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Table of zeta-stretched edos: Difference between revisions

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BudjarnLambeth (talk | contribs)
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21,263 edits
Added data to some blank cells in some rows
Line 1: Line 1:
'''Explanation of what this is''': [[The Riemann Zeta Function and Tuning#Optimal Octave Stretch]].
'''Explanation of what a 'zeta stretched edo' is''': [[The Riemann Zeta Function and Tuning#Optimal Octave Stretch]].


'''Instructions on how to calculate the second column using the free version of Wolfram Cloud''':
'''Instructions on how to calculate the second column using the free version of Wolfram Cloud''':
Line 9: Line 9:
{| class="wikitable sortable"
{| class="wikitable sortable"
!Edo
!Edo
!No. of steps per 1200 [[cents]]
!No. of steps per 1200 cents
!Step size (cents)
!Step size (cents)
![[Octave]] size (cents)
!Octave size (cents)
!Zeta peak height
!Zeta peak height
![[ZPI|Zeta peak index]]
!Zeta peak index
!Gram point index
!Gram point index
|-
|-
|'''[[1edo]]'''
|1edo
|'''1.127'''
|1.127
|'''1064.774'''
|1064.774
|'''1064.774'''
|1064.774
|'''1.6'''
|1.6
|1
|1
| -1
| -1
|-
|-
|'''[[2edo]]'''
|2edo
|'''1.972'''
|1.972
|'''608.519'''
|608.519
|'''1217.039'''
|1217.039
|'''2.3'''
|2.3
|2
|2
|0
|0
|-
|-
|'''[[3edo]]'''
|3edo
|'''3.06'''
|3.06
|'''392.157'''
|392.157
|'''1176.471'''
|1176.471
|'''2.8'''
|2.8
|4
|4
|2
|2
|-
|-
|'''[[4edo]]'''
|4edo
|'''3.904'''
|3.904
|'''307.377'''
|307.377
|'''1229.508'''
|1229.508
|'''3.0'''
|3.0
|6
|6
|4
|4
|-
|-
|'''[[5edo]]'''
|5edo
|'''5.034'''
|5.034
|'''238.379'''
|238.379
|'''1191.895'''
|1191.895
|'''3.7'''
|3.7
|9
|9
|7
|7
|-
|-
|[[6edo]]
|6edo
|6.035
|6.035
|198.840
|198.840
Line 64: Line 64:
|10
|10
|-
|-
|'''[[7edo]]'''
|7edo
|'''6.957'''
|6.957
|'''172.488'''
|172.488
|'''1207.417'''
|1207.417
|'''4.2'''
|4.2
|15
|15
|13
|13
|-
|-
|[[8edo]]
|8edo
|8.137
|8.137
|147.474
|147.474
Line 80: Line 80:
|17
|17
|-
|-
|[[9edo]]
|9edo
|8.95
|8.95
|134.078
|134.078
Line 88: Line 88:
|20
|20
|-
|-
|'''[[10edo]]'''
|10edo
|'''10.008'''
|10.008
|'''119.904'''
|119.904
|'''1199.041'''
|1199.041
|'''4.5'''
|4.5
|26
|26
|24
|24
|-
|-
|[[11edo]]
|11edo
|11.037
|11.037
|108.725
|108.725
Line 104: Line 104:
|28
|28
|-
|-
|'''[[12edo]]'''
|12edo
|'''12.023'''
|12.023
|'''99.809'''
|99.809
|'''1197.704'''
|1197.704
|'''5.2'''
|5.2
|34
|34
|32
|32
|-
|-
|[[13edo]]
|13edo
|12.969
|12.969
|92.528
|92.528
Line 120: Line 120:
|36
|36
|-
|-
|[[14edo]]
|14edo
|13.9
|13.9
|86.331
|86.331
Line 128: Line 128:
|40
|40
|-
|-
|[[15edo]]
|15edo
|15.053
|15.053
|79.718
|79.718
Line 136: Line 136:
|45
|45
|-
|-
|[[16edo]]
|16edo
|15.945
|15.945
|75.259
|75.259
Line 144: Line 144:
|49
|49
|-
|-
|[[17edo]]
|17edo
|17.045
|17.045
|70.402
|70.402
Line 152: Line 152:
|54
|54
|-
|-
|[[18edo]]
|18edo
|18.119
|18.119
|66.229
|66.229
Line 160: Line 160:
|59
|59
|-
|-
|'''[[19edo]]'''
|19edo
|'''18.948'''
|18.948
|'''63.331'''
|63.331
|'''1203.293'''
|1203.293
|'''6.0'''
|6.0
|65
|65
|63
|63
|-
|-
|[[20edo]]
|20edo
|19.982
|19.982
|60.054
|60.054
Line 176: Line 176:
|
|
|-
|-
|[[21edo]]
|21edo
|21.028
|21.028
|57.067
|57.067
Line 184: Line 184:
|
|
|-
|-
|'''[[22edo]]'''
|22edo
|'''22.025'''
|22.025
|'''54.484'''
|54.484
|'''1198.638'''
|1198.638
|'''6.1'''
|6.1
|
|
|
|
|-
|-
|[[23edo]] (1st peak)
|23edo (1st peak)
|22.807
|22.807
|52.615
|52.615
Line 200: Line 200:
|
|
|-
|-
|[[23edo]] (2nd peak)
|23edo (2nd peak)
|23.026
|23.026
|52.115
|52.115
Line 208: Line 208:
|
|
|-
|-
|[[24edo]]
|24edo
|24.006
|24.006
|49.988
|49.988
Line 216: Line 216:
|
|
|-
|-
|[[25edo]]
|25edo
|24.965
|24.965
|48.067
|48.067
Line 224: Line 224:
|
|
|-
|-
|[[26edo]]
|26edo
|25.936
|25.936
|46.268
|46.268
Line 232: Line 232:
|
|
|-
|-
|'''[[27edo]]'''
|27edo
|'''27.087'''
|27.087
|'''44.302'''
|44.302
|'''1196.146'''
|1196.146
|'''6.1'''
|6.1
|
|
|
|
|-
|-
|[[28edo]]
|28edo
|28.032
|28.032
|42.808
|42.808
Line 248: Line 248:
|
|
|-
|-
|[[29edo]]
|29edo
|28.94
|28.94
|41.465
|41.465
Line 256: Line 256:
|
|
|-
|-
|[[30edo]]
|30edo
|30.062
|30.062
|39.918
|39.918
Line 264: Line 264:
|
|
|-
|-
|'''[[31edo]]'''
|31edo
|'''30.978'''
|30.978
|'''38.737'''
|38.737
|'''1200.852'''
|1200.852
|'''7.0'''
|7.0
|127
|127
|125
|125
|-
|-
|[[32edo]]
|32edo
|32.07
|32.07
|37.418
|37.418
Line 280: Line 280:
|
|
|-
|-
|[[33edo]]
|33edo
|32.972
|32.972
|36.395
|36.395
Line 288: Line 288:
|
|
|-
|-
|[[34edo]]
|34edo
|34.045
|34.045
|35.247
|35.247
Line 296: Line 296:
|
|
|-
|-
|[[35edo]]
|35edo
|34.926
|34.926
|34.358
|34.358
Line 304: Line 304:
|
|
|-
|-
|[[36edo]]
|36edo
|35.982
|35.982
|33.350
|33.350
Line 312: Line 312:
|
|
|-
|-
|[[37edo]]
|37edo
|37.027
|37.027
|32.409
|32.409
Line 320: Line 320:
|
|
|-
|-
|[[38edo]] (1st peak)
|38edo (1st peak)
|37.89
|37.89
|31.671
|31.671
Line 328: Line 328:
|
|
|-
|-
|[[38edo]] (2nd peak)
|38edo (2nd peak)
|38.103
|38.103
|31.494
|31.494
Line 336: Line 336:
|
|
|-
|-
|[[39edo]] (1st peak)
|39edo (1st peak)
|38.916
|38.916
|30.836
|30.836
Line 344: Line 344:
|
|
|-
|-
|[[39edo]] (2nd peak)
|39edo (2nd peak)
|39.124
|39.124
|30.672
|30.672
Line 352: Line 352:
|
|
|-
|-
|[[40edo]]
|40edo
|39.968
|39.968
|30.024
|30.024
Line 360: Line 360:
|
|
|-
|-
|'''[[41edo]]'''
|41edo
|'''40.988'''
|40.988
|'''29.277'''
|29.277
|'''1200.351'''
|1200.351
|'''7.6'''
|7.6
|184
|184
|182
|182
|-
|-
|[[42edo]]
|42edo
|41.999
|41.999
|28.572
|28.572
Line 376: Line 376:
|
|
|-
|-
|[[43edo]]
|43edo
|43.027
|43.027
|27.889
|27.889
Line 384: Line 384:
|
|
|-
|-
|[[44edo]]
|44edo
|44.015
|44.015
|27.263
|27.263
Line 392: Line 392:
|
|
|-
|-
|[[45edo]] (1st peak)
|45edo (1st peak)
|44.84
|44.84
|26.762
|26.762
Line 400: Line 400:
|
|
|-
|-
|[[45edo]] (2nd peak)
|45edo (2nd peak)
|45.035
|45.035
|26.646
|26.646
Line 408: Line 408:
|
|
|-
|-
|[[46edo]]
|46edo
|46.009
|46.009
|26.082
|26.082
Line 416: Line 416:
|
|
|-
|-
|[[47edo]]
|47edo
|47.006
|47.006
|25.529
|25.529
Line 424: Line 424:
|
|
|-
|-
|[[48edo]]
|48edo
|47.988
|47.988
|25.006
|25.006
Line 432: Line 432:
|
|
|-
|-
|[[49edo]] (1st peak)
|49edo (1st peak)
|48.945
|48.945
|24.517
|24.517
Line 440: Line 440:
|
|
|-
|-
|[[49edo]] (2nd peak)
|49edo (2nd peak)
|49.141
|49.141
|24.420
|24.420
Line 448: Line 448:
|
|
|-
|-
|[[50edo]]
|50edo
|49.939
|49.939
|24.029
|24.029
Line 456: Line 456:
|
|
|-
|-
|[[51edo]]
|51edo
|51.079
|51.079
|23.493
|23.493
Line 464: Line 464:
|
|
|-
|-
|[[52edo]]
|52edo
|52.043
|52.043
|23.058
|23.058
Line 472: Line 472:
|
|
|-
|-
|'''[[53edo]]'''
|53edo
|'''52.997'''
|52.997
|'''22.643'''
|22.643
|'''1200.068'''
|1200.068
|'''8.2'''
|8.2
|257
|257
|255
|255
|-
|-
|[[54edo]] (1st peak)
|54edo (1st peak)
|53.949
|53.949
|22.243
|22.243
Line 488: Line 488:
|
|
|-
|-
|[[54edo]] (2nd peak)
|54edo (2nd peak)
|54.116
|54.116
|22.175
|22.175
Line 496: Line 496:
|
|
|-
|-
|[[55edo]]
|55edo
|54.894
|54.894
|21.860
|21.860
Line 504: Line 504:
|
|
|-
|-
|[[56edo]]
|56edo
|56.008
|56.008
|21.426
|21.426
Line 512: Line 512:
|
|
|-
|-
|[[57edo]]
|57edo
|56.968
|56.968
|21.064
|21.064
Line 520: Line 520:
|
|
|-
|-
|[[58edo]]
|58edo
|58.067
|58.067
|20.666
|20.666
Line 528: Line 528:
|
|
|-
|-
|[[59edo]]
|59edo
|58.992
|58.992
|20.342
|20.342
Line 536: Line 536:
|
|
|-
|-
|[[60edo]]
|60edo
|59.92
|59.92
|20.027
|20.027
Line 544: Line 544:
|
|
|-
|-
|[[61edo]]
|61edo
|61.003
|61.003
|19.671
|19.671
Line 552: Line 552:
|
|
|-
|-
|[[62edo]]
|62edo
|61.938
|61.938
|19.374
|19.374
Line 560: Line 560:
|
|
|-
|-
|[[63edo]]
|63edo
|63.019
|63.019
|19.042
|19.042
Line 568: Line 568:
|
|
|-
|-
|[[64edo]]
|64edo
|64.099
|64.099
|18.721
|18.721
Line 576: Line 576:
|
|
|-
|-
|[[65edo]]
|65edo
|65.016
|65.016
|18.457
|18.457
Line 584: Line 584:
|
|
|-
|-
|[[66edo]]
|66edo
|65.916
|65.916
|18.205
|18.205
Line 592: Line 592:
|
|
|-
|-
|[[67edo]]
|67edo
|66.998
|66.998
|17.911
|17.911
Line 600: Line 600:
|
|
|-
|-
|[[68edo]]
|68edo
|68.049
|68.049
|17.634
|17.634
Line 608: Line 608:
|
|
|-
|-
|[[69edo]]
|69edo
|68.96
|68.96
|17.401
|17.401
Line 616: Line 616:
|
|
|-
|-
|[[70edo]]
|70edo
|70.004
|70.004
|17.142
|17.142
Line 624: Line 624:
|
|
|-
|-
|[[71edo]]
|71edo
|71.059
|71.059
|16.887
|16.887
Line 632: Line 632:
|
|
|-
|-
|'''[[72edo]]'''
|72edo
|'''71.951'''
|71.951
|'''16.678'''
|16.678
|'''1200.817'''
|1200.817
|'''9.2'''
|9.2
|380
|380
|378
|378
|-
|-
|[[73edo]]
|73edo
|72.984
|72.984
|16.442
|16.442
Line 648: Line 648:
|
|
|-
|-
|[[74edo]]
|74edo
|74.052
|74.052
|16.205
|16.205
Line 656: Line 656:
|
|
|-
|-
|[[75edo]]
|75edo
|75.091
|75.091
|15.981
|15.981
Line 664: Line 664:
|
|
|-
|-
|[[76edo]]
|76edo
|75.968
|75.968
|15.796
|15.796
Line 672: Line 672:
|
|
|-
|-
|[[77edo]]
|77edo
|76.992
|76.992
|15.586
|15.586
Line 680: Line 680:
|
|
|-
|-
|[[78edo]]
|78edo
|78.021
|78.021
|15.380
|15.380
Line 688: Line 688:
|
|
|-
|-
|[[79edo]]
|79edo
|78.892
|78.892
|15.211
|15.211
Line 696: Line 696:
|
|
|-
|-
|[[80edo]]
|80edo
|80.073
|80.073
|14.986
|14.986
Line 704: Line 704:
|
|
|-
|-
|[[81edo]]
|81edo
|80.947
|80.947
|14.825
|14.825
Line 712: Line 712:
|
|
|-
|-
|[[82edo]]
|82edo
|81.954
|81.954
|14.642
|14.642
Line 720: Line 720:
|
|
|-
|-
|[[83edo]]
|83edo
|82.967
|82.967
|14.464
|14.464
Line 728: Line 728:
|
|
|-
|-
|[[84edo]]
|84edo
|83.997
|83.997
|14.286
|14.286
Line 736: Line 736:
|
|
|-
|-
|[[85edo]]
|85edo
|84.991
|84.991
|14.119
|14.119
Line 744: Line 744:
|
|
|-
|-
|[[86edo]]
|86edo
|86.019
|86.019
|13.950
|13.950
Line 752: Line 752:
|
|
|-
|-
|[[87edo]]
|87edo
|87.014
|87.014
|13.791
|13.791
Line 760: Line 760:
|
|
|-
|-
|[[88edo]]
|88edo
|88.027
|88.027
|13.632
|13.632
Line 768: Line 768:
|
|
|-
|-
|[[89edo]]
|89edo
|89.023
|89.023
|13.480
|13.480
Line 776: Line 776:
|
|
|-
|-
|[[90edo]]
|90edo
|90.006
|90.006
|13.332
|13.332
Line 784: Line 784:
|
|
|-
|-
|[[91edo]] (1st peak)
|91edo (1st peak)
|90.852
|90.852
|13.208
|13.208
Line 792: Line 792:
|
|
|-
|-
|[[91edo]] (2nd peak)
|91edo (2nd peak)
|91.033
|91.033
|13.182
|13.182
Line 800: Line 800:
|
|
|-
|-
|[[92edo]]
|92edo
|91.993
|91.993
|13.044
|13.044
Line 808: Line 808:
|
|
|-
|-
|[[93edo]]
|93edo
|93.002
|93.002
|12.903
|12.903
Line 816: Line 816:
|
|
|-
|-
|[[94edo]]
|94edo
|93.984
|93.984
|12.768
|12.768
Line 824: Line 824:
|
|
|-
|-
|[[95edo]] (1st peak)
|95edo (1st peak)
|94.962
|94.962
|12.637
|12.637
Line 832: Line 832:
|
|
|-
|-
|[[95edo]] (2nd peak)
|95edo (2nd peak)
|95.117
|95.117
|12.616
|12.616
Line 840: Line 840:
|
|
|-
|-
|[[96edo]]
|96edo
|95.954
|95.954
|12.506
|12.506
Line 848: Line 848:
|
|
|-
|-
|[[97edo]]
|97edo
|96.925
|96.925
|12.381
|12.381
Line 856: Line 856:
|
|
|-
|-
|[[98edo]]
|98edo
|97.923
|97.923
|12.255
|12.255
Line 864: Line 864:
|
|
|-
|-
|'''[[99edo]]'''
|99edo
|'''99.047'''
|99.047
|'''12.115'''
|12.115
|'''1199.431'''
|1199.431
|'''9.4'''
|9.4
|
|
|
|
|-
|-
|[[100edo]]
|100edo
|100.024
|100.024
|11.997
|11.997
Line 880: Line 880:
|
|
|-
|-
|[[270edo]]
|270edo
|
|270.018
|
|4.444
|
|1199.920
|
|13.4
|1936
|1936
|1934
|1934
|-
|-
|[[311edo]]
|311edo
|
|311.004
|
|3.858
|
|1199.985
|
|13.1
|2293
|2293
|2291
|2291
|-
|-
|[[342edo]]
|342edo
|
|341.975
|
|3.509
|
|1200.088
|
|13.5
|2568
|2568
|2566
|2566
|-
|-
|[[494edo]]
|494edo
|
|494.014
|
|2.429
|
|1199.966
|
|14.7
|3971
|3971
|3969
|3969
|-
|-
|[[684edo]]
|684edo
|
|683.939
|
|1.755
|
|1200.107
|
|14.3
|5818
|5818
|
|
Retrieved from "https://en.xen.wiki/w/Table_of_zeta-stretched_edos"