12321/12320
| Interval information |
bithiso-alurugu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
12321/12320, the zurakowskisma, is a 37-limit superparticular comma of about 0.14 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 111/110 and 112/111
- 666/665 and 704/703
- 925/924 and 1000/999
- 1665/1664 and 1925/1924
- 3774/3773 and 5440/5439
It can be factored into the following superparticular intervals:
- 12376/12375 and 2772225/2772224
- 12636/12635 and 494209/494208
- 12673/12672 and 443556/443555
- 13311/13310 and 165649/165648
- 13377/13376 and 156066/156065
- 13690/13689 and 123201/123200
- 14652/14651 and 77441/77440
- 18241/18240 and 37962/37961
- 19251/19250 and 34225/34224
- 23409/23408 and 26011/26010
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament zurakowskismic. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament zurakowskic.
Zurakowskic
Subgroup: 2.3.5.7.11.37
Comma list: 12321/12320
| [⟨ | 1 | 1 | 2 | 2 | 3 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | -2 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.950, ~5/4 = 386.319, ~7/4 = 968.834, ~140/111 = 401.911
Optimal ET sequence: 5, 7d, 8d, 9, 10, 12, 15, 19, 24, 27e, 45e, 53, 60el, 72, 140, 152, 224, 301, 311, 400, 472, 525, 540, 612, 836, 1084, 1236, 1848, 2684, 3920, 4079, 4231, 4532, 5315, 5927, 6079, 7163, 7927, 7999, 8611l, 9847
Etymology
This comma was named by Francium in 2025. It refers to 12321 Zurakowski, the asteroid, which in turn was named after Paul R. Zurakowski, a volunteer director of the Chabot Observatory Telescope Maker’s Workshop for more than 30 years.