15793
|0.428042
|[[185edt]]
|10.508697
|1901.74570218
|[[115ed5]]
|29
|2789.95565692132
|29
|25
|25
|-
|-
|[[no-2 no-3 284zpi analog]]
|[[no-2 777zpi (σ = 1)]]
|57.2705618247184
|127.486291223
|20.9531731794898
|9.41277676594
|3.913350
|2.21095
|0.465932
|[[202edt]]
|11.922515
|1901.38090672
|[[133ed5]]
|2786.77203287214
|17
|17
|17
|17
|-
|-
|[[no-2 no-3 298zpi analog]]
|[[no-2 810zpi (σ = 1)]]
|59.4923782274424
|131.822840677
|20.1706510271339
|9.10312654342
|4.083075
|2.25360
|0.465782
|[[209edt]]
|11.463643
|1902.55344758
|[[138ed5]]
|21
|2783.54984174448
|21
|23
|-
|23
|[[no-2 829zpi (σ = 1)]]
|134.373782790
|8.93031345169
|2.13475
|[[213edt]]
|1902.15676521
|29
|29
|-
|[[no-2 839zpi (σ = 1)]]
|135.657892938
|8.84578091263
|2.11125
|[[215edt]]
|1901.84289622
|15
|15
|-
|[[no-2 858zpi (σ = 1)]]
|138.196070465
|8.68331491602
|2.20051
|[[219edt]]
|1901.64596661
|11
|11
|-
|[[no-2 902zpi (σ = 1)]]
|143.873905513
|8.34063686336
|2.09948
|[[228edt]]
|1901.66520485
|11
|11
|-
|[[no-2 965zpi (σ = 1)]]
|152.075713777
|7.89080629768
|2.10893
|[[241edt]]
|1901.68431774
|15
|15
|-
|[[no-2 985zpi (σ = 1)]]
|154.604034485
|7.76176381166
|2.40811
|[[245edt]]
|1901.63213386
|21
|21
|-
|[[no-2 1029zpi (σ = 1)]]
|160.260260060
|7.48782012177
|2.17192
|[[254edt]]
|1901.90631093
|9
|9
|-
|[[no-2 1049zpi (σ = 1)]]
|162.750022676
|7.37327086209
|2.14738
|[[258edt]]
|1902.30388242
|17
|17
|-
|-
|[[no-2 no-3 312zpi analog]]
|[[no-2 1069zpi (σ = 1)]]
|61.6047959566046
|165.332187903
|19.4790029147292
|7.25811480039
|4.416896
|2.19607
|0.501431
|[[262edt]]
|11.339301
|1901.62607770
|[[143ed5]]
|17
|2785.49741680628
|17
|25
|23
|-
|-
|[[no-2 no-3 340zpi analog]]
|[[no-2 1134zpi (σ = 1)]]
|65.8904943328257
|173.506549648
|18.2120351676004
|6.91616542681
|4.092923
|2.26764
|0.526694
|[[275edt]]
|13.998526
|1901.94549237
|[[153ed5]]
|29
|2786.44138064287
|29
|13
|13
|-
|-
|[[no-2 no-3 368zpi analog]]
|[[no-2 1159zpi (σ = 1)]]
|70.2158409653819
|176.625850825
|17.0901606176251
|6.79402247404
|4.382540
|2.14379
|0.518334
|[[280edt]]
|12.481351
|1902.32629273
|[[163ed5]]
|11
|2785.69618067290
|11
|19
|19
|-
|-
|[[no-2 no-3 423zpi analog]]
|[[no-2 1179zpi (σ = 1)]]
|78.3601842342727
|179.167803205
|15.3138996765548
|6.69763193238
|4.270381
|2.29964
|0.502072
|[[284edt]]
|12.963711
|1902.12746880
|[[182ed5]]
|15
|2787.12974113297
|15
|19
|19
|-
|-
|[[no-2 no-3 438zpi analog]]
|[[no-2 1245zpi (σ = 1)]]
|80.4944089071946
|187.354933401
|14.9078677176639
|6.40495544056
|4.243838
|2.28021
|0.450422
|[[297edt]]
|11.371118
|1902.27176585
|[[187ed5]]
|21
|2787.77126320314
|21
|7
|7
|-
|-
|[[no-2 no-3 465zpi analog]]
|[[no-2 1266zpi (σ = 1)]]
|84.4075187897342
|189.909845446
|14.2167429774745
|6.31878772364
|4.301350
|2.17116
|0.486089
|[[301edt]]
|12.332303
|1901.95510482
|[[196ed5]]
|2786.48162358500
|17
|17
|17
|17
|-
|-
|[[no-2 no-3 477zpi analog]]
|[[no-2 1297zpi (σ = 1)]]
|86.1814871554687
|193.736743714
|13.9241041157161
|6.19397217583
|4.459348
|2.12380
|0.505570
|[[307edt]]
|12.446285
|1901.54945798
|[[200ed5]]
|21
|2784.82082314323
|21
|25
|-
|25
|[[no-2 1343zpi (σ = 1)]]
|199.415414525
|6.01758897555
|2.36503
|[[316edt]]
|1901.55811627
|39
|39
|}
 
=== Notable Local Maxima of the Riemann Zeta Function after removing the primes 2 and 3 from the zeta product ===
 
{|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="1"|Strength
!colspan="2"|Closest ED5
!colspan="2"|No-2 No-3 Integer limit
|-
!No-2 No-3 ZPI analog
!Steps per octave
!Cents
!Height
!ED5
!Pentave
!Consistent
!Distinct
|-
|[[no-2 no-3 186zpi (σ = 1)]]
|41.3464998527
|29.0230129340
|1.75534
|[[96ed5]]
|2786.20924167
|35
|23
|-
|-
|[[no-2 no-3 565zpi analog]]
|[[no-2 no-3 565zpi (σ = 1)]]
|98.6257548378926
|98.6253027359
|12.1672072570942
|12.1672630320
|4.883729
|1.74188
|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
|}
|}


Retrieved from "https://en.xen.wiki/w/User:Contribution/Collection_of_tunings"