4000/3999
4000/3999, the hipparchusisma, is a 43-limit superparticular comma of about 0.43 cents.
| Interval information |
fothuthiwutriyo unison
reduced
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 125/124 and 129/128
- 280/279 and 301/300
- 560/559 and 651/650
- 775/774 and 961/960
- 1936/1935 and 3751/3750
It can be factored into the following superparticular intervals:
- 4096/4095 and 170625/170624
- 4186/4185 and 90000/89999
- 4200/4199 and 83980/83979
- 4375/4374 and 46656/46655
- 4992/4991 and 20125/20124
- 5376/5375 and 15625/15624
- 6325/6324 and 10880/10879
- 6480/6479 and 10450/10449
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament hipparchusismic. Using the 2.3.5.31.43 subgroup leads to the rank-4 temperament hipparchusic.
Hipparchusic
Subgroup: 2.3.5.31.43
Comma list: 4000/3999
| [⟨ | 1 | 1 | 2 | 4 | 6 | ], |
| ⟨ | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.965, ~5/4 = 386.247, ~31/16 = 1145.137
Optimal ET sequence: 5n, 7k, 10k, 12k, 19, 41, 46, 65, 87, 106, 152, 171, 277, 323, 335, 441, 612, 1053, 1665, 3942kn, 5101kn, 5607kn, 5694kn, 5713kn, 6306kn, 6918knn, 7971kknn, 8583kknn
Badness (Sintel): 0.028
Etymology
This comma was named by Francium in 2025. It refers to 4000 Hipparchus, the asteroid, which in turn was named after Hipparchus, an Ancient Greek scientist.