5577/5576
| Interval information |
fowusuthotholo unison
reduced
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
5577/5576, the priestlisma, is a 41-limit superparticular comma of about 0.31 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular ratios:
- 5643/5642 and 476749/476748
- 5985/5984 and 81796/81795
- 6138/6137 and 61009/61008
- 6325/6324 and 47151/47150
- 6561/6560 and 37180/37179
- 6930/6929 and 28561/28560
- 7176/7175 and 25025/25024
Temperaments
Tempering out this comma in the full 41-limit leads to the rank-12 temperament priestlismic. Using the 2.3.11.13.17.41 subgroup leads to the rank-5 temperament priestlic.
Priestlic
Subgroup: 2.3.11.13.17.41
Comma list: 5577/5576
| [⟨ | 1 | 1 | 3 | 3 | 4 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.948, ~11/8 = 551.286, ~13/8 = 840.454, ~17/16 = 105.001
Optimal ET sequence: 5fm, 7m, 8mm, 9g, 10, 15gm, 17g, 24, 41, 70, 111, 137, 166g, 183, 207, 390, 460, 470, 511, 581, 607, 677, 718, 788, 971, 1178, 1395, 1648, 1689, 1855, 1966, 2366, 3154, 3361, 4332, 5727, 6698f
Badness (Sintel): 0.040
Etymology
This comma was named by Francium in 2025. It refers to 5577 Priestley, the asteroid, which in turn was named after Joseph Priestley, an English clergyman.