Table of zeta-stretched edos
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:
- Copy-paste Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9,12.1}] into a cell.
- 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".
- Ensure that cell is still selected
- 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 | 1 | -1 |
| 2edo | 1.972 | 608.519 | 1217.039 | 2.3 | 2 | 0 |
| 3edo | 3.06 | 392.157 | 1176.471 | 2.8 | 4 | 2 |
| 4edo | 3.904 | 307.377 | 1229.508 | 3.0 | 6 | 4 |
| 5edo | 5.034 | 238.379 | 1191.895 | 3.7 | 9 | 7 |
| 6edo | 6.035 | 198.840 | 1193.041 | 2.9 | 12 | 10 |
| 7edo | 6.957 | 172.488 | 1207.417 | 4.2 | 15 | 13 |
| 8edo | 8.137 | 147.474 | 1179.796 | 3.6 | 19 | 17 |
| 9edo | 8.95 | 134.078 | 1206.704 | 4.0 | 22 | 20 |
| 10edo | 10.008 | 119.904 | 1199.041 | 4.5 | 26 | 24 |
| 11edo | 11.037 | 108.725 | 1195.977 | 2.7 | 30 | 28 |
| 12edo | 12.023 | 99.809 | 1197.704 | 5.2 | 34 | 32 |
| 13edo | 12.969 | 92.528 | 1202.868 | 3.1 | 38 | 36 |
| 14edo | 13.9 | 86.331 | 1208.633 | 4.6 | 42 | 40 |
| 15edo | 15.053 | 79.718 | 1195.775 | 5.1 | 47 | 45 |
| 16edo | 15.945 | 75.259 | 1204.139 | 4.2 | 51 | 49 |
| 17edo | 17.045 | 70.402 | 1196.832 | 5.1 | 56 | 54 |
| 18edo | 18.119 | 66.229 | 1192.119 | 3.5 | 61 | 59 |
| 19edo | 18.948 | 63.331 | 1203.293 | 6.0 | 65 | 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 | 127 | 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 | 184 | 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 | 257 | 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 | 380 | 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 | 1936 | 1934 | ||||
| 311edo | 2293 | 2291 | ||||
| 342edo | 2568 | 2566 | ||||
| 494edo | 3971 | 3969 |