110565/110561

Interval information

Ratio	110565/110561
Factorization	35 × 5 × 7 × 11-1 × 13 × 19-1 × 23-2
Monzo	[0 5 1 1 -1 1 0 -1 -2⟩
Size in cents	0.0626334¢
Name	jeffbenisma
Color name	L23uu19u3o1uzy-2 labitwethu-anutholuzoyo negative 2nd
FJS name	[math]\text{m2}^{5,7,13}_{11,19,23,23}[/math]
Special properties	reduced
Tenney height (log2 nd)	33.509
Weil height (log2 max(n, d))	33.5091
Wilson height (sopfr(nd))	116
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19986 bits
Comma size	unnoticeable
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110565/110561, the jeffbenisma, is a 23-limit (also 3.5.7.11.13.19.23 subgroup) unnoticeable comma of about 0.063 cents.

Commatic relationships

This comma is the difference between the following intervals:

• 2025/2024 and 2185/2184
• 12168/12167 and 21736/21735
• 12636/12635 and 23276/23275
• 13377/13376 and 25921/25920

It can be factored into the ratios 43264/43263 and 76545/76544.

Temperaments

Tempering out this comma in the full 23-limit leads to the rank-8 temperament jeffbenismic. Using the 3.5.7.11.13.19.23 subgroup leads to the rank-6 temperament jeffbenite.

Jeffbenite

Subgroup: 3.5.7.11.13.19.23

Comma list: 110565/110561

Mapping:

[⟨	1	1	1	2	2	1	3	],
⟨	0	1	0	0	0	1	0	],
⟨	0	0	1	0	0	1	0	],
⟨	0	0	0	1	0	0	-1	],
⟨	0	0	0	0	1	1	0	],
⟨	0	0	0	0	0	-2	1	]]

Optimal tuning (CTE): ~3 = 1\1, ~5/3 = 884.356, ~7/3 = 1466.867, ~11/9 = 347.413, ~13/9 = 636.611, ~253/243 = 69.841

Optimal ET sequence: b7h, b10f, b13, b20efh, b21, b23, b26, b33, b34, b39, b46, b54, b56, b60, b71, b75, b110, b131, b241, b275, b301, b316, b376, b437, b447, b460, b591, b712, b822, b953, b1198, b1329, b1473, b2151, b2282, b2295, b2426, b3624, b3755, b6050, b6181, b8682, b9805

Etymology

This comma was named by Francium in 2025. It refers to Jeffbenite, the mineral.

See also

• Unnoticeable comma