5577/5576

Interval information

Ratio	5577/5576
Subgroup monzo	2.3.11.13.17.41 [-3 1 1 2 -1 -1⟩
Size in cents	0.3104517 ¢
Name	priestlisma
Color name	41u17u3oo1o1 fowusuthotholo unison
FJS name	[math]\displaystyle{ \text{d1}^{11,13,13}_{17,41} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	24.8903
Weil norm (log2 max(n, d))	24.8905
Wilson norm (sopfr(nd))	104
Comma size	unnoticeable
Open this interval in xen-calc

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:

• 165/164 and 170/169
• 273/272 and 287/286

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

Mapping:

[⟨	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.

See also

• Unnoticeable comma
• List of superparticular intervals