4186/4185
| Interval information |
thiwutwethothozogu 3rd
reduced
(Shannon, [math]\sqrt{nd}[/math])
4186/4185, the tamashimisma, is a 31-limit superparticular comma of about 0.41 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 91/90 and 93/92
- 156/155 and 162/161
- 280/279 and 300/299
- 621/620 and 729/728
- 676/675 and 806/805
- 931/930 and 1197/1196
- 1288/1287 and 1860/1859
- 1365/1364 and 2025/2024
- 1729/1728 and 2945/2944
- 1768/1767 and 3060/3059
- 2016/2015 and 3888/3887
It can be factored into the following superparticular ratios:
- 4200/4199 and 1255501/1255500
- 4225/4224 and 453376/453375
- 4375/4374 and 96876/96875
- 4641/4640 and 42688/42687
- 4992/4991 and 25921/25920
- 5083/5082 and 23716/23715
- 6076/6075 and 13455/13454
- 6325/6324 and 12376/12375
- 8092/8091 and 8671/8670
- 8281/8280 and 8464/8463
Temperaments
Tempering out this comma in the full 31-limit leads to the rank-10 temperament tamashimismic. Using the 2.3.5.7.13.23.31 subgroup leads to the rank-6 temperament tamashimic.
Tamashimic
Subgroup: 2.3.5.7.13.23.31
Comma list: 4186/4185
| [⟨ | 1 | 1 | 2 | 2 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ], |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.988, ~5/4 = 386.337, ~7/4 = 968.791, ~13/8 = 840.468, ~23/16 = 628.185
Optimal ET sequence: 5, 7dik, 8di, 9ik, 10k, 12, 12fk, 14cf, 15, 17c, 19ikk, 19, 29k, 31fk, 31, 34dk, 39dfik, 41, 53, 68, 87, 94, 99fk, 111, 121ik, 130, 198, 224, 243, 251i, 311, 373, 383i, 422, 441, 954, 1205, 1646, 2159, 2600, 3171, 4376, 4817k, 5771, 6976k, 7417k
Etymology
This comma was named by Francium in 2025. It refers to 4186 Tamashima, the asteroid, which in turn was named after a town in Japan.