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Table of zeta-stretched edos: Difference between revisions

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BudjarnLambeth (talk | contribs)
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BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,280 edits
Corrected my maths mistakes, and chose a single zeta tuning for those edos where I previously listed two (I was originally indecisive over whether to prioritise peak height or closeness to the edo, but after looking at the Tenney and Weil tunings for the edos I decided to prioritise peak height because that lines up better)
Line 16: Line 16:
!No. of steps per 1200 cents
!No. of steps per 1200 cents
!Step size (cents)
!Step size (cents)
!Octave size (cents)
!Tuning of 2/1 (cents)
!Zeta peak height
!Gram point index
!Gram point index
|-
|-
Line 23: Line 22:
|1edo
|1edo
|1.127
|1.127
|1064.774
|1065.177
|1064.774
|1065.177
|1.6
|  -1
|  -1
|-
|-
|[[2zpi]]
|[[2zpi]]
|2edo
|2edo
|1.972
|1.973
|608.519
|608.283
|1217.039
|1216.565
|2.3
|0
|0
|-
|-
|[[4zpi]]
|[[4zpi]]
|3edo
|3edo
|3.06
|3.060
|392.157
|392.187
|1176.471
|1176.562
|2.8
|2
|2
|-
|-
Line 47: Line 43:
|4edo
|4edo
|3.904
|3.904
|307.377
|307.342
|1229.508
|1229.367
|3.0
|4
|4
|-
|-
Line 55: Line 50:
|5edo
|5edo
|5.034
|5.034
|238.379
|238.357
|1191.895
|1191.783
|3.7
|7
|7
|-
|-
Line 63: Line 57:
|6edo
|6edo
|6.035
|6.035
|198.840
|198.843
|1193.041
|1193.056
|2.9
|10
|10
|-
|-
Line 71: Line 64:
|7edo
|7edo
|6.957
|6.957
|172.488
|172.496
|1207.417
|1207.471
|4.2
|13
|13
|-
|-
Line 79: Line 71:
|8edo
|8edo
|8.137
|8.137
|147.474
|147.467
|1179.796
|1179.734
|3.6
|17
|17
|-
|-
|[[22zpi]]
|[[22zpi]]
|9edo
|9edo
|8.95
|8.950
|134.078
|134.078
|1206.704
|1206.705
|4.0
|20
|20
|-
|-
Line 95: Line 85:
|10edo
|10edo
|10.008
|10.008
|119.904
|119.899
|1199.041
|1198.986
|4.5
|24
|24
|-
|-
Line 103: Line 92:
|11edo
|11edo
|11.037
|11.037
|108.725
|108.722
|1195.977
|1195.938
|2.7
|28
|28
|-
|-
Line 111: Line 99:
|12edo
|12edo
|12.023
|12.023
|99.809
|99.807
|1197.704
|1197.686
|5.2
|32
|32
|-
|-
Line 119: Line 106:
|13edo
|13edo
|12.969
|12.969
|92.528
|92.531
|1202.868
|1202.900
|3.1
|36
|36
|-
|-
|[[42zpi]]
|[[42zpi]]
|14edo
|14edo
|13.9
|13.900
|86.331
|86.329
|1208.633
|1208.611
|4.6
|40
|40
|-
|-
Line 135: Line 120:
|15edo
|15edo
|15.053
|15.053
|79.718
|79.716
|1195.775
|1195.736
|5.1
|45
|45
|-
|-
|[[51zpi]]
|[[51zpi]]
|16edo
|16edo
|15.945
|15.944
|75.259
|75.262
|1204.139
|1204.187
|4.2
|49
|49
|-
|-
Line 151: Line 134:
|17edo
|17edo
|17.045
|17.045
|70.402
|70.404
|1196.832
|1196.861
|5.1
|54
|54
|-
|-
Line 159: Line 141:
|18edo
|18edo
|18.119
|18.119
|66.229
|66.228
|1192.119
|1192.113
|3.5
|59
|59
|-
|-
Line 168: Line 149:
|18.948
|18.948
|63.331
|63.331
|1203.293
|1203.288
|6.0
|63
|63
|-
|-
Line 176: Line 156:
|19.982
|19.982
|60.054
|60.054
|1201.081
|1201.087
|3.4
|68
|68
|-
|-
Line 184: Line 163:
|21.028
|21.028
|57.067
|57.067
|1198.402
|1198.406
|4.1
|73
|73
|-
|-
Line 191: Line 169:
|22edo
|22edo
|22.025
|22.025
|54.484
|54.483
|1198.638
|1198.630
|6.1
|78
|78
|-
|-
|[[84zpi]]
|[[84zpi]]
|23edo (1st peak)
|23edo
|22.807
|22.807
|52.615
|52.615
|1210.148
|1210.148
|3.7
|82
|82
|-
|[[85zpi]]
|23edo (2nd peak)
|23.026
|52.115
|1198.645
|2.2
|83
|-
|-
|[[90zpi]]
|[[90zpi]]
Line 216: Line 184:
|24.006
|24.006
|49.988
|49.988
|1199.700
|1199.713
|5.7
|88
|88
|-
|-
Line 224: Line 191:
|24.965
|24.965
|48.067
|48.067
|1201.682
|1201.678
|3.9
|93
|93
|-
|-
Line 232: Line 198:
|25.936
|25.936
|46.268
|46.268
|1202.961
|1202.975
|5.6
|98
|98
|-
|-
Line 240: Line 205:
|27.087
|27.087
|44.302
|44.302
|1196.146
|1196.163
|6.1
|104
|104
|-
|-
Line 248: Line 212:
|28.032
|28.032
|42.808
|42.808
|1198.630
|1198.629
|3.7
|109
|109
|-
|-
|[[116zpi]]
|[[116zpi]]
|29edo
|29edo
|28.94
|28.940
|41.465
|41.465
|1202.488
|1202.489
|5.6
|114
|114
|-
|-
|[[122zpi]]
|[[122zpi]]
|30edo
|30edo
|30.062
|30.061
|39.918
|39.918
|1197.525
|1197.555
|3.3
|120
|120
|-
|-
Line 272: Line 233:
|30.978
|30.978
|38.737
|38.737
|1200.852
|1200.837
|7.0
|125
|125
|-
|-
|[[133zpi]]
|[[133zpi]]
|32edo
|32edo
|32.07
|32.070
|37.418
|37.418
|1197.381
|1197.375
|4.5
|131
|131
|-
|-
Line 287: Line 246:
|33edo
|33edo
|32.972
|32.972
|36.395
|36.394
|1201.019
|1201.009
|3.3
|136
|136
|-
|-
Line 295: Line 253:
|34edo
|34edo
|34.045
|34.045
|35.247
|35.248
|1198.414
|1198.419
|6.7
|142
|142
|-
|-
|[[149zpi]]
|[[149zpi]]
|35edo
|35edo
|34.926
|34.925
|34.358
|34.359
|1202.543
|1202.564
|4.2
|147
|147
|-
|-
Line 312: Line 268:
|35.982
|35.982
|33.350
|33.350
|1200.600
|1200.587
|6.0
|153
|153
|-
|-
|[[161zpi]]
|[[161zpi]]
|37edo
|37edo
|37.027
|37.028
|32.409
|32.408
|1199.125
|1199.108
|5.3
|159
|159
|-
|-
|[[166zpi]]
|[[166zpi]]
|38edo (1st peak)
|38edo
|37.89
|37.890
|31.671
|31.671
|1203.484
|1203.480
|5.8
|164
|164
|-
|[[167zpi]]
|38edo (2nd peak)
|38.103
|31.494
|1196.756
|2.5
|165
|-
|[[172zpi]]
|39edo (1st peak)
|38.916
|30.836
|1202.590
|2.6
|170
|-
|-
|[[173zpi]]
|[[173zpi]]
|39edo (2nd peak)
|39edo
|39.124
|39.124
|30.672
|30.672
|1196.197
|1196.204
|5.6
|171
|171
|-
|-
Line 360: Line 296:
|39.968
|39.968
|30.024
|30.024
|1200.961
|1200.965
|4.0
|176
|176
|-
|-
Line 368: Line 303:
|40.988
|40.988
|29.277
|29.277
|1200.351
|1200.349
|7.6
|182
|182
|-
|-
Line 376: Line 310:
|41.999
|41.999
|28.572
|28.572
|1200.029
|1200.032
|2.7
|188
|188
|-
|-
|[[196zpi]]
|[[196zpi]]
|43edo
|43edo
|43.027
|43.026
|27.889
|27.890
|1199.247
|1199.261
|6.2
|194
|194
|-
|-
Line 392: Line 324:
|44.015
|44.015
|27.263
|27.263
|1199.591
|1199.579
|4.6
|200
|200
|-
|-
|[[207zpi]]
|[[207zpi]]
|45edo (1st peak)
|45edo
|44.84
|44.840
|26.762
|26.762
|1204.282
|1204.289
|5.3
|205
|205
|-
|[[208zpi]]
|45edo (2nd peak)
|45.035
|26.646
|1199.067
|2.1
|206
|-
|-
|[[214zpi]]
|[[214zpi]]
Line 416: Line 338:
|46.009
|46.009
|26.082
|26.082
|1199.765
|1199.766
|7.5
|212
|212
|-
|-
Line 424: Line 345:
|47.006
|47.006
|25.529
|25.529
|1199.847
|1199.846
|4.3
|218
|218
|-
|-
Line 432: Line 352:
|47.988
|47.988
|25.006
|25.006
|1200.300
|1200.292
|5.8
|224
|224
|-
|[[232zpi]]
|49edo (1st peak)
|48.945
|24.517
|1201.348
|2.2
|230
|-
|-
|[[233zpi]]
|[[233zpi]]
|49edo (2nd peak)
|49edo
|49.141
|49.141
|24.420
|24.419
|1196.557
|1196.552
|5.7
|231
|231
|-
|-
Line 455: Line 365:
|50edo
|50edo
|49.939
|49.939
|24.029
|24.030
|1201.466
|1201.477
|6.7
|236
|236
|-
|-
|[[245zpi]]
|[[245zpi]]
|51edo
|51edo
|51.079
|51.080
|23.493
|23.493
|1198.144
|1198.128
|4.8
|243
|243
|-
|-
Line 472: Line 380:
|52.043
|52.043
|23.058
|23.058
|1199.009
|1199.018
|4.1
|249
|249
|-
|-
Line 480: Line 387:
|52.997
|52.997
|22.643
|22.643
|1200.068
|1200.072
|8.2
|255
|255
|-
|[[263zpi]]
|54edo (1st peak)
|53.949
|22.243
|1201.134
|2.0
|261
|-
|-
|[[264zpi]]
|[[264zpi]]
|54edo (2nd peak)
|54edo
|54.116
|54.116
|22.175
|22.175
|1197.428
|1197.430
|3.5
|262
|262
|-
|-
Line 504: Line 401:
|54.894
|54.894
|21.860
|21.860
|1202.317
|1202.325
|5.3
|267
|267
|-
|-
Line 511: Line 407:
|56edo
|56edo
|56.008
|56.008
|21.426
|21.425
|1199.829
|1199.821
|6.1
|274
|274
|-
|-
Line 520: Line 415:
|56.968
|56.968
|21.064
|21.064
|1200.674
|1200.668
|4.9
|280
|280
|-
|-
Line 528: Line 422:
|58.067
|58.067
|20.666
|20.666
|1198.615
|1198.621
|7.8
|287
|287
|-
|-
Line 536: Line 429:
|58.992
|58.992
|20.342
|20.342
|1200.163
|1200.157
|4.0
|293
|293
|-
|-
|[[301zpi]]
|[[301zpi]]
|60edo
|60edo
|59.92
|59.920
|20.027
|20.027
|1201.602
|1201.599
|7.1
|299
|299
|-
|-
Line 552: Line 443:
|61.003
|61.003
|19.671
|19.671
|1199.941
|1199.937
|3.7
|306
|306
|-
|-
Line 560: Line 450:
|61.938
|61.938
|19.374
|19.374
|1201.201
|1201.200
|6.3
|312
|312
|-
|-
Line 568: Line 457:
|63.019
|63.019
|19.042
|19.042
|1199.638
|1199.633
|6.8
|319
|319
|-
|-
Line 576: Line 464:
|64.099
|64.099
|18.721
|18.721
|1198.147
|1198.140
|3.6
|326
|326
|-
|-
Line 584: Line 471:
|65.016
|65.016
|18.457
|18.457
|1199.705
|1199.708
|7.8
|332
|332
|-
|-
Line 592: Line 478:
|65.916
|65.916
|18.205
|18.205
|1201.529
|1201.533
|4.5
|338
|338
|-
|-
Line 600: Line 485:
|66.998
|66.998
|17.911
|17.911
|1200.036
|1200.029
|5.3
|345
|345
|-
|-
Line 608: Line 492:
|68.049
|68.049
|17.634
|17.634
|1199.136
|1199.131
|7.7
|352
|352
|-
|-
|[[360zpi]]
|[[360zpi]]
|69edo
|69edo
|68.96
|68.960
|17.401
|17.401
|1200.696
|1200.696
|4.1
|358
|358
|-
|-
Line 625: Line 507:
|17.142
|17.142
|1199.931
|1199.931
|5.7
|365
|365
|-
|-
Line 632: Line 513:
|71.059
|71.059
|16.887
|16.887
|1199.004
|1198.998
|3.8
|372
|372
|-
|-
Line 640: Line 520:
|71.951
|71.951
|16.678
|16.678
|1200.817
|1200.824
|9.2
|378
|378
|-
|-
|[[387zpi]]
|[[387zpi]]
|73edo
|73edo
|72.984
|72.983
|16.442
|16.442
|1200.263
|1200.273
|3.4
|385
|385
|-
|-
Line 656: Line 534:
|74.052
|74.052
|16.205
|16.205
|1199.157
|1199.155
|5.1
|392
|392
|-
|-
Line 664: Line 541:
|75.091
|75.091
|15.981
|15.981
|1198.546
|1198.544
|6.0
|399
|399
|-
|-
Line 672: Line 548:
|75.968
|75.968
|15.796
|15.796
|1200.505
|1200.503
|2.6
|405
|405
|-
|-
Line 680: Line 555:
|76.992
|76.992
|15.586
|15.586
|1200.125
|1200.127
|8.2
|412
|412
|-
|-
|[[420zpi]]
|[[420zpi]]
|78edo
|78edo
|78.021
|77.851
|15.380
|15.414
|1199.677
|1202.292
|5.4
|418
|418
|-
|-
Line 696: Line 569:
|78.892
|78.892
|15.211
|15.211
|1201.643
|1201.637
|5.8
|425
|425
|-
|-
Line 704: Line 576:
|80.073
|80.073
|14.986
|14.986
|1198.906
|1198.904
|7.9
|433
|433
|-
|-
|[[441zpi]]
|[[441zpi]]
|81edo
|81edo
|80.947
|80.948
|14.825
|14.824
|1200.786
|1200.777
|5.2
|439
|439
|-
|-
Line 720: Line 590:
|81.954
|81.954
|14.642
|14.642
|1200.674
|1200.671
|6.7
|446
|446
|-
|-
Line 728: Line 597:
|82.967
|82.967
|14.464
|14.464
|1200.477
|1200.484
|3.9
|453
|453
|-
|-
Line 736: Line 604:
|83.997
|83.997
|14.286
|14.286
|1200.043
|1200.040
|8.0
|460
|460
|-
|-
Line 744: Line 611:
|84.991
|84.991
|14.119
|14.119
|1200.127
|1200.131
|3.0
|467
|467
|-
|-
Line 752: Line 618:
|86.019
|86.019
|13.950
|13.950
|1199.735
|1199.741
|2.4
|474
|474
|-
|-
Line 760: Line 625:
|87.014
|87.014
|13.791
|13.791
|1199.807
|1199.808
|8.9
|481
|481
|-
|-
Line 768: Line 632:
|88.027
|88.027
|13.632
|13.632
|1199.632
|1199.635
|2.6
|488
|488
|-
|-
Line 776: Line 639:
|89.023
|89.023
|13.480
|13.480
|1199.690
|1199.691
|7.6
|495
|495
|-
|-
Line 784: Line 646:
|90.006
|90.006
|13.332
|13.332
|1199.920
|1199.917
|4.8
|502
|502
|-
|-
|[[510zpi]]
|[[510zpi]]
|91edo (1st peak)
|91edo
|90.852
|90.852
|13.208
|13.208
|1201.955
|1201.956
|6.7
|508
|508
|-
|[[511zpi]]
|91edo (2nd peak)
|91.033
|13.182
|1199.565
|3.4
|509
|-
|-
|[[518zpi]]
|[[518zpi]]
Line 808: Line 660:
|91.993
|91.993
|13.044
|13.044
|1200.091
|1200.089
|4.5
|516
|516
|-
|-
Line 816: Line 667:
|93.002
|93.002
|12.903
|12.903
|1199.974
|1199.969
|5.6
|523
|523
|-
|-
Line 824: Line 674:
|93.984
|93.984
|12.768
|12.768
|1200.204
|1200.208
|8.8
|530
|530
|-
|[[539zpi]]
|95edo (1st peak)
|94.962
|12.637
|1200.480
|0.9
|537
|-
|-
|[[540zpi]]
|[[540zpi]]
|95edo (2nd peak)
|95edo
|95.117
|95.117
|12.616
|12.616
|1198.524
|1198.526
|5.3
|538
|538
|-
|-
Line 848: Line 688:
|95.954
|95.954
|12.506
|12.506
|1200.575
|1200.570
|7.3
|544
|544
|-
|-
Line 856: Line 695:
|96.925
|96.925
|12.381
|12.381
|1200.929
|1200.927
|4.2
|551
|551
|-
|-
Line 863: Line 701:
|98edo
|98edo
|97.923
|97.923
|12.255
|12.254
|1200.944
|1200.941
|4.3
|558
|558
|-
|-
Line 872: Line 709:
|99.047
|99.047
|12.115
|12.115
|1199.431
|1199.427
|9.4
|566
|566
|-
|-
|[[575zpi]]
|[[575zpi]]
|100edo
|100edo
|100.024
|99.869
|11.997
|12.016
|1199.712
|1201.577
|4.3
|573
|573
|-
|-
Line 889: Line 724:
|4.444
|4.444
|1199.920
|1199.920
|13.4
|1934
|1934
|-
|-
Line 897: Line 731:
|3.858
|3.858
|1199.985
|1199.985
|13.1
|2291
|2291
|-
|-
Line 905: Line 738:
|3.509
|3.509
|1200.088
|1200.088
|13.5
|2566
|2566
|-
|-
Line 913: Line 745:
|2.429
|2.429
|1199.966
|1199.966
|14.7
|3969
|3969
|-
|-
Line 921: Line 752:
|1.755
|1.755
|1200.107
|1200.107
|14.3
|5816
|5816
|}
|}
Retrieved from "https://en.xen.wiki/w/Table_of_zeta-stretched_edos"