646/645
| Interval information |
fothunosogu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
646/645, the kastalisma, is a 43-limit superparticular comma of about 2.7 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
- 651/650 and 83980/83979
- 676/675 and 14535/14534
- 703/702 and 7956/7955
- 741/740 and 5032/5031
- 760/759 and 4301/4300
- 775/774 and 3876/3875
- 931/930 and 2108/2107
- 969/968 and 1936/1935
- 1156/1155 and 1463/1462
- 1216/1215 and 1377/1376
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament kastalismic. Using the 2.3.5.17.19.43 subgroup leads to the rank-5 temperament kastalic.
Kastalic
Subgroup: 2.3.5.17.19.43
Comma list: 646/645
| [⟨ | 1 | 1 | 2 | 4 | 4 | 6 | ], |
| ⟨ | 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 = 702.048, ~5/4 = 386.514, ~17/16 = 104.334, ~19/16 = 296.842
Optimal ET sequence: 5g, 5ghn, 7ghn, 9, 10, 12, 27g, 34, 34hn, 38, 46h, 50, 53, 65, 77, 94, 106, 171, 183, 205n, 217n, 323, 506, 723n
Badness (Sintel): 0.120
Etymology
This comma was named by Francium in 2025. It refers to 646 Kastalia, the asteroid, which in turn was named after Castalia, a Greek nymph.