2109/2108
| Interval information |
thisothiwunosu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
2109/2108, the dhotelisma, is a 37-limit superparticular comma of about 0.82 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 171/170 and 186/185
- 222/221 and 248/247
- 342/341 and 408/407
- 528/527 and 704/703
- 703/702 and 1054/1053
- 851/850 and 1426/1425
- 931/930 and 1666/1665
- 962/961 and 1768/1767
It can be factored into the following superparticular intervals:
- 2146/2145 and 122265/122264
- 2185/2184 and 60606/60605
- 2233/2232 and 37962/37961
- 2432/2431 and 15873/15872
- 2553/2552 and 12122/12121
- 2738/2737 and 9177/9176
- 2755/2754 and 8991/8990
- 3256/3255 and 5985/5984
- 3367/3366 and 5643/5642
- 3876/3875 and 4625/4624
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament dhotelismic. Using the 2.3.17.19.31.37 subgroup leads to the rank-5 temperament dhotelic.
Dhotelic
Subgroup: 2.3.17.19.31.37
Comma list: 2109/2108
| [⟨ | 1 | 1 | 4 | 4 | 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 = 701.932, ~17/16 = 105.110, ~19/16 = 297.346, ~31/16 = 1145.262
Optimal ET sequence: 5, 7ghk, 7l, 9gkl, 10k, 10h, 12l, 17l, 19, 24, 65, 75, 82, 99k, 101, 106, 130, 157, 181, 205, 231, 282, 306, 330, 388, 412, 436, 706, 937, 1118, 1142, 1554, 2491hl
Badness (Sintel): 0.033
Etymology
This comma was named by Francium in 2025. It refers to 2109 Dhôtel, the asteroid, which in turn was named after André Dhôtel, a French writer.