Table of zeta-stretched edos: Difference between revisions

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m Added column
Line 12: Line 12:
|'''Step size (cents)'''
|'''Step size (cents)'''
|'''[[Octave]] size (cents)'''
|'''[[Octave]] size (cents)'''
|'''Zeta peak height'''
|-
|-
|'''[[1edo]]'''
|'''[[1edo]]'''
Line 17: Line 18:
|'''1064.774'''
|'''1064.774'''
|'''1064.774'''
|'''1064.774'''
|
|-
|-
|'''[[2edo]]'''
|'''[[2edo]]'''
Line 22: Line 24:
|'''608.519'''
|'''608.519'''
|'''1217.039'''
|'''1217.039'''
|
|-
|-
|'''[[3edo]]'''
|'''[[3edo]]'''
Line 27: Line 30:
|'''392.157'''
|'''392.157'''
|'''1176.471'''
|'''1176.471'''
|
|-
|-
|'''[[4edo]]'''
|'''[[4edo]]'''
Line 32: Line 36:
|'''307.377'''
|'''307.377'''
|'''1229.508'''
|'''1229.508'''
|
|-
|-
|'''[[5edo]]'''
|'''[[5edo]]'''
Line 37: Line 42:
|'''238.379'''
|'''238.379'''
|'''1191.895'''
|'''1191.895'''
|
|-
|-
|[[6edo]]
|[[6edo]]
Line 42: Line 48:
|198.840
|198.840
|1193.041
|1193.041
|
|-
|-
|'''[[7edo]]'''
|'''[[7edo]]'''
Line 47: Line 54:
|'''172.488'''
|'''172.488'''
|'''1207.417'''
|'''1207.417'''
|
|-
|-
|[[8edo]]
|[[8edo]]
Line 52: Line 60:
|147.474
|147.474
|1179.796
|1179.796
|
|-
|-
|[[9edo]]
|[[9edo]]
Line 57: Line 66:
|134.078
|134.078
|1206.704
|1206.704
|
|-
|-
|'''[[10edo]]'''
|'''[[10edo]]'''
Line 62: Line 72:
|'''119.904'''
|'''119.904'''
|'''1199.041'''
|'''1199.041'''
|
|-
|-
|[[11edo]]
|[[11edo]]
Line 67: Line 78:
|108.725
|108.725
|1195.977
|1195.977
|
|-
|-
|'''[[12edo]]'''
|'''[[12edo]]'''
Line 72: Line 84:
|'''99.809'''
|'''99.809'''
|'''1197.704'''
|'''1197.704'''
|
|-
|-
|[[13edo]]
|[[13edo]]
Line 77: Line 90:
|92.528
|92.528
|1202.868
|1202.868
|
|-
|-
|[[14edo]]
|[[14edo]]
Line 82: Line 96:
|86.331
|86.331
|1208.633
|1208.633
|
|-
|-
|[[15edo]]
|[[15edo]]
Line 87: Line 102:
|79.718
|79.718
|1195.775
|1195.775
|
|-
|-
|[[16edo]]
|[[16edo]]
Line 92: Line 108:
|75.259
|75.259
|1204.139
|1204.139
|
|-
|-
|[[17edo]]
|[[17edo]]
Line 97: Line 114:
|70.402
|70.402
|1196.832
|1196.832
|
|-
|-
|[[18edo]]
|[[18edo]]
Line 102: Line 120:
|66.229
|66.229
|1192.119
|1192.119
|
|-
|-
|'''[[19edo]]'''
|'''[[19edo]]'''
Line 107: Line 126:
|'''63.331'''
|'''63.331'''
|'''1203.293'''
|'''1203.293'''
|
|-
|-
|[[20edo]]
|[[20edo]]
Line 112: Line 132:
|60.054
|60.054
|1201.081
|1201.081
|
|-
|-
|[[21edo]]
|[[21edo]]
Line 117: Line 138:
|57.067
|57.067
|1198.402
|1198.402
|
|-
|-
|'''[[22edo]]'''
|'''[[22edo]]'''
Line 122: Line 144:
|'''54.484'''
|'''54.484'''
|'''1198.638'''
|'''1198.638'''
|
|-
|-
|[[23edo]]
|[[23edo]]
Line 127: Line 150:
|52.115
|52.115
|1198.645
|1198.645
|
|-
|-
|[[24edo]]
|[[24edo]]
Line 132: Line 156:
|49.988
|49.988
|1199.700
|1199.700
|
|-
|-
|[[25edo]]
|[[25edo]]
Line 137: Line 162:
|48.067
|48.067
|1201.682
|1201.682
|
|-
|-
|[[26edo]]
|[[26edo]]
Line 142: Line 168:
|46.268
|46.268
|1202.961
|1202.961
|
|-
|-
|'''[[27edo]]'''
|'''[[27edo]]'''
Line 147: Line 174:
|'''44.302'''
|'''44.302'''
|'''1196.146'''
|'''1196.146'''
|
|-
|-
|[[28edo]]
|[[28edo]]
Line 152: Line 180:
|42.808
|42.808
|1198.630
|1198.630
|
|-
|-
|[[29edo]]
|[[29edo]]
Line 157: Line 186:
|41.465
|41.465
|1202.488
|1202.488
|
|-
|-
|[[30edo]]
|[[30edo]]
Line 162: Line 192:
|39.918
|39.918
|1197.525
|1197.525
|
|-
|-
|'''[[31edo]]'''
|'''[[31edo]]'''
Line 167: Line 198:
|'''38.737'''
|'''38.737'''
|'''1200.852'''
|'''1200.852'''
|
|-
|-
|[[32edo]]
|[[32edo]]
Line 172: Line 204:
|37.418
|37.418
|1197.381
|1197.381
|
|-
|-
|[[33edo]]
|[[33edo]]
Line 177: Line 210:
|36.395
|36.395
|1201.019
|1201.019
|
|-
|-
|[[34edo]]
|[[34edo]]
Line 182: Line 216:
|35.247
|35.247
|1198.414
|1198.414
|
|-
|-
|[[35edo]]
|[[35edo]]
Line 187: Line 222:
|34.358
|34.358
|1202.543
|1202.543
|
|-
|-
|[[36edo]]
|[[36edo]]
Line 192: Line 228:
|33.350
|33.350
|1200.600
|1200.600
|
|-
|-
|[[37edo]]
|[[37edo]]
Line 197: Line 234:
|32.409
|32.409
|1199.125
|1199.125
|
|-
|-
|[[38edo]] (1st peak)
|[[38edo]] (1st peak)
Line 202: Line 240:
|31.671
|31.671
|1203.484
|1203.484
|
|-
|-
|[[38edo]] (2nd peak)
|[[38edo]] (2nd peak)
Line 207: Line 246:
|31.494
|31.494
|1196.756
|1196.756
|
|-
|-
|[[39edo]] (1st peak)
|[[39edo]] (1st peak)
Line 212: Line 252:
|30.836
|30.836
|1202.590
|1202.590
|
|-
|-
|[[39edo]] (2nd peak)
|[[39edo]] (2nd peak)
Line 217: Line 258:
|30.672
|30.672
|1196.197
|1196.197
|
|-
|-
|[[40edo]]
|[[40edo]]
Line 222: Line 264:
|30.024
|30.024
|1200.961
|1200.961
|
|-
|-
|'''[[41edo]]'''
|'''[[41edo]]'''
Line 227: Line 270:
|'''29.277'''
|'''29.277'''
|'''1200.351'''
|'''1200.351'''
|
|-
|-
|[[42edo]]
|[[42edo]]
Line 232: Line 276:
|28.572
|28.572
|1200.029
|1200.029
|
|-
|-
|[[43edo]]
|[[43edo]]
Line 237: Line 282:
|27.889
|27.889
|1199.247
|1199.247
|
|-
|-
|[[44edo]]
|[[44edo]]
Line 242: Line 288:
|27.263
|27.263
|1199.591
|1199.591
|
|-
|-
|[[45edo]]
|[[45edo]]
Line 247: Line 294:
|26.762
|26.762
|1204.282
|1204.282
|
|-
|-
|[[45edo]]
|[[45edo]]
Line 252: Line 300:
|26.646
|26.646
|1199.067
|1199.067
|
|-
|-
|[[46edo]]
|[[46edo]]
Line 257: Line 306:
|26.082
|26.082
|1199.765
|1199.765
|
|-
|-
|[[47edo]]
|[[47edo]]
Line 262: Line 312:
|25.529
|25.529
|1199.847
|1199.847
|
|-
|-
|[[48edo]]
|[[48edo]]
Line 267: Line 318:
|25.006
|25.006
|1200.300
|1200.300
|
|-
|-
|[[49edo]] (1st peak)
|[[49edo]] (1st peak)
Line 272: Line 324:
|24.517
|24.517
|1201.348
|1201.348
|
|-
|-
|[[49edo]] (2nd peak)
|[[49edo]] (2nd peak)
Line 277: Line 330:
|24.420
|24.420
|1196.557
|1196.557
|
|-
|-
|[[50edo]]
|[[50edo]]
Line 282: Line 336:
|24.029
|24.029
|1201.466
|1201.466
|
|-
|-
|[[51edo]]
|[[51edo]]
Line 287: Line 342:
|23.493
|23.493
|1198.144
|1198.144
|
|-
|-
|[[52edo]]
|[[52edo]]
Line 292: Line 348:
|23.058
|23.058
|1199.009
|1199.009
|
|-
|-
|'''[[53edo]]'''
|'''[[53edo]]'''
Line 297: Line 354:
|'''22.643'''
|'''22.643'''
|'''1200.068'''
|'''1200.068'''
|
|-
|-
|[[54edo]] (1st peak)
|[[54edo]] (1st peak)
Line 302: Line 360:
|22.243
|22.243
|1201.134
|1201.134
|
|-
|-
|[[54edo]] (2nd peak)
|[[54edo]] (2nd peak)
Line 307: Line 366:
|22.175
|22.175
|1197.428
|1197.428
|
|-
|-
|[[55edo]]
|[[55edo]]
Line 312: Line 372:
|21.860
|21.860
|1202.317
|1202.317
|
|-
|-
|[[56edo]]
|[[56edo]]
Line 317: Line 378:
|21.426
|21.426
|1199.829
|1199.829
|
|-
|-
|[[57edo]]
|[[57edo]]
Line 322: Line 384:
|21.064
|21.064
|1200.674
|1200.674
|
|-
|-
|[[58edo]]
|[[58edo]]
Line 327: Line 390:
|20.666
|20.666
|1198.615
|1198.615
|
|-
|-
|[[59edo]]
|[[59edo]]
Line 332: Line 396:
|20.342
|20.342
|1200.163
|1200.163
|
|-
|-
|[[60edo]]
|[[60edo]]
Line 337: Line 402:
|20.027
|20.027
|1201.602
|1201.602
|
|-
|-
|[[61edo]]
|[[61edo]]
Line 342: Line 408:
|19.671
|19.671
|1199.941
|1199.941
|
|-
|-
|[[62edo]]
|[[62edo]]
Line 347: Line 414:
|19.374
|19.374
|1201.201
|1201.201
|
|-
|-
|[[63edo]]
|[[63edo]]
Line 352: Line 420:
|19.042
|19.042
|1199.638
|1199.638
|
|-
|-
|[[64edo]]
|[[64edo]]
Line 357: Line 426:
|18.721
|18.721
|1198.147
|1198.147
|
|-
|-
|[[65edo]]
|[[65edo]]
Line 362: Line 432:
|18.457
|18.457
|1199.705
|1199.705
|
|-
|-
|[[66edo]]
|[[66edo]]
Line 367: Line 438:
|18.205
|18.205
|1201.529
|1201.529
|
|-
|-
|[[67edo]]
|[[67edo]]
Line 372: Line 444:
|17.911
|17.911
|1200.036
|1200.036
|
|-
|-
|[[68edo]]
|[[68edo]]
Line 377: Line 450:
|17.634
|17.634
|1199.136
|1199.136
|
|-
|-
|[[69edo]]
|[[69edo]]
Line 382: Line 456:
|17.401
|17.401
|1200.696
|1200.696
|
|-
|-
|[[70edo]]
|[[70edo]]
Line 387: Line 462:
|17.142
|17.142
|1199.931
|1199.931
|
|-
|-
|[[71edo]]
|[[71edo]]
Line 392: Line 468:
|16.887
|16.887
|1199.004
|1199.004
|
|-
|-
|'''[[72edo]]'''
|'''[[72edo]]'''
Line 397: Line 474:
|'''16.678'''
|'''16.678'''
|'''1200.817'''
|'''1200.817'''
|
|-
|-
|[[73edo]]
|[[73edo]]
Line 402: Line 480:
|16.442
|16.442
|1200.263
|1200.263
|
|-
|-
|[[74edo]]
|[[74edo]]
Line 407: Line 486:
|16.205
|16.205
|1199.157
|1199.157
|
|-
|-
|[[75edo]]
|[[75edo]]
Line 412: Line 492:
|15.981
|15.981
|1198.546
|1198.546
|
|-
|-
|[[76edo]]
|[[76edo]]
Line 417: Line 498:
|15.796
|15.796
|1200.505
|1200.505
|
|-
|-
|[[77edo]]
|[[77edo]]
Line 422: Line 504:
|15.586
|15.586
|1200.125
|1200.125
|
|-
|-
|[[78edo]]
|[[78edo]]
Line 427: Line 510:
|15.380
|15.380
|1199.677
|1199.677
|
|-
|-
|[[79edo]]
|[[79edo]]
Line 432: Line 516:
|15.211
|15.211
|1201.643
|1201.643
|
|-
|-
|[[80edo]]
|[[80edo]]
Line 437: Line 522:
|14.986
|14.986
|1198.906
|1198.906
|
|-
|-
|[[81edo]]
|[[81edo]]
Line 442: Line 528:
|14.825
|14.825
|1200.786
|1200.786
|
|-
|-
|[[82edo]]
|[[82edo]]
Line 447: Line 534:
|14.642
|14.642
|1200.674
|1200.674
|
|-
|-
|[[83edo]]
|[[83edo]]
Line 452: Line 540:
|14.464
|14.464
|1200.477
|1200.477
|
|-
|-
|[[84edo]]
|[[84edo]]
Line 457: Line 546:
|14.286
|14.286
|1200.043
|1200.043
|
|-
|-
|[[85edo]]
|[[85edo]]
Line 462: Line 552:
|14.119
|14.119
|1200.127
|1200.127
|
|-
|-
|[[86edo]]
|[[86edo]]
Line 467: Line 558:
|13.950
|13.950
|1199.735
|1199.735
|
|-
|-
|[[87edo]]
|[[87edo]]
Line 472: Line 564:
|13.791
|13.791
|1199.807
|1199.807
|
|-
|-
|[[88edo]]
|[[88edo]]
Line 477: Line 570:
|13.632
|13.632
|1199.632
|1199.632
|
|-
|-
|[[89edo]]
|[[89edo]]
Line 482: Line 576:
|13.480
|13.480
|1199.690
|1199.690
|
|-
|-
|[[90edo]]
|[[90edo]]
Line 487: Line 582:
|13.332
|13.332
|1199.920
|1199.920
|
|-
|-
|[[91edo]] (1st peak)
|[[91edo]] (1st peak)
Line 492: Line 588:
|13.208
|13.208
|1201.955
|1201.955
|
|-
|-
|[[91edo]] (2nd peak)
|[[91edo]] (2nd peak)
Line 497: Line 594:
|13.182
|13.182
|1199.565
|1199.565
|
|-
|-
|[[92edo]]
|[[92edo]]
Line 502: Line 600:
|13.044
|13.044
|1200.091
|1200.091
|
|-
|-
|[[93edo]]
|[[93edo]]
Line 507: Line 606:
|12.903
|12.903
|1199.974
|1199.974
|
|-
|-
|[[94edo]]
|[[94edo]]
Line 512: Line 612:
|12.768
|12.768
|1200.204
|1200.204
|
|-
|-
|[[95edo]] (1st peak)
|[[95edo]] (1st peak)
Line 517: Line 618:
|12.637
|12.637
|1200.480
|1200.480
|
|-
|-
|[[95edo]] (2nd peak)
|[[95edo]] (2nd peak)
Line 522: Line 624:
|12.616
|12.616
|1198.524
|1198.524
|
|-
|-
|[[96edo]]
|[[96edo]]
Line 527: Line 630:
|12.506
|12.506
|1200.575
|1200.575
|
|-
|-
|[[97edo]]
|[[97edo]]
Line 532: Line 636:
|12.381
|12.381
|1200.929
|1200.929
|
|-
|-
|[[98edo]]
|[[98edo]]
Line 537: Line 642:
|12.255
|12.255
|1200.944
|1200.944
|
|-
|-
|'''[[99edo]]'''
|'''[[99edo]]'''
Line 542: Line 648:
|'''12.115'''
|'''12.115'''
|'''1199.431'''
|'''1199.431'''
|
|-
|-
|[[100edo]]
|[[100edo]]
Line 547: Line 654:
|11.997
|11.997
|1199.712
|1199.712
|
|}
|}
[[Category:Tables]]
[[Category:Tables]]
[[Category:Zeta]]
[[Category:Zeta]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]

Revision as of 22:08, 9 February 2024

Explanation of what this 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:

  1. Copy-paste Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9,12.1}] into a cell.
  2. Change "11.9" and "12.1" to whatever values you want, e.g. to view the curve around 15edo you might use the values "14.9" and "15.1".
  3. Ensure that cell is still selected
  4. In the menu select Evaluation > Evaluate Cells
Edo No. of steps per 1200 cents Step size (cents) Octave size (cents) Zeta peak height
1edo 1.127 1064.774 1064.774
2edo 1.972 608.519 1217.039
3edo 3.06 392.157 1176.471
4edo 3.904 307.377 1229.508
5edo 5.034 238.379 1191.895
6edo 6.035 198.840 1193.041
7edo 6.957 172.488 1207.417
8edo 8.137 147.474 1179.796
9edo 8.95 134.078 1206.704
10edo 10.008 119.904 1199.041
11edo 11.037 108.725 1195.977
12edo 12.023 99.809 1197.704
13edo 12.969 92.528 1202.868
14edo 13.9 86.331 1208.633
15edo 15.053 79.718 1195.775
16edo 15.945 75.259 1204.139
17edo 17.045 70.402 1196.832
18edo 18.119 66.229 1192.119
19edo 18.948 63.331 1203.293
20edo 19.982 60.054 1201.081
21edo 21.028 57.067 1198.402
22edo 22.025 54.484 1198.638
23edo 23.026 52.115 1198.645
24edo 24.006 49.988 1199.700
25edo 24.965 48.067 1201.682
26edo 25.936 46.268 1202.961
27edo 27.087 44.302 1196.146
28edo 28.032 42.808 1198.630
29edo 28.94 41.465 1202.488
30edo 30.062 39.918 1197.525
31edo 30.978 38.737 1200.852
32edo 32.07 37.418 1197.381
33edo 32.972 36.395 1201.019
34edo 34.045 35.247 1198.414
35edo 34.926 34.358 1202.543
36edo 35.982 33.350 1200.600
37edo 37.027 32.409 1199.125
38edo (1st peak) 37.89 31.671 1203.484
38edo (2nd peak) 38.103 31.494 1196.756
39edo (1st peak) 38.916 30.836 1202.590
39edo (2nd peak) 39.124 30.672 1196.197
40edo 39.968 30.024 1200.961
41edo 40.988 29.277 1200.351
42edo 41.999 28.572 1200.029
43edo 43.027 27.889 1199.247
44edo 44.015 27.263 1199.591
45edo 44.84 26.762 1204.282
45edo 45.035 26.646 1199.067
46edo 46.009 26.082 1199.765
47edo 47.006 25.529 1199.847
48edo 47.988 25.006 1200.300
49edo (1st peak) 48.945 24.517 1201.348
49edo (2nd peak) 49.141 24.420 1196.557
50edo 49.939 24.029 1201.466
51edo 51.079 23.493 1198.144
52edo 52.043 23.058 1199.009
53edo 52.997 22.643 1200.068
54edo (1st peak) 53.949 22.243 1201.134
54edo (2nd peak) 54.116 22.175 1197.428
55edo 54.894 21.860 1202.317
56edo 56.008 21.426 1199.829
57edo 56.968 21.064 1200.674
58edo 58.067 20.666 1198.615
59edo 58.992 20.342 1200.163
60edo 59.92 20.027 1201.602
61edo 61.003 19.671 1199.941
62edo 61.938 19.374 1201.201
63edo 63.019 19.042 1199.638
64edo 64.099 18.721 1198.147
65edo 65.016 18.457 1199.705
66edo 65.916 18.205 1201.529
67edo 66.998 17.911 1200.036
68edo 68.049 17.634 1199.136
69edo 68.96 17.401 1200.696
70edo 70.004 17.142 1199.931
71edo 71.059 16.887 1199.004
72edo 71.951 16.678 1200.817
73edo 72.984 16.442 1200.263
74edo 74.052 16.205 1199.157
75edo 75.091 15.981 1198.546
76edo 75.968 15.796 1200.505
77edo 76.992 15.586 1200.125
78edo 78.021 15.380 1199.677
79edo 78.892 15.211 1201.643
80edo 80.073 14.986 1198.906
81edo 80.947 14.825 1200.786
82edo 81.954 14.642 1200.674
83edo 82.967 14.464 1200.477
84edo 83.997 14.286 1200.043
85edo 84.991 14.119 1200.127
86edo 86.019 13.950 1199.735
87edo 87.014 13.791 1199.807
88edo 88.027 13.632 1199.632
89edo 89.023 13.480 1199.690
90edo 90.006 13.332 1199.920
91edo (1st peak) 90.852 13.208 1201.955
91edo (2nd peak) 91.033 13.182 1199.565
92edo 91.993 13.044 1200.091
93edo 93.002 12.903 1199.974
94edo 93.984 12.768 1200.204
95edo (1st peak) 94.962 12.637 1200.480
95edo (2nd peak) 95.117 12.616 1198.524
96edo 95.954 12.506 1200.575
97edo 96.925 12.381 1200.929
98edo 97.923 12.255 1200.944
99edo 99.047 12.115 1199.431
100edo 100.024 11.997 1199.712
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