1176/1175

Interval information

Ratio	1176/1175
Subgroup monzo	2.3.5.7.47 [3 1 -2 2 -1⟩
Size in cents	1.472764¢
Name	lucidorisma
Color name	47uzzgg2 fosubizogu 2nd
FJS name	[math]\displaystyle{ \text{d2}^{7,7}_{5,5,47} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.3981
Weil height (log2 max(n, d))	20.3993
Wilson height (sopfr(nd))	80
Comma size	unnoticeable
S-expression	S48 × S49
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1176/1175, the lucidorisma, is a 47-limit superparticular comma of about 1.5 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 126/125 and 141/140
• 189/188 and 225/224
• 196/195 and 235/234

It can be factored into the following superparticular ratios:

• 1184/1183 and 173901/173900
• 1190/1189 and 99876/99875
• 1197/1196 and 66976/66975
• 1216/1215 and 35721/35720
• 1225/1224 and 29376/29375
• 1276/1275 and 14994/14993
• 1296/1295 and 12691/12690
• 1364/1363 and 8526/8525
• 1458/1457 and 6076/6075
• 1596/1595 and 4466/4465
• 1666/1665 and 3996/3995
• 1701/1700 and 3808/3807
• 1740/1739 and 3626/3625
• 1764/1763 and 3526/3525
• 1881/1880 and 3136/3135
• 2016/2015 and 2821/2820
• 2116/2115 and 2646/2645
• 2304/2303 and 2401/2400

Temperaments

Tempering out this comma in the full 47-limit leads to the rank-14 temperament lucidorismic. Using the 2.3.5.7.47 subgroup leads to the rank-4 temperament lucidoric.

Lucidoric

Subgroup:2.3.5.7.47

Comma list: 1176/1175

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.912, ~5/4 = 386.497, ~7/4 = 968.557

Optimal ET sequence: 7do, 8do, 10, 12, 19o, 27, 31, 53o, 60, 68, 72, 99, 171, 270, 571, 742, 841o, 1012o, 1583oo, 1853oo

Badness (Sintel): 0.087

Etymology

Francium proposed the name lucidorisma in 2025. It refers to 1176 Lucidor, the asteroid, which in turn was named after an amateur astronomer.

See also

• Unnoticeable comma
• List of superparticular intervals