780/779
| Interval information |
fowunuthoyo unison
reduced
(Shannon, [math]\sqrt{nd}[/math])
780/779, the wiesentisma, is a 41-limit superparticular comma of about 2.2 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 39/38 and 41/40
- 165/164 and 209/208
- 210/209 and 287/286
- 247/246 and 361/360
- 286/285 and 451/450
- 288/287 and 456/455
It can be factored into the following superparticular ratios:
- 783/782 and 203320/203319
- 784/783 and 152685/152684
- 806/805 and 24150/24149
- 837/836 and 11440/11439
- 875/874 and 7176/7175
- 936/935 and 4675/4674
- 1026/1025 and 3250/3249
- 1190/1189 and 2262/2261
- 1395/1394 and 1768/1767
- 1521/1520 and 1600/1599
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament wiesentismic. Using the 2.3.5.13.19.41 subgroup leads to the rank-5 temperament wiesentic.
Wiesentic
Subgroup: 2.3.5.13.19.41
Comma list: 780/779
| [⟨ | 1 | 1 | 2 | 3 | 4 | 4 | ], |
| ⟨ | 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: ~2 = 1\1, ~3/2 = 701.873, ~5/4 = 386.139, ~13/8 = 840.083, ~19/16 = 298.099
Optimal ET sequence: 5h, 7fhm, 7m, 9, 12, 15m, 22, 22fh, 24, 27, 31, 34h, 38fm, 41, 50, 53, 137, 164, 217, 354, 407, 494h, 547, 764hm, 901hm, 954m
Badness (Sintel): 0.109
Etymology
This comma was named by Francium in 2025. It refers to Wiesent, Bavaria, which was first mentioned in 780.