9633/9632

Interval information

Ratio	9633/9632
Subgroup monzo	2.3.7.13.19.43 [-5 1 -1 2 1 -1⟩
Size in cents	0.1797284 ¢
Name	coturisma
Color name	43u19o3oor1 fothunothothoru unison
FJS name	[math]\displaystyle{ \text{d1}^{13,13,19}_{7,43} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	26.4674
Weil norm (log2 max(n, d))	26.4675
Wilson norm (sopfr(nd))	108
Comma size	unnoticeable
S-expression	S169⋅S170⋅S171
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9633/9632, the coturisma, is a 43-limit superparticular comma of about 0.18 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 169/168 and 172/171
• 2366/2365 and 3136/3135
• 2925/2924 and 4200/4199

It can be factored into the following superparticular ratios:

• 9801/9800 and 561925/561924
• 9802/9801 and 558657/558656
• 10241/10240 and 162240/162239
• 10374/10373 and 134849/134848
• 10450/10449 and 123201/123200
• 14365/14364 and 29241/29240
• 14535/14534 and 28561/28560

Temperaments

Tempering out this comma in the full 43-limit leads to the rank-13 temperament coturismic. Using the 2.3.7.13.19.43 subgroup leads to the rank-5 temperament coturic.

Coturic

Subgroup: 2.3.7.13.19.43

Comma list: 9633/9632

Mapping:

[⟨	1	1	2	3	4	4	],
⟨	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 = 701.951, ~7/4 = 968.838, ~13/8 = 840.484, ~19/16 = 297.484

Optimal ET sequence: 7dh, 7, 9n, 10, 14, 17, 26nn, 27, 36, 63, 77, 113, 130, 207, 234, 270, 347, 477, 701, 795, 831, 908, 935, 1065, 1142, 1178, 1412, 2590, 6592, 9182

Badness (Sintel): 0.036

Etymology

This comma was named by Francium in 2025. It refers to 9633 Cotur, the asteroid, which in turn was named after Peter Cotur, a Belgian scientific journalist.

See also

• Unnoticeable comma
• List of superparticular intervals