3773/3772

3773/3772, the smithsonianisma, is a 41-limit superparticular comma of about 0.46 cents.

Interval information

Ratio	3773/3772
Factorization	2-2 × 73 × 11 × 23-1 × 41-1
Monzo	[-2 0 0 3 1 0 0 0 -1 0 0 0 -1⟩
Size in cents	0.458909 ¢
Name	smithsonianisma
Color name	41u23u1oz32 fowutwethulotrizo 2nd
FJS name	[math]\displaystyle{ \text{dd3}^{7,7,7,11}_{23,41} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	23.7626
Weil norm (log2 max(n, d))	23.763
Wilson norm (sopfr(nd))	100
Comma size	unnoticeable
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Commatic relationships

This comma is the difference between the following superparticular pairs:

• 231/230 and 246/245
• 616/615 and 736/735

It can be factored into the following superparticular ratios:

• 3774/3773 and 14235529/14235528
• 3969/3968 and 76384/76383
• 4675/4674 and 19551/19550
• 4785/4784 and 17836/17835
• 5577/5576 and 11662/11661
• 5929/5928 and 10374/10373
• 6930/6929 and 8281/8280

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament smithsonianismic. Using the 2.7.11.23.41 subgroup leads to the rank-4 temperament smithsonianic.

Smithsonianic

Subgroup: 2.7.11.23.41

Comma list: 3773/3772

Mapping:

[⟨	1	2	3	4	3	],
⟨	0	1	0	0	3	],
⟨	0	0	1	0	1	],
⟨	0	0	0	1	-1	]]

Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 968.744, ~11/8 = 551.276, ~23/16 = 628.345

Optimal ET sequence: 4, 6m, 7, 9i, 11, 20, 31, 46, 63, 67, 78, 109, 187, 296, 529, 638, 825, 1759, 2584, 3705, 4530, 6278d

Etymology

This comma was named by Francium in 2025. It refers to 3773 Smithsonian, the asteroid, which in turn was named after the Smithsonian Institution.

See also

• Unnoticeable comma
• List of superparticular intervals