Hemifamity/Patent vals
From Xenharmonic Reference
The following patent vals support 2.3.5.7 Hemifamity (aka Aberschismic). Vals that are contorted in 2.3.5.7 are not included.
Note on extensions:
- 11-limit extensions: 41 & 46 & 53 is called Akea (tempers out 385/384), and 41 & 46 & 58 is called Pele (tempers out 896/891). The intersection of the two is Rodan (41 & 46).
- 13-limit extensions: 41 & 46 & 53 tempers out 4096/4095.
| Edo | Extension to 11 | Extension to 13 | 81/80 tuning | 3/2 tuning | 5/4 tuning | 7/4 tuning |
|---|---|---|---|---|---|---|
| 7 | 41 & 46 & 53 | 41 & 46 & 53 | 0.000 | 685.714 | 342.857 | 1028.571 |
| 12 | 41 & 46 & 58 | 41 & 46 & 53 | 0.000 | 700.000 | 400.000 | 1000.000 |
| 5 | 41 & 46 & 53, 41 & 46 & 58 | 0.000 | 720.000 | 480.000 | 960.000 | |
| 70 | 17.143 | 702.857 | 394.286 | 977.143 | ||
| 58 | 41 & 46 & 58 | 20.690 | 703.448 | 393.103 | 972.414 | |
| 111 | 21.622 | 702.703 | 389.189 | 972.973 | ||
| 53 | 41 & 46 & 53 | 41 & 46 & 53 | 22.642 | 701.887 | 384.906 | 973.585 |
| 210 | 22.857 | 702.857 | 388.571 | 971.429 | ||
| 157 | 22.930 | 703.185 | 389.809 | 970.701 | ||
| 205 | 23.415 | 702.439 | 386.341 | 971.707 | ||
| 152 | 41 & 46 & 53 | 23.684 | 702.632 | 386.842 | 971.053 | |
| 251 | 23.904 | 702.789 | 387.251 | 970.518 | ||
| 350 | 24.000 | 702.857 | 387.429 | 970.286 | ||
| 449 | 24.053 | 702.895 | 387.528 | 970.156 | ||
| 99 | 41 & 46 & 53 | 41 & 46 & 53 | 24.242 | 703.030 | 387.879 | 969.697 |
| 198 | 24.242 | 703.030 | 387.879 | 969.697 | ||
| 297 | 24.242 | 703.030 | 387.879 | 969.697 | ||
| 345 | 24.348 | 702.609 | 386.087 | 970.435 | ||
| 246 | 41 & 46 & 53 | 24.390 | 702.439 | 385.366 | 970.732 | |
| 589 | 24.448 | 702.886 | 387.097 | 969.779 | ||
| 147 | 41 & 46 & 53 | 24.490 | 702.041 | 383.673 | 971.429 | |
| 490 | 24.490 | 702.857 | 386.939 | 969.796 | ||
| 391 | 24.552 | 702.813 | 386.701 | 969.821 | ||
| 244 | 24.590 | 703.279 | 388.525 | 968.852 | ||
| 536 | 24.627 | 702.985 | 387.313 | 969.403 | ||
| 292 | 24.658 | 702.740 | 386.301 | 969.863 | ||
| 340 | 41 & 46 & 53 | 24.706 | 702.353 | 384.706 | 970.588 | |
| 437 | 24.714 | 702.975 | 387.185 | 969.336 | ||
| 485 | 24.742 | 702.680 | 385.979 | 969.897 | ||
| 630 | 24.762 | 702.857 | 386.667 | 969.524 | ||
| 145 | 41 & 46 & 58 | 24.828 | 703.448 | 388.966 | 968.276 | |
| 338 | 24.852 | 702.959 | 386.982 | 969.231 | ||
| 531 | 24.859 | 702.825 | 386.441 | 969.492 | ||
| 724 | 24.862 | 702.762 | 386.188 | 969.613 | ||
| 193 | 41 & 46 & 53 | 24.870 | 702.591 | 385.492 | 969.948 | |
| 386 | 24.870 | 702.591 | 385.492 | 969.948 | ||
| 577 | 24.957 | 702.946 | 386.828 | 969.151 | ||
| 625 | 24.960 | 702.720 | 385.920 | 969.600 | ||
| 48 | 41 & 46 & 53 | 41 & 46 & 53 | 25.000 | 700.000 | 375.000 | 975.000 |
| 432 | 25.000 | 702.778 | 386.111 | 969.444 | ||
| 384 | 25.000 | 703.125 | 387.500 | 968.750 | ||
| 671 | 25.037 | 702.832 | 386.289 | 969.300 | ||
| 287 | 41 & 46 & 53 | 25.087 | 702.439 | 384.669 | 970.035 | |
| 526 | 41 & 46 & 53 | 25.095 | 702.662 | 385.551 | 969.582 | |
| 239 | 41 & 46 & 53 | 25.105 | 702.929 | 386.611 | 969.038 | |
| 572 | 25.175 | 702.797 | 386.014 | 969.231 | ||
| 524 | 25.191 | 703.053 | 387.023 | 968.702 | ||
| 333 | 41 & 46 & 53 | 25.225 | 702.703 | 385.586 | 969.369 | |
| 618 | 25.243 | 702.913 | 386.408 | 968.932 | ||
| 285 | 25.263 | 703.158 | 387.368 | 968.421 | ||
| 427 | 41 & 46 & 53 | 25.293 | 702.576 | 385.012 | 969.555 | |
| 379 | 41 & 46 & 53 | 25.330 | 702.902 | 386.280 | 968.865 | |
| 473 | 41 & 46 & 53 | 25.370 | 702.748 | 385.624 | 969.133 | |
| 331 | 25.378 | 703.323 | 387.915 | 967.976 | ||
| 425 | 25.412 | 703.059 | 386.824 | 968.471 | ||
| 519 | 25.434 | 702.890 | 386.127 | 968.786 | ||
| 613 | 41 & 46 & 53 | 25.449 | 702.773 | 385.644 | 969.005 | |
| 471 | 25.478 | 703.185 | 387.261 | 968.153 | ||
| 565 | 25.487 | 703.009 | 386.549 | 968.496 | ||
| 94 | 41 & 46 & 53 | 41 & 46 & 53 | 25.532 | 702.128 | 382.979 | 970.213 |
| 234 | 41 & 46 & 53 | 25.641 | 702.564 | 384.615 | 969.231 | |
| 374 | 41 & 46 & 53 | 25.668 | 702.674 | 385.027 | 968.984 | |
| 514 | 41 & 46 & 53 | 25.681 | 702.724 | 385.214 | 968.872 | |
| 140 | 41 & 46 & 53 | 41 & 46 & 53 | 25.714 | 702.857 | 385.714 | 968.571 |
| 466 | 41 & 46 & 53 | 25.751 | 703.004 | 386.266 | 968.240 | |
| 326 | 41 & 46 & 53 | 25.767 | 703.067 | 386.503 | 968.098 | |
| 512 | 25.781 | 703.125 | 386.719 | 967.969 | ||
| 186 | 41 & 46 & 53 | 41 & 46 & 53 | 25.806 | 703.226 | 387.097 | 967.742 |
| 418 | 25.837 | 703.349 | 387.560 | 967.464 | ||
| 232 | 41 & 46 & 58 | 25.862 | 703.448 | 387.931 | 967.241 | |
| 601 | 41 & 46 & 53 | 25.957 | 702.829 | 385.358 | 968.386 | |
| 461 | 41 & 46 & 53 | 26.030 | 702.820 | 385.249 | 968.330 | |
| 507 | 41 & 46 & 53 | 26.036 | 702.959 | 385.799 | 968.047 | |
| 46 | 41 & 46 & 53, 41 & 46 & 58 | 41 & 46 & 53 | 26.087 | 704.348 | 391.304 | 965.217 |
| 413 | 41 & 46 & 53 | 26.150 | 703.148 | 386.441 | 967.554 | |
| 367 | 41 & 46 & 53 | 26.158 | 702.997 | 385.831 | 967.847 | |
| 321 | 41 & 46 & 53 | 41 & 46 & 53 | 26.168 | 702.804 | 385.047 | 968.224 |
| 548 | 41 & 46 & 53 | 26.277 | 702.920 | 385.401 | 967.883 | |
| 273 | 41 & 46 & 53 | 41 & 46 & 53 | 26.374 | 703.297 | 386.813 | 967.033 |
| 227 | 41 & 46 & 53 | 41 & 46 & 53 | 26.432 | 703.084 | 385.903 | 967.401 |
| 408 | 41 & 46 & 53 | 41 & 46 & 53 | 26.471 | 702.941 | 385.294 | 967.647 |
| 181 | 41 & 46 & 53 | 41 & 46 & 53 | 26.519 | 702.762 | 384.530 | 967.956 |
| 135 | 41 & 46 & 53 | 41 & 46 & 53 | 26.667 | 702.222 | 382.222 | 968.889 |
| 268 | 41 & 46 & 53 | 41 & 46 & 53 | 26.866 | 702.985 | 385.075 | 967.164 |
| 222 | 41 & 46 & 53 | 27.027 | 702.703 | 383.784 | 967.568 | |
| 133 | 41 & 46 & 53, 41 & 46 & 58 | 41 & 46 & 53 | 27.068 | 703.759 | 387.970 | 965.414 |
| 309 | 41 & 46 & 53 | 27.184 | 702.913 | 384.466 | 966.990 | |
| 87 | 41 & 46 & 53, 41 & 46 & 58 | 41 & 46 & 53 | 27.586 | 703.448 | 386.207 | 965.517 |
| 128 | 41 & 46 & 53, 41 & 46 & 58 | 41 & 46 & 53 | 28.125 | 703.125 | 384.375 | 965.625 |
| 169 | 41 & 46 & 53, 41 & 46 & 58 | 28.402 | 702.959 | 383.432 | 965.680 | |
| 41 | 41 & 46 & 53, 41 & 46 & 58 | 41 & 46 & 53 | 29.268 | 702.439 | 380.488 | 965.854 |
| 39 | 41 & 46 & 53 | 41 & 46 & 53 | 30.769 | 707.692 | 400.000 | 953.846 |
| 34 | 41 & 46 & 53 | 41 & 46 & 53 | 35.294 | 705.882 | 388.235 | 952.941 |
| 29 | 41 & 46 & 58 | 41.379 | 703.448 | 372.414 | 951.724 |
