Amity
From Xenharmonic Reference
Amity (from "acute minor third"), 2.3.5.7[46 & 53], is a complex temperament splitting 8/3 into 5 supraminor thirds about 339c-340c in size. It has a tuning that is very accurate in the 7-limit (namely 99edo).
Amity is a 7-cluster temperament due to its generator being only slightly flatter than 2\7.
Interval chain
Notes:
- 243/200 is 6/5 sharpened by 81/80.
- The extension to 13 given is called Hitchcock, whose 13 mapping tend to be flat due to tempering out S13.
- 1 gen = 128/105 ~ 243/200 ~ 39/32 (=> tempers out 5120/5103 = S8/S9 and 4096/4095 = S64)
- 2 gens = 40/27
- 3 gens = 9/5
- 4 gens = 35/32
- 5 gens = 4/3
- 6 gens = 13/8 ~ 21/13 (=> S13 is tempered out)
- 7 gens = 80/81 ~ 63/64 ~ 64/65
- 8 gens = 6/5
- 9 gens = 48/35
- 10 gens = 16/9
- 11 gens = 13/12 ~ 14/13
- 12 gens = 21/16
- 13 gens = 8/5
- 14 gens = 35/36
- 15 gens = 32/27
- 16 gens = 36/25 ~ 13/9
- 17 gens = 7/4
- 18 gens = 16/15
- 19 gens = 13/10
- 20 gens = 128/81
- 21 gens = 20/21 ~ 24/25
- 22 gens = 7/6
- 23 gens = 64/45
- 24 gens = 26/15
- 25 gens = 256/243
- 26 gens = 32/25
- 27 gens = 14/9
List of patent vals
The following are non-contorted 5-limit patent vals supporting Amity:
| Edo | Generator | Fifth |
|---|---|---|
| 39 | 338.462 | 707.692 |
| 46 | 339.130 | 704.348 |
| 92 | 339.130 | 704.348 |
| 145 | 339.310 | 703.448 |
| 244 | 339.344 | 703.279 |
| 99 | 339.394 | 703.030 |
| 198 | 339.394 | 703.030 |
| 297 | 339.394 | 703.030 |
| 449 | 339.421 | 702.895 |
| 350 | 339.429 | 702.857 |
| 251 | 339.442 | 702.789 |
| 502 | 339.442 | 702.789 |
| 654 | 339.450 | 702.752 |
| 403 | 339.454 | 702.730 |
| 555 | 339.459 | 702.703 |
| 707 | 339.463 | 702.687 |
| 152 | 339.474 | 702.632 |
| 304 | 339.474 | 702.632 |
| 456 | 339.474 | 702.632 |
| 608 | 339.474 | 702.632 |
| 760 | 339.474 | 702.632 |
| 813 | 339.483 | 702.583 |
| 661 | 339.486 | 702.572 |
| 509 | 339.489 | 702.554 |
| 866 | 339.492 | 702.540 |
| 357 | 339.496 | 702.521 |
| 714 | 339.496 | 702.521 |
| 919 | 339.499 | 702.503 |
| 562 | 339.502 | 702.491 |
| 767 | 339.505 | 702.477 |
| 972 | 339.506 | 702.469 |
| 1177 | 339.507 | 702.464 |
| 205 | 339.512 | 702.439 |
| 410 | 339.512 | 702.439 |
| 615 | 339.512 | 702.439 |
| 820 | 339.512 | 702.439 |
| 1025 | 339.512 | 702.439 |
| 1230 | 339.512 | 702.439 |
| 1283 | 339.517 | 702.416 |
| 1078 | 339.518 | 702.412 |
| 873 | 339.519 | 702.405 |
| 668 | 339.521 | 702.395 |
| 1336 | 339.521 | 702.395 |
| 1131 | 339.523 | 702.387 |
| 463 | 339.525 | 702.376 |
| 926 | 339.525 | 702.376 |
| 1389 | 339.525 | 702.376 |
| 1184 | 339.527 | 702.365 |
| 721 | 339.528 | 702.358 |
| 1442 | 339.528 | 702.358 |
| 979 | 339.530 | 702.349 |
| 1237 | 339.531 | 702.344 |
| 1495 | 339.532 | 702.341 |
| 258 | 339.535 | 702.326 |
| 516 | 339.535 | 702.326 |
| 774 | 339.535 | 702.326 |
| 1032 | 339.535 | 702.326 |
| 1290 | 339.535 | 702.326 |
| 1548 | 339.535 | 702.326 |
| 1601 | 339.538 | 702.311 |
| 1343 | 339.538 | 702.308 |
| 1085 | 339.539 | 702.304 |
| 827 | 339.541 | 702.297 |
| 1654 | 339.541 | 702.297 |
| 1396 | 339.542 | 702.292 |
| 569 | 339.543 | 702.285 |
| 1138 | 339.543 | 702.285 |
| 1449 | 339.545 | 702.277 |
| 880 | 339.545 | 702.273 |
| 1191 | 339.547 | 702.267 |
| 311 | 339.550 | 702.251 |
| 622 | 339.550 | 702.251 |
| 933 | 339.550 | 702.251 |
| 1244 | 339.550 | 702.251 |
| 986 | 339.554 | 702.231 |
| 675 | 339.556 | 702.222 |
| 1039 | 339.557 | 702.214 |
| 364 | 339.560 | 702.198 |
| 728 | 339.560 | 702.198 |
| 781 | 339.565 | 702.177 |
| 417 | 339.568 | 702.158 |
| 834 | 339.568 | 702.158 |
| 470 | 339.574 | 702.128 |
| 523 | 339.579 | 702.103 |
| 576 | 339.583 | 702.083 |
| 629 | 339.587 | 702.067 |
| 53 | 339.623 | 701.887 |
| 106 | 339.623 | 701.887 |
| 159 | 339.623 | 701.887 |
| 212 | 339.623 | 701.887 |
| 265 | 339.623 | 701.887 |
| 318 | 339.623 | 701.887 |
| 371 | 339.623 | 701.887 |
| 424 | 339.623 | 701.887 |
| 166 | 339.759 | 701.205 |
| 113 | 339.823 | 700.885 |
| 60 | 340.000 | 700.000 |
| 7 | 342.857 | 685.714 |
