2205/2197
| Interval information |
trithu-azozoyo unison
(Shannon, [math]\sqrt{nd}[/math])
2205/2197, the brontesisma, is a 13-limit (also 3.5.7.13 subgroup) small comma of about 6.3 cents.
Commatic relationships
This comma is the difference between the following pairs:
- 105/104 and 169/168
- 126/125 and 4394/4375
- 245/243 and 2197/2187
- 351/343 and 1215/1183
- 507/500 and 1323/1300
- 1617/1600 and 24167/24000
- 1875/1859 and 1625/1617
It can be factored into the following ratios:
- 325/324 and 142884/142805
- 351/350 and 85750/85683
- 352/351 and 59535/59488
- 364/363 and 114345/114244
- 441/440 and 2200/2197
- 625/624 and 21168/21125
- 729/728 and 13720/13689
- 847/845 and 1575/1573
- 3136/3125 and 140625/140608
- 31213/31104 and 1399680/1399489
Temperaments
Tempering out this comma in the full 13-limit leads to the rank-5 temperament brontesismic. Using the 3.5.7.13 subgroup leads to the rank-3 temperament brontesite.
Adding the schismina leads to septidiasemi.
Adding the tunbarsma, the squbema and the breedsma leads to schisennealimmal.
Adding the swetisma, the tunbarsma and the squbema leads to enneadecal.
Adding the tunbarsma, the ibnsinma, and the unisquarisma leads to piracy.
Brontesismic
Subgroup: 2.3.5.7.11.13
Comma list: 2205/2197
| [⟨ | 1 | 1 | 2 | 4 | 3 | 4 | ], |
| ⟨ | 0 | 1 | 0 | 2 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 1 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | -3 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.769, ~5/4 = 386.114, ~13/7 = 1073.803, ~11/8 = 551.318
Optimal ET sequence: 7, 9, 10, 16, 19e, 19, 26, 29, 38df, 45ef, 49f, 58, 84, 87, 103, 145, 152f, 190, 248, 342
Brontesite
Subgroup: 3.5.7.13
Comma list: 2205/2197
| [⟨ | 1 | 1 | 3 | 3 | ], |
| ⟨ | 0 | 1 | 1 | 1 | ], |
| ⟨ | 0 | 0 | -3 | -2 | ] |
Optimal tuning (CTE): ~3 = 1\1, ~5/3 = 884.147, ~13/7 = 1073.935
Optimal ET sequence: b7, b9, b21, b23, b30, b39, b62, b69, b101, b131, b170, b271, b572f, b673f
Etymology
This comma was named by Francium in 2025. It refers to Brontesite, the mineral.