4992/4991
| Interval information |
thiwutwethuthoru unison
reduced
4992/4991, the kalmanisma, is a 31-limit superparticular comma of about 0.35 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 156/155 and 161/160
- 208/207 and 217/216
- 576/575 and 651/650
- 806/805 and 961/960
- 1024/1023 and 1288/1287
- 1520/1519 and 2185/2184
- 1768/1767 and 2737/2736
- 2016/2015 and 3381/3380
- 2080/2079 and 3565/3564
It can be factored into the following superparticular ratios:
- 5083/5082 and 278784/278783
- 5104/5103 and 227448/227447
- 5643/5642 and 43264/43263
- 5888/5887 and 32799/32798
- 6480/6479 and 21736/21735
- 6656/6655 and 19965/19964
- 6728/6727 and 19344/19343
- 7936/7935 and 13455/13454
- 8464/8463 and 12168/12167
- 8960/8959 and 11271/11270
Temperaments
Tempering out this comma in the full 31-limit leads to the rank-10 temperament kalmanismic. Using the 2.3.7.13.23.31 subgroup leads to the rank-5 temperament kalmanic.
Kalmanismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Comma list: 4992/4991
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 5 | ], |
| [⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| [⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| [⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| [⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.942, ~5/4 = 386.314, ~7/4 = 968.865, ~11/8 = 551.318, ~13/8 = 840.459, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.377, ~29/16 = 1029.577
Kalmanic
Subgroup: 2.3.7.13.23.31
Comma list: 4992/4991
| [⟨ | 1 | 1 | 2 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.942, ~7/4 = 968.865, ~13/8 = 840.459, ~23/16 = 628.377
Optimal ET sequence: 5fi, 5, 9k, 10, 14f, 17, 27, 36, 46, 63, 82, 84, 94, 113, 130, 311, 436, 441, 571, 1335, 1470, 1600, 1776, 1906, 2347k, 2477, 2954, 3525, 3853i, 3983i, 4554ik, 6330ik, 6460ik, 6901ikk, 7031ikk
Etymology
This comma was named by Francium in 2024. It refers to 4992 Kálmán, the asteroid, which in turn was named after Emmerich Kálmán, a Hungarian composer of operettas.