1184/1183

Interval information

Ratio	1184/1183
Subgroup monzo	2.7.13.37 [5 -1 -2 1⟩
Size in cents	1.462809¢
Name	gaeisma
Color name	37o3uur1 thisothuthuru unison
FJS name	[math]\text{d}{-2}^{37}_{7,13,13}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.4177
Weil height (log2 max(n, d))	20.4189
Wilson height (sopfr(nd))	80
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.2198 bits
Comma size	unnoticeable
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1184/1183, the gaeisma, is a 37-limit superparticular comma of about 1.5 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 148/147 and 169/168
• 456/455 and 741/740

It can be factored into the following superparticular intervals:

• 1197/1196 and 108928/108927
• 1210/1209 and 55056/55055
• 1216/1215 and 44955/44954
• 1275/1274 and 16576/16575
• 1288/1287 and 14652/14651
• 1296/1295 and 13690/13689
• 1332/1331 and 10648/10647
• 1480/1479 and 5916/5915
• 1665/1664 and 4096/4095
• 1702/1701 and 3888/3887
• 1860/1859 and 3256/3255
• 2146/2145 and 2640/2639

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament gaeismic. Using the 2.7.13.37 subgroup leads to the rank-3 temperament gaeic.

Gaeic

Subgroup: 2.7.13.37

Comma list: 1184/1183

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 968.954, ~13/8 = 840.974

Optimal ET sequence: 4, 6, 7l, 9l, 10, 27, 36l, 37, 47, 57, 104, 130, 167, 177, 187, 234), 291, 478, 525, 1003, 1294f, 1528f

Badness (Sintel): 0.014

Etymology

This comma was named by Francium in 2025. It refers to 1184 Gaea, the asteroid, which in turn was named after Gaia, a Greek goddess.

See also

• Unnoticeable comma
• List of superparticular intervals