Hemififths
The hemififths temperament tempers out the breedsma, 2401/2400, and the hemifamity comma, 5120/5103, and as the name suggests, uses a neutral-third generator. Hemif is the no-5 subgroup version of hemififths.
See Breedsmic temperaments #Hemififths for more technical data.
Interval chain
In the following table, prime harmonics are labeled in bold.
| # | Cents* | Approximate Ratios | |
|---|---|---|---|
| 7-limit | 13-limit Extension | ||
| 0 | 0.000 | 1/1 | |
| 1 | 351.477 | 49/40, 60/49 | 11/9, 16/13, 27/22, 39/32 |
| 2 | 702.955 | 3/2 | |
| 3 | 1054.432 | 90/49 | 11/6, 24/13 |
| 4 | 205.910 | 9/8 | |
| 5 | 557.387 | 112/81 | 11/8, 18/13 |
| 6 | 908.865 | 27/16 | 22/13 |
| 7 | 60.342 | 28/27 | 33/32, 27/26 |
| 8 | 411.819 | 81/64, 80/63 | 14/11, 33/26 |
| 9 | 763.297 | 14/9 | |
| 10 | 1114.774 | 40/21 | 21/11 |
| 11 | 266.252 | 7/6 | |
| 12 | 617.729 | 10/7 | |
| 13 | 969.206 | 7/4 | |
| 14 | 120.684 | 15/14 | 14/13 |
| 15 | 472.161 | 21/16 | |
| 16 | 823.639 | 45/28 | 21/13 |
| 17 | 1175.116 | 63/32, 160/81 | |
| 18 | 326.594 | 98/81, 135/112 | 40/33 |
| 19 | 678.071 | 40/27 | |
| 20 | 1029.549 | 49/27 | 20/11 |
| 21 | 181.026 | 10/9 | |
| 22 | 532.503 | 49/36 | 15/11 |
| 23 | 883.981 | 5/3 | |
| 24 | 35.458 | 49/48, 50/49 | 45/44, 55/54 |
| 25 | 386.936 | 5/4 | |
* in 7-limit POTE tuning
Chords
Scales
Tuning spectrum
Gencom: [2 11/9; 144/143 196/195 243/242 364/363]
Gencom map: [⟨1 1 -5 -1 2 4], ⟨0 2 25 13 5 -1]]
| Eigenmonzo | Generator | Comments |
|---|---|---|
| 11/9 | 347.408 | |
| 12/11 | 349.788 | |
| (7\24) | 350.000 | |
| 11/8 | 350.264 | |
| 4/3 | 350.978 | |
| (12\41) | 351.220 | |
| 15/14 | 351.389 | |
| 16/15 | 351.417 | |
| (41\140) | 351.429 | |
| 8/7 | 351.448 | 7-, 9- and 11-odd-limit hemif minimax |
| 5/4 | 351.453 | 5-, 7-, 9- and 11-odd-limit minimax |
| 7/5 | 351.457 | |
| 6/5 | 351.494 | |
| (29\99) | 351.515 | |
| 7/6 | 351.534 | |
| 10/9 | 351.543 | |
| 9/7 | 351.657 | |
| 15/11 | 351.680 | |
| 15/13 | 351.705 | 15-odd-limit minimax |
| (17\58) | 351.724 | |
| 11/10 | 351.750 | |
| 13/10 | 351.761 | 13-odd-limit minimax |
| 13/11 | 351.798 | 13- and 15-odd-limit hemif minimax |
| (22\75) | 352.000 | |
| 14/13 | 352.021 | |
| 14/11 | 352.188 | |
| 18/13 | 352.676 | |
| 13/12 | 353.809 | |
| 16/13 | 359.472 |