4774/4773

Interval information

Ratio	4774/4773
Subgroup monzo	2.3.7.11.31.37.43 [1 -1 1 1 1 -1 -1⟩
Size in cents	0.362676 ¢
Name	hobetsisma
Color name	43u37u31o1oz-2 fothuthisuthiwolozo negative 2nd
FJS name	[math]\displaystyle{ \text{P1}^{7,11,31}_{37,43} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	24.4417
Weil norm (log2 max(n, d))	24.442
Wilson norm (sopfr(nd))	134
Comma size	unnoticeable
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4774/4773, the hobetsisma, is a 43-limit superparticular comma of about 0.36 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 775/774 and 925/924
• 1333/1332 and 1849/1848
• 1463/1462 and 2109/2108
• 1936/1935 and 3256/3255
• 2108/2107 and 3774/3773

It can be factored into the following superparticular ratios:

• 4785/4784 and 2076256/2076255
• 4960/4959 and 127281/127280
• 5292/5291 and 48763/48762
• 5720/5719 and 28861/28860
• 5797/5796 and 27048/27047
• 6076/6075 and 22275/22274
• 7956/7955 and 11935/11934

Temperaments

Tempering out this comma in the full 43-limit leads to the rank-13 temperament hobetsismic. Using the 2.3.7.11.31.37.43 subgroup leads to the rank-6 temperament hobetsic.

Hobetsic

Subgroup: 2.3.7.11.31.37.43

Comma list: 4774/4773

Mapping:

[⟨	1	1	2	3	4	5	4	],
⟨	0	1	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	1	],
⟨	0	0	0	1	0	0	1	],
⟨	0	0	0	0	1	0	1	],
⟨	0	0	0	0	0	1	-1	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.964, ~7/4 = 968.798, ~11/8 = 551.276, ~31/16 = 1144.950, ~37/32 = 251.439

Optimal ET sequence: 5, 8dn, 9kn, 10k, 10n, 12kn, 14l, 17, 17kn, 22, 24, 27e, 31k, 41, 48n, 55l, 63, 72, 82, 87, 89, 121kl, 135, 152, 176, 301, 383, 400, 477, 612, 701, 877, 940, 1084, 1241, 1417, 1641, 2118, 3202, 3814, 3966, 4142, 4843ln, 6872ln

Badness (Sintel): 0.060

Etymology

This comma was named by Francium in 2025. It refers to 4774 Hobetsu, the asteroid, which in turn was named after a town in Japan.

See also

• Unnoticeable comma
• List of superparticular intervals