Table of zeta-stretched edos: Difference between revisions

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Line 13: Line 13:
|'''[[Octave]] size (cents)'''
|'''[[Octave]] size (cents)'''
|'''Zeta peak height'''
|'''Zeta peak height'''
|'''Peak number'''
|'''Gram point index'''
|'''Gram point index'''
|-
|-
Line 21: Line 20:
|'''1064.774'''
|'''1064.774'''
|'''1.6'''
|'''1.6'''
|1
| -1
| -1
|-
|-
Line 29: Line 27:
|'''1217.039'''
|'''1217.039'''
|'''2.3'''
|'''2.3'''
|2
|0
|0
|-
|-
Line 37: Line 34:
|'''1176.471'''
|'''1176.471'''
|'''2.8'''
|'''2.8'''
|4
|2
|2
|-
|-
Line 45: Line 41:
|'''1229.508'''
|'''1229.508'''
|'''3.0'''
|'''3.0'''
|6
|4
|
|-
|-
|'''[[5edo]]'''
|'''[[5edo]]'''
Line 53: Line 48:
|'''1191.895'''
|'''1191.895'''
|'''3.7'''
|'''3.7'''
|9
|7
|7
|-
|-
Line 61: Line 55:
|1193.041
|1193.041
|2.9
|2.9
|12
|10
|
|-
|-
|'''[[7edo]]'''
|'''[[7edo]]'''
Line 69: Line 62:
|'''1207.417'''
|'''1207.417'''
|'''4.2'''
|'''4.2'''
|15
|13
|13
|-
|-
Line 77: Line 69:
|1179.796
|1179.796
|3.6
|3.6
|19
|17
|
|-
|-
|[[9edo]]
|[[9edo]]
Line 85: Line 76:
|1206.704
|1206.704
|4.0
|4.0
|22
|20
|
|-
|-
|'''[[10edo]]'''
|'''[[10edo]]'''
Line 93: Line 83:
|'''1199.041'''
|'''1199.041'''
|'''4.5'''
|'''4.5'''
|26
|24
|
|-
|-
|[[11edo]]
|[[11edo]]
Line 101: Line 90:
|1195.977
|1195.977
|2.7
|2.7
|
|
|
|-
|-
Line 109: Line 97:
|'''1197.704'''
|'''1197.704'''
|'''5.2'''
|'''5.2'''
|34
|32
|32
|-
|-
Line 117: Line 104:
|1202.868
|1202.868
|3.1
|3.1
|38
|36
|
|-
|-
|[[14edo]]
|[[14edo]]
Line 125: Line 111:
|1208.633
|1208.633
|4.6
|4.6
|
|40
|
|-
|-
|[[15edo]]
|[[15edo]]
Line 133: Line 118:
|1195.775
|1195.775
|5.1
|5.1
|
|45
|
|-
|-
|[[16edo]]
|[[16edo]]
Line 141: Line 125:
|1204.139
|1204.139
|4.2
|4.2
|
|49
|
|-
|-
|[[17edo]]
|[[17edo]]
Line 149: Line 132:
|1196.832
|1196.832
|5.1
|5.1
|
|54
|
|-
|-
|[[18edo]]
|[[18edo]]
Line 157: Line 139:
|1192.119
|1192.119
|3.5
|3.5
|
|59
|
|-
|-
|'''[[19edo]]'''
|'''[[19edo]]'''
Line 165: Line 146:
|'''1203.293'''
|'''1203.293'''
|'''6.0'''
|'''6.0'''
|
|63
|63
|-
|-
Line 173: Line 153:
|1201.081
|1201.081
|3.4
|3.4
|
|
|
|-
|-
Line 181: Line 160:
|1198.402
|1198.402
|4.1
|4.1
|
|
|
|-
|-
Line 189: Line 167:
|'''1198.638'''
|'''1198.638'''
|'''6.1'''
|'''6.1'''
|
|
|
|-
|-
Line 197: Line 174:
|1210.148
|1210.148
|3.7
|3.7
|
|
|
|-
|-
Line 205: Line 181:
|1198.645
|1198.645
|2.2
|2.2
|
|
|
|-
|-
Line 213: Line 188:
|1199.700
|1199.700
|5.7
|5.7
|
|
|
|-
|-
Line 221: Line 195:
|1201.682
|1201.682
|3.9
|3.9
|
|
|
|-
|-
Line 229: Line 202:
|1202.961
|1202.961
|5.6
|5.6
|
|
|
|-
|-
Line 237: Line 209:
|'''1196.146'''
|'''1196.146'''
|'''6.1'''
|'''6.1'''
|
|
|
|-
|-
Line 245: Line 216:
|1198.630
|1198.630
|3.7
|3.7
|
|
|
|-
|-
Line 253: Line 223:
|1202.488
|1202.488
|5.6
|5.6
|
|
|
|-
|-
Line 261: Line 230:
|1197.525
|1197.525
|3.3
|3.3
|
|
|
|-
|-
Line 269: Line 237:
|'''1200.852'''
|'''1200.852'''
|'''7.0'''
|'''7.0'''
|
|125
|125
|-
|-
Line 277: Line 244:
|1197.381
|1197.381
|4.5
|4.5
|
|
|
|-
|-
Line 285: Line 251:
|1201.019
|1201.019
|3.3
|3.3
|
|
|
|-
|-
Line 293: Line 258:
|1198.414
|1198.414
|6.7
|6.7
|
|
|
|-
|-
Line 301: Line 265:
|1202.543
|1202.543
|4.2
|4.2
|
|
|
|-
|-
Line 309: Line 272:
|1200.600
|1200.600
|6.0
|6.0
|
|
|
|-
|-
Line 317: Line 279:
|1199.125
|1199.125
|5.3
|5.3
|
|
|
|-
|-
Line 325: Line 286:
|1203.484
|1203.484
|5.8
|5.8
|
|
|
|-
|-
Line 333: Line 293:
|1196.756
|1196.756
|2.5
|2.5
|
|
|
|-
|-
Line 341: Line 300:
|1202.590
|1202.590
|2.6
|2.6
|
|
|
|-
|-
Line 349: Line 307:
|1196.197
|1196.197
|5.6
|5.6
|
|
|
|-
|-
Line 357: Line 314:
|1200.961
|1200.961
|4.0
|4.0
|
|
|
|-
|-
Line 365: Line 321:
|'''1200.351'''
|'''1200.351'''
|'''7.6'''
|'''7.6'''
|
|182
|182
|-
|-
Line 373: Line 328:
|1200.029
|1200.029
|2.7
|2.7
|
|
|
|-
|-
Line 381: Line 335:
|1199.247
|1199.247
|6.2
|6.2
|
|
|
|-
|-
Line 389: Line 342:
|1199.591
|1199.591
|4.6
|4.6
|
|
|
|-
|-
Line 397: Line 349:
|1204.282
|1204.282
|5.3
|5.3
|
|
|
|-
|-
Line 405: Line 356:
|1199.067
|1199.067
|2.1
|2.1
|
|
|
|-
|-
Line 413: Line 363:
|1199.765
|1199.765
|7.5
|7.5
|
|
|
|-
|-
Line 421: Line 370:
|1199.847
|1199.847
|4.3
|4.3
|
|
|
|-
|-
Line 429: Line 377:
|1200.300
|1200.300
|5.8
|5.8
|
|
|
|-
|-
Line 437: Line 384:
|1201.348
|1201.348
|2.2
|2.2
|
|
|
|-
|-
Line 445: Line 391:
|1196.557
|1196.557
|5.7
|5.7
|
|
|
|-
|-
Line 453: Line 398:
|1201.466
|1201.466
|6.7
|6.7
|
|
|
|-
|-
Line 461: Line 405:
|1198.144
|1198.144
|4.8
|4.8
|
|
|
|-
|-
Line 469: Line 412:
|1199.009
|1199.009
|4.1
|4.1
|
|
|
|-
|-
Line 477: Line 419:
|'''1200.068'''
|'''1200.068'''
|'''8.2'''
|'''8.2'''
|
|255
|255
|-
|-
Line 485: Line 426:
|1201.134
|1201.134
|2.0
|2.0
|
|
|
|-
|-
Line 493: Line 433:
|1197.428
|1197.428
|3.5
|3.5
|
|
|
|-
|-
Line 501: Line 440:
|1202.317
|1202.317
|5.3
|5.3
|
|
|
|-
|-
Line 509: Line 447:
|1199.829
|1199.829
|6.1
|6.1
|
|
|
|-
|-
Line 517: Line 454:
|1200.674
|1200.674
|4.9
|4.9
|
|
|
|-
|-
Line 525: Line 461:
|1198.615
|1198.615
|7.8
|7.8
|
|
|
|-
|-
Line 533: Line 468:
|1200.163
|1200.163
|4.0
|4.0
|
|
|
|-
|-
Line 541: Line 475:
|1201.602
|1201.602
|7.1
|7.1
|
|
|
|-
|-
Line 549: Line 482:
|1199.941
|1199.941
|3.7
|3.7
|
|
|
|-
|-
Line 557: Line 489:
|1201.201
|1201.201
|6.3
|6.3
|
|
|
|-
|-
Line 565: Line 496:
|1199.638
|1199.638
|6.8
|6.8
|
|
|
|-
|-
Line 573: Line 503:
|1198.147
|1198.147
|3.6
|3.6
|
|
|
|-
|-
Line 581: Line 510:
|1199.705
|1199.705
|7.8
|7.8
|
|
|
|-
|-
Line 589: Line 517:
|1201.529
|1201.529
|4.5
|4.5
|
|
|
|-
|-
Line 597: Line 524:
|1200.036
|1200.036
|5.3
|5.3
|
|
|
|-
|-
Line 605: Line 531:
|1199.136
|1199.136
|7.7
|7.7
|
|
|
|-
|-
Line 613: Line 538:
|1200.696
|1200.696
|4.1
|4.1
|
|
|
|-
|-
Line 621: Line 545:
|1199.931
|1199.931
|5.7
|5.7
|
|
|
|-
|-
Line 629: Line 552:
|1199.004
|1199.004
|3.8
|3.8
|
|
|
|-
|-
Line 637: Line 559:
|'''1200.817'''
|'''1200.817'''
|'''9.2'''
|'''9.2'''
|
|378
|378
|-
|-
Line 645: Line 566:
|1200.263
|1200.263
|3.4
|3.4
|
|
|
|-
|-
Line 653: Line 573:
|1199.157
|1199.157
|5.1
|5.1
|
|
|
|-
|-
Line 661: Line 580:
|1198.546
|1198.546
|6.0
|6.0
|
|
|
|-
|-
Line 669: Line 587:
|1200.505
|1200.505
|2.6
|2.6
|
|
|
|-
|-
Line 677: Line 594:
|1200.125
|1200.125
|8.2
|8.2
|
|
|
|-
|-
Line 685: Line 601:
|1199.677
|1199.677
|5.4
|5.4
|
|
|
|-
|-
Line 693: Line 608:
|1201.643
|1201.643
|5.8
|5.8
|
|
|
|-
|-
Line 701: Line 615:
|1198.906
|1198.906
|7.9
|7.9
|
|
|
|-
|-
Line 709: Line 622:
|1200.786
|1200.786
|5.2
|5.2
|
|
|
|-
|-
Line 717: Line 629:
|1200.674
|1200.674
|6.7
|6.7
|
|
|
|-
|-
Line 725: Line 636:
|1200.477
|1200.477
|3.9
|3.9
|
|
|
|-
|-
Line 733: Line 643:
|1200.043
|1200.043
|8.0
|8.0
|
|
|
|-
|-
Line 741: Line 650:
|1200.127
|1200.127
|3.0
|3.0
|
|
|
|-
|-
Line 749: Line 657:
|1199.735
|1199.735
|2.4
|2.4
|
|
|
|-
|-
Line 757: Line 664:
|1199.807
|1199.807
|8.9
|8.9
|
|
|
|-
|-
Line 765: Line 671:
|1199.632
|1199.632
|2.6
|2.6
|
|
|
|-
|-
Line 773: Line 678:
|1199.690
|1199.690
|7.6
|7.6
|
|
|
|-
|-
Line 781: Line 685:
|1199.920
|1199.920
|4.8
|4.8
|
|
|
|-
|-
Line 789: Line 692:
|1201.955
|1201.955
|6.7
|6.7
|
|
|
|-
|-
Line 797: Line 699:
|1199.565
|1199.565
|3.4
|3.4
|
|
|
|-
|-
Line 805: Line 706:
|1200.091
|1200.091
|4.5
|4.5
|
|
|
|-
|-
Line 813: Line 713:
|1199.974
|1199.974
|5.6
|5.6
|
|
|
|-
|-
Line 821: Line 720:
|1200.204
|1200.204
|8.8
|8.8
|
|
|
|-
|-
Line 829: Line 727:
|1200.480
|1200.480
|0.9
|0.9
|
|
|
|-
|-
Line 837: Line 734:
|1198.524
|1198.524
|5.3
|5.3
|
|
|
|-
|-
Line 845: Line 741:
|1200.575
|1200.575
|7.3
|7.3
|
|
|
|-
|-
Line 853: Line 748:
|1200.929
|1200.929
|4.2
|4.2
|
|
|
|-
|-
Line 861: Line 755:
|1200.944
|1200.944
|4.3
|4.3
|
|
|
|-
|-
Line 869: Line 762:
|'''1199.431'''
|'''1199.431'''
|'''9.4'''
|'''9.4'''
|
|
|
|-
|-
Line 877: Line 769:
|1199.712
|1199.712
|4.3
|4.3
|
|
|
|-
|-
|[[270edo]]
|[[270edo]]
|
|
|
|
|
Line 889: Line 779:
|-
|-
|[[311edo]]
|[[311edo]]
|
|
|
|
|
Line 897: Line 786:
|-
|-
|[[342edo]]
|[[342edo]]
|
|
|
|
|
Line 905: Line 793:
|-
|-
|[[494edo]]
|[[494edo]]
|
|
|
|
|

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