3312/3311

Interval information

Ratio	3312/3311
Subgroup monzo	2.3.7.11.23.43 [4 2 -1 -1 1 -1⟩
Size in cents	0.5227945 ¢
Name	pedersenisma
Color name	43u23o1ur1 fothutwetholuru unison
FJS name	[math]\displaystyle{ \text{d}{-2}^{23}_{7,11,43} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	23.3865
Weil norm (log2 max(n, d))	23.387
Wilson norm (sopfr(nd))	98
Comma size	unnoticeable
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3312/3311, the pedersenisma, is a 43-limit superparticular comma of about 0.52 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 216/215 and 231/230
• 276/275 and 301/300
• 345/344 and 385/384

It can be factored into the following superparticular intervals:

• 3381/3380 and 162240/162239
• 3510/3509 and 58696/58695
• 3565/3564 and 46656/46655
• 3774/3773 and 27048/27047
• 4000/3999 and 19251/19250
• 4301/4300 and 14400/14399
• 4761/4760 and 10880/10879
• 5083/5082 and 9504/9503
• 5376/5375 and 8625/8624
• 5720/5719 and 7866/7865
• 5888/5887 and 7569/7568

Temperaments

Tempering out this comma in the full 43-limit leads to the rank-13 temperament pedersenismic. Using the 2.3.7.11.23.43 subgroup leads to the rank-5 temperament pedersenic.

Pedersenic

Subgroup: 2.3.7.11.23.43

Comma list: 3312/3311

Mapping:

[⟨	1	1	2	3	4	5	],
⟨	0	1	0	0	0	2	],
⟨	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 = 701.922, ~7/4 = 968.878, ~11/8 = 551.396, ~23/16 = 628.140

Optimal ET sequence: 5i, 7di, 7, 8din, 9in, 10, 12e, 12i, 14, 17, 22n, 24i, 31, 58i, 63, 89, 94, 113, 135, 152, 176, 176, 207, 165, 328, 342, 359, 535, 670, 701, 877, 1029, 1236, 1906n, 2607n, 3142n, 3843n

Etymology

This comma was named by Francium in 2025. It refers to 3312 Pedersen, the asteroid, which in turn was named after Holger Pedersen, a Danish astronomer.

See also

• Unnoticeable comma
• List of superparticular intervals