5720/5719
| Interval information |
fothunutholoruyo negative 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
5720/5719, the halweaverisma, is a 43-limit superparticular comma of about 0.30 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
- 5776/5775 and 589875/589874
- 5797/5796 and 430560/430559
- 5929/5928 and 162240/162239
- 6138/6137 and 83980/83979
- 6175/6174 and 77616/77615
- 6480/6479 and 48763/48762
- 7225/7224 and 27456/27455
- 7696/7695 and 22275/22274
- 9504/9503 and 14365/14364
- 9633/9632 and 14080/14079
- 10450/10449 and 12636/12635
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament halweaverismic. Using the 2.5.7.11.13.19.43 subgroup leads to the rank-6 temperament halweaveric.
Halwearic
Subgroup: 2.5.7.11.13.19.43
Comma list: 5720/5719
| [⟨ | 1 | 2 | 2 | 3 | 3 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 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, ~5/4 = 386.295, ~7/4 = 968.854, ~11/8 = 551.276, ~13/8 = 840.480, ~19/16 = 297.576
Optimal ET sequence: 4, 5ehn, 6en, 6, 6fh, 8cefh, 8dn, 9, 12fn, 14cfn, 15f, 15n, 18eh, 20n, 21h, 22, 25fn, 27e, 28, 29, 31, 37, 66, 84, 93, 103h, 109, 124, 161, 233, 270, 488, 515, 581, 690, 758, 851, 1273, 1339, 1448, 1609, 1693, 1963, 2814, 3302, 3572, 4299, 5265hn, 5992n, 7601hn, 9564hnn
Badness (Sintel): 0.043
Etymology
This comma was named by Francium in 2025. It refers to 5720 Halweaver, the asteroid, which in turn was named after Harold Anthony Weaver, an American astronomer.