Table of zeta-stretched edos: Difference between revisions

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BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
Added data to some blank cells in some rows
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
Added links to zpis
Line 21: Line 21:
|1064.774
|1064.774
|1.6
|1.6
|1
|[[1zpi]]
| -1
| -1
|-
|-
Line 29: Line 29:
|1217.039
|1217.039
|2.3
|2.3
|2
|[[2zpi]]
|0
|0
|-
|-
Line 37: Line 37:
|1176.471
|1176.471
|2.8
|2.8
|4
|[[4zpi]]
|2
|2
|-
|-
Line 45: Line 45:
|1229.508
|1229.508
|3.0
|3.0
|6
|[[6zpi]]
|4
|4
|-
|-
Line 53: Line 53:
|1191.895
|1191.895
|3.7
|3.7
|9
|[[9zpi]]
|7
|7
|-
|-
Line 61: Line 61:
|1193.041
|1193.041
|2.9
|2.9
|12
|[[12zpi]]
|10
|10
|-
|-
Line 69: Line 69:
|1207.417
|1207.417
|4.2
|4.2
|15
|[[15zpi]]
|13
|13
|-
|-
Line 77: Line 77:
|1179.796
|1179.796
|3.6
|3.6
|19
|[[19zpi]]
|17
|17
|-
|-
Line 85: Line 85:
|1206.704
|1206.704
|4.0
|4.0
|22
|[[22zpi]]
|20
|20
|-
|-
Line 93: Line 93:
|1199.041
|1199.041
|4.5
|4.5
|26
|[[26zpi]]
|24
|24
|-
|-
Line 101: Line 101:
|1195.977
|1195.977
|2.7
|2.7
|30
|[[30zpi]]
|28
|28
|-
|-
Line 109: Line 109:
|1197.704
|1197.704
|5.2
|5.2
|34
|[[34zpi]]
|32
|32
|-
|-
Line 117: Line 117:
|1202.868
|1202.868
|3.1
|3.1
|38
|[[38zpi]]
|36
|36
|-
|-
Line 125: Line 125:
|1208.633
|1208.633
|4.6
|4.6
|42
|[[42zpi]]
|40
|40
|-
|-
Line 133: Line 133:
|1195.775
|1195.775
|5.1
|5.1
|47
|[[47zpi]]
|45
|45
|-
|-
Line 141: Line 141:
|1204.139
|1204.139
|4.2
|4.2
|51
|[[51zpi]]
|49
|49
|-
|-
Line 149: Line 149:
|1196.832
|1196.832
|5.1
|5.1
|56
|[[56zpi]]
|54
|54
|-
|-
Line 157: Line 157:
|1192.119
|1192.119
|3.5
|3.5
|61
|[[61zpi]]
|59
|59
|-
|-
Line 165: Line 165:
|1203.293
|1203.293
|6.0
|6.0
|65
|[[65zpi]]
|63
|63
|-
|-
Line 173: Line 173:
|1201.081
|1201.081
|3.4
|3.4
|
|[[70zpi]]
|
|68
|-
|-
|21edo
|21edo
Line 181: Line 181:
|1198.402
|1198.402
|4.1
|4.1
|
|[[75zpi]]
|
|73
|-
|-
|22edo
|22edo
Line 189: Line 189:
|1198.638
|1198.638
|6.1
|6.1
|
|[[80zpi]]
|
|78
|-
|-
|23edo (1st peak)
|23edo (1st peak)
Line 197: Line 197:
|1210.148
|1210.148
|3.7
|3.7
|
|[[84zpi]]
|
|82
|-
|-
|23edo (2nd peak)
|23edo (2nd peak)
Line 205: Line 205:
|1198.645
|1198.645
|2.2
|2.2
|
|[[85zpi]]
|
|83
|-
|-
|24edo
|24edo
Line 213: Line 213:
|1199.700
|1199.700
|5.7
|5.7
|
|[[90zpi]]
|
|88
|-
|-
|25edo
|25edo
Line 221: Line 221:
|1201.682
|1201.682
|3.9
|3.9
|
|[[95zpi]]
|
|93
|-
|-
|26edo
|26edo
Line 229: Line 229:
|1202.961
|1202.961
|5.6
|5.6
|
|[[100zpi]]
|
|98
|-
|-
|27edo
|27edo
Line 237: Line 237:
|1196.146
|1196.146
|6.1
|6.1
|
|[[106zpi]]
|
|104
|-
|-
|28edo
|28edo
Line 245: Line 245:
|1198.630
|1198.630
|3.7
|3.7
|
|[[111zpi]]
|
|109
|-
|-
|29edo
|29edo
Line 253: Line 253:
|1202.488
|1202.488
|5.6
|5.6
|
|[[116zpi]]
|
|114
|-
|-
|30edo
|30edo
Line 261: Line 261:
|1197.525
|1197.525
|3.3
|3.3
|
|[[122zpi]]
|
|120
|-
|-
|31edo
|31edo
Line 269: Line 269:
|1200.852
|1200.852
|7.0
|7.0
|127
|[[127zpi]]
|125
|125
|-
|-
Line 277: Line 277:
|1197.381
|1197.381
|4.5
|4.5
|
|[[133zpi]]
|
|
|-
|-
Line 285: Line 285:
|1201.019
|1201.019
|3.3
|3.3
|
|[[138zpi]]
|
|
|-
|-
Line 293: Line 293:
|1198.414
|1198.414
|6.7
|6.7
|
|[[144zpi]]
|
|
|-
|-
Line 301: Line 301:
|1202.543
|1202.543
|4.2
|4.2
|
|[[149zpi]]
|
|
|-
|-
Line 309: Line 309:
|1200.600
|1200.600
|6.0
|6.0
|
|[[155zpi]]
|
|
|-
|-
Line 317: Line 317:
|1199.125
|1199.125
|5.3
|5.3
|
|[[161zpi]]
|
|
|-
|-
Line 325: Line 325:
|1203.484
|1203.484
|5.8
|5.8
|
|[[166zpi]]
|
|
|-
|-
Line 333: Line 333:
|1196.756
|1196.756
|2.5
|2.5
|
|[[167zpi]]
|
|
|-
|-
Line 341: Line 341:
|1202.590
|1202.590
|2.6
|2.6
|
|[[172zpi]]
|
|
|-
|-
Line 349: Line 349:
|1196.197
|1196.197
|5.6
|5.6
|
|[[173zpi]]
|
|
|-
|-
Line 357: Line 357:
|1200.961
|1200.961
|4.0
|4.0
|
|[[178zpi]]
|
|
|-
|-
Line 365: Line 365:
|1200.351
|1200.351
|7.6
|7.6
|184
|[[184zpi]]
|182
|182
|-
|-
Line 373: Line 373:
|1200.029
|1200.029
|2.7
|2.7
|
|[[190zpi]]
|
|
|-
|-
Line 381: Line 381:
|1199.247
|1199.247
|6.2
|6.2
|
|[[196zpi]]
|
|
|-
|-
Line 389: Line 389:
|1199.591
|1199.591
|4.6
|4.6
|
|[[202zpi]]
|
|
|-
|-
Line 397: Line 397:
|1204.282
|1204.282
|5.3
|5.3
|
|[[207zpi]]
|
|
|-
|-
Line 405: Line 405:
|1199.067
|1199.067
|2.1
|2.1
|
|[[208zpi]]
|
|
|-
|-
Line 413: Line 413:
|1199.765
|1199.765
|7.5
|7.5
|
|[[214zpi]]
|
|
|-
|-
Line 421: Line 421:
|1199.847
|1199.847
|4.3
|4.3
|
|[[220zpi]]
|
|
|-
|-
Line 429: Line 429:
|1200.300
|1200.300
|5.8
|5.8
|
|[[226zpi]]
|
|
|-
|-
Line 437: Line 437:
|1201.348
|1201.348
|2.2
|2.2
|
|[[232zpi]]
|
|
|-
|-
Line 445: Line 445:
|1196.557
|1196.557
|5.7
|5.7
|
|[[233zpi]]
|
|
|-
|-
Line 453: Line 453:
|1201.466
|1201.466
|6.7
|6.7
|
|[[238zpi]]
|
|
|-
|-
Line 461: Line 461:
|1198.144
|1198.144
|4.8
|4.8
|
|[[245zpi]]
|
|
|-
|-
Line 469: Line 469:
|1199.009
|1199.009
|4.1
|4.1
|
|[[251zpi]]
|
|
|-
|-
Line 477: Line 477:
|1200.068
|1200.068
|8.2
|8.2
|257
|[[257zpi]]
|255
|255
|-
|-
Line 485: Line 485:
|1201.134
|1201.134
|2.0
|2.0
|
|[[263zpi]]
|
|
|-
|-
Line 493: Line 493:
|1197.428
|1197.428
|3.5
|3.5
|
|[[264zpi]]
|
|
|-
|-
Line 501: Line 501:
|1202.317
|1202.317
|5.3
|5.3
|
|[[269zpi]]
|
|
|-
|-
Line 509: Line 509:
|1199.829
|1199.829
|6.1
|6.1
|
|[[276zpi]]
|
|
|-
|-
Line 517: Line 517:
|1200.674
|1200.674
|4.9
|4.9
|
|[[282zpi]]
|
|
|-
|-
Line 525: Line 525:
|1198.615
|1198.615
|7.8
|7.8
|
|[[289zpi]]
|
|
|-
|-
Line 533: Line 533:
|1200.163
|1200.163
|4.0
|4.0
|
|[[295zpi]]
|
|
|-
|-
Line 541: Line 541:
|1201.602
|1201.602
|7.1
|7.1
|
|[[301zpi]]
|
|
|-
|-
Line 549: Line 549:
|1199.941
|1199.941
|3.7
|3.7
|
|[[308zpi]]
|
|
|-
|-
Line 557: Line 557:
|1201.201
|1201.201
|6.3
|6.3
|
|[[314zpi]]
|
|
|-
|-
Line 565: Line 565:
|1199.638
|1199.638
|6.8
|6.8
|
|[[321zpi]]
|
|
|-
|-
Line 573: Line 573:
|1198.147
|1198.147
|3.6
|3.6
|
|[[328zpi]]
|
|
|-
|-
Line 581: Line 581:
|1199.705
|1199.705
|7.8
|7.8
|
|[[334zpi]]
|
|
|-
|-
Line 589: Line 589:
|1201.529
|1201.529
|4.5
|4.5
|
|[[340zpi]]
|
|
|-
|-
Line 597: Line 597:
|1200.036
|1200.036
|5.3
|5.3
|
|[[347zpi]]
|
|
|-
|-
Line 605: Line 605:
|1199.136
|1199.136
|7.7
|7.7
|
|[[354zpi]]
|
|
|-
|-
Line 613: Line 613:
|1200.696
|1200.696
|4.1
|4.1
|
|[[360zpi]]
|
|
|-
|-
Line 621: Line 621:
|1199.931
|1199.931
|5.7
|5.7
|
|[[367zpi]]
|
|
|-
|-
Line 629: Line 629:
|1199.004
|1199.004
|3.8
|3.8
|
|[[374zpi]]
|
|
|-
|-
Line 637: Line 637:
|1200.817
|1200.817
|9.2
|9.2
|380
|[[380zpi]]
|378
|378
|-
|-
Line 645: Line 645:
|1200.263
|1200.263
|3.4
|3.4
|
|[[387zpi]]
|
|
|-
|-
Line 653: Line 653:
|1199.157
|1199.157
|5.1
|5.1
|
|[[394zpi]]
|
|
|-
|-
Line 661: Line 661:
|1198.546
|1198.546
|6.0
|6.0
|
|[[401zpi]]
|
|
|-
|-
Line 669: Line 669:
|1200.505
|1200.505
|2.6
|2.6
|
|[[407zpi]]
|
|
|-
|-
Line 677: Line 677:
|1200.125
|1200.125
|8.2
|8.2
|
|[[414zpi]]
|
|
|-
|-
Line 685: Line 685:
|1199.677
|1199.677
|5.4
|5.4
|
|[[420zpi]]
|
|
|-
|-
Line 693: Line 693:
|1201.643
|1201.643
|5.8
|5.8
|
|[[427zpi]]
|
|
|-
|-
Line 701: Line 701:
|1198.906
|1198.906
|7.9
|7.9
|
|[[435zpi]]
|
|
|-
|-
Line 709: Line 709:
|1200.786
|1200.786
|5.2
|5.2
|
|[[441zpi]]
|
|
|-
|-
Line 717: Line 717:
|1200.674
|1200.674
|6.7
|6.7
|
|[[448zpi]]
|
|
|-
|-
Line 725: Line 725:
|1200.477
|1200.477
|3.9
|3.9
|
|[[455zpi]]
|
|
|-
|-
Line 733: Line 733:
|1200.043
|1200.043
|8.0
|8.0
|
|[[462zpi]]
|
|
|-
|-
Line 741: Line 741:
|1200.127
|1200.127
|3.0
|3.0
|
|[[469zpi]]
|
|
|-
|-
Line 749: Line 749:
|1199.735
|1199.735
|2.4
|2.4
|
|[[476zpi]]
|
|
|-
|-
Line 757: Line 757:
|1199.807
|1199.807
|8.9
|8.9
|
|[[483zpi]]
|
|
|-
|-
Line 765: Line 765:
|1199.632
|1199.632
|2.6
|2.6
|
|[[490zpi]]
|
|
|-
|-
Line 773: Line 773:
|1199.690
|1199.690
|7.6
|7.6
|
|[[497zpi]]
|
|
|-
|-
Line 781: Line 781:
|1199.920
|1199.920
|4.8
|4.8
|
|[[504zpi]]
|
|
|-
|-
Line 789: Line 789:
|1201.955
|1201.955
|6.7
|6.7
|
|[[510zpi]]
|
|
|-
|-
Line 797: Line 797:
|1199.565
|1199.565
|3.4
|3.4
|
|[[511zpi]]
|
|
|-
|-
Line 805: Line 805:
|1200.091
|1200.091
|4.5
|4.5
|
|[[518zpi]]
|
|
|-
|-
Line 813: Line 813:
|1199.974
|1199.974
|5.6
|5.6
|
|[[525zpi]]
|
|
|-
|-
Line 821: Line 821:
|1200.204
|1200.204
|8.8
|8.8
|
|[[532zpi]]
|
|
|-
|-
Line 829: Line 829:
|1200.480
|1200.480
|0.9
|0.9
|
|[[539zpi]]
|
|
|-
|-
Line 837: Line 837:
|1198.524
|1198.524
|5.3
|5.3
|
|[[540zpi]]
|
|
|-
|-
Line 845: Line 845:
|1200.575
|1200.575
|7.3
|7.3
|
|[[546zpi]]
|
|
|-
|-
Line 853: Line 853:
|1200.929
|1200.929
|4.2
|4.2
|
|[[553zpi]]
|
|
|-
|-
Line 861: Line 861:
|1200.944
|1200.944
|4.3
|4.3
|
|[[560zpi]]
|
|
|-
|-
Line 869: Line 869:
|1199.431
|1199.431
|9.4
|9.4
|
|[[568zpi]]
|
|
|-
|-
Line 877: Line 877:
|1199.712
|1199.712
|4.3
|4.3
|
|[[575zpi]]
|
|
|-
|-
Line 885: Line 885:
|1199.920
|1199.920
|13.4
|13.4
|1936
|[[1936zpi]]
|1934
|1934
|-
|-
Line 893: Line 893:
|1199.985
|1199.985
|13.1
|13.1
|2293
|[[2293zpi]]
|2291
|2291
|-
|-
Line 901: Line 901:
|1200.088
|1200.088
|13.5
|13.5
|2568
|[[2568zpi]]
|2566
|2566
|-
|-
Line 909: Line 909:
|1199.966
|1199.966
|14.7
|14.7
|3971
|[[3971zpi]]
|3969
|3969
|-
|-
Line 917: Line 917:
|1200.107
|1200.107
|14.3
|14.3
|5818
|[[5818zpi]]
|
|5816
|}
|}


Revision as of 05:37, 30 March 2024

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:

  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 Zeta peak index Gram point index
1edo 1.127 1064.774 1064.774 1.6 1zpi -1
2edo 1.972 608.519 1217.039 2.3 2zpi 0
3edo 3.06 392.157 1176.471 2.8 4zpi 2
4edo 3.904 307.377 1229.508 3.0 6zpi 4
5edo 5.034 238.379 1191.895 3.7 9zpi 7
6edo 6.035 198.840 1193.041 2.9 12zpi 10
7edo 6.957 172.488 1207.417 4.2 15zpi 13
8edo 8.137 147.474 1179.796 3.6 19zpi 17
9edo 8.95 134.078 1206.704 4.0 22zpi 20
10edo 10.008 119.904 1199.041 4.5 26zpi 24
11edo 11.037 108.725 1195.977 2.7 30zpi 28
12edo 12.023 99.809 1197.704 5.2 34zpi 32
13edo 12.969 92.528 1202.868 3.1 38zpi 36
14edo 13.9 86.331 1208.633 4.6 42zpi 40
15edo 15.053 79.718 1195.775 5.1 47zpi 45
16edo 15.945 75.259 1204.139 4.2 51zpi 49
17edo 17.045 70.402 1196.832 5.1 56zpi 54
18edo 18.119 66.229 1192.119 3.5 61zpi 59
19edo 18.948 63.331 1203.293 6.0 65zpi 63
20edo 19.982 60.054 1201.081 3.4 70zpi 68
21edo 21.028 57.067 1198.402 4.1 75zpi 73
22edo 22.025 54.484 1198.638 6.1 80zpi 78
23edo (1st peak) 22.807 52.615 1210.148 3.7 84zpi 82
23edo (2nd peak) 23.026 52.115 1198.645 2.2 85zpi 83
24edo 24.006 49.988 1199.700 5.7 90zpi 88
25edo 24.965 48.067 1201.682 3.9 95zpi 93
26edo 25.936 46.268 1202.961 5.6 100zpi 98
27edo 27.087 44.302 1196.146 6.1 106zpi 104
28edo 28.032 42.808 1198.630 3.7 111zpi 109
29edo 28.94 41.465 1202.488 5.6 116zpi 114
30edo 30.062 39.918 1197.525 3.3 122zpi 120
31edo 30.978 38.737 1200.852 7.0 127zpi 125
32edo 32.07 37.418 1197.381 4.5 133zpi
33edo 32.972 36.395 1201.019 3.3 138zpi
34edo 34.045 35.247 1198.414 6.7 144zpi
35edo 34.926 34.358 1202.543 4.2 149zpi
36edo 35.982 33.350 1200.600 6.0 155zpi
37edo 37.027 32.409 1199.125 5.3 161zpi
38edo (1st peak) 37.89 31.671 1203.484 5.8 166zpi
38edo (2nd peak) 38.103 31.494 1196.756 2.5 167zpi
39edo (1st peak) 38.916 30.836 1202.590 2.6 172zpi
39edo (2nd peak) 39.124 30.672 1196.197 5.6 173zpi
40edo 39.968 30.024 1200.961 4.0 178zpi
41edo 40.988 29.277 1200.351 7.6 184zpi 182
42edo 41.999 28.572 1200.029 2.7 190zpi
43edo 43.027 27.889 1199.247 6.2 196zpi
44edo 44.015 27.263 1199.591 4.6 202zpi
45edo (1st peak) 44.84 26.762 1204.282 5.3 207zpi
45edo (2nd peak) 45.035 26.646 1199.067 2.1 208zpi
46edo 46.009 26.082 1199.765 7.5 214zpi
47edo 47.006 25.529 1199.847 4.3 220zpi
48edo 47.988 25.006 1200.300 5.8 226zpi
49edo (1st peak) 48.945 24.517 1201.348 2.2 232zpi
49edo (2nd peak) 49.141 24.420 1196.557 5.7 233zpi
50edo 49.939 24.029 1201.466 6.7 238zpi
51edo 51.079 23.493 1198.144 4.8 245zpi
52edo 52.043 23.058 1199.009 4.1 251zpi
53edo 52.997 22.643 1200.068 8.2 257zpi 255
54edo (1st peak) 53.949 22.243 1201.134 2.0 263zpi
54edo (2nd peak) 54.116 22.175 1197.428 3.5 264zpi
55edo 54.894 21.860 1202.317 5.3 269zpi
56edo 56.008 21.426 1199.829 6.1 276zpi
57edo 56.968 21.064 1200.674 4.9 282zpi
58edo 58.067 20.666 1198.615 7.8 289zpi
59edo 58.992 20.342 1200.163 4.0 295zpi
60edo 59.92 20.027 1201.602 7.1 301zpi
61edo 61.003 19.671 1199.941 3.7 308zpi
62edo 61.938 19.374 1201.201 6.3 314zpi
63edo 63.019 19.042 1199.638 6.8 321zpi
64edo 64.099 18.721 1198.147 3.6 328zpi
65edo 65.016 18.457 1199.705 7.8 334zpi
66edo 65.916 18.205 1201.529 4.5 340zpi
67edo 66.998 17.911 1200.036 5.3 347zpi
68edo 68.049 17.634 1199.136 7.7 354zpi
69edo 68.96 17.401 1200.696 4.1 360zpi
70edo 70.004 17.142 1199.931 5.7 367zpi
71edo 71.059 16.887 1199.004 3.8 374zpi
72edo 71.951 16.678 1200.817 9.2 380zpi 378
73edo 72.984 16.442 1200.263 3.4 387zpi
74edo 74.052 16.205 1199.157 5.1 394zpi
75edo 75.091 15.981 1198.546 6.0 401zpi
76edo 75.968 15.796 1200.505 2.6 407zpi
77edo 76.992 15.586 1200.125 8.2 414zpi
78edo 78.021 15.380 1199.677 5.4 420zpi
79edo 78.892 15.211 1201.643 5.8 427zpi
80edo 80.073 14.986 1198.906 7.9 435zpi
81edo 80.947 14.825 1200.786 5.2 441zpi
82edo 81.954 14.642 1200.674 6.7 448zpi
83edo 82.967 14.464 1200.477 3.9 455zpi
84edo 83.997 14.286 1200.043 8.0 462zpi
85edo 84.991 14.119 1200.127 3.0 469zpi
86edo 86.019 13.950 1199.735 2.4 476zpi
87edo 87.014 13.791 1199.807 8.9 483zpi
88edo 88.027 13.632 1199.632 2.6 490zpi
89edo 89.023 13.480 1199.690 7.6 497zpi
90edo 90.006 13.332 1199.920 4.8 504zpi
91edo (1st peak) 90.852 13.208 1201.955 6.7 510zpi
91edo (2nd peak) 91.033 13.182 1199.565 3.4 511zpi
92edo 91.993 13.044 1200.091 4.5 518zpi
93edo 93.002 12.903 1199.974 5.6 525zpi
94edo 93.984 12.768 1200.204 8.8 532zpi
95edo (1st peak) 94.962 12.637 1200.480 0.9 539zpi
95edo (2nd peak) 95.117 12.616 1198.524 5.3 540zpi
96edo 95.954 12.506 1200.575 7.3 546zpi
97edo 96.925 12.381 1200.929 4.2 553zpi
98edo 97.923 12.255 1200.944 4.3 560zpi
99edo 99.047 12.115 1199.431 9.4 568zpi
100edo 100.024 11.997 1199.712 4.3 575zpi
270edo 270.018 4.444 1199.920 13.4 1936zpi 1934
311edo 311.004 3.858 1199.985 13.1 2293zpi 2291
342edo 341.975 3.509 1200.088 13.5 2568zpi 2566
494edo 494.014 2.429 1199.966 14.7 3971zpi 3969
684edo 683.939 1.755 1200.107 14.3 5818zpi 5816

See also

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