5797/5796

Interval information

Ratio	5797/5796
Factorization	2-2 × 3-2 × 7-1 × 11 × 17 × 23-1 × 31
Monzo	[-2 -2 0 -1 1 0 1 0 -1 0 1⟩
Size in cents	0.2986689¢
Name	bivojisma
Color name	31o23u17o1or-2 thiwotwethusoloru negative 2nd
FJS name	[math]\displaystyle{ \text{d1}^{11,17,31}_{7,23} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	25.0019
Weil height (log2 max(n, d))	25.0022
Wilson height (sopfr(nd))	99
Comma size	unnoticeable
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5797/5796, the bivojisma, is a 31-limit superparticular comma of about 0.30 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 323/322 and 342/341
• 484/483 and 528/527
• 561/560 and 621/620
• 806/805 and 936/935
• 1054/1053 and 1288/1287
• 1105/1104 and 1365/1364
• 1496/1495 and 2016/2015
• 1519/1518 and 2058/2057
• 2431/2430 and 4186/4185

It can be factored into the following superparticular ratios:

• 5916/5915 and 288145/288144
• 5929/5928 and 260338/260337
• 6076/6075 and 126225/126224
• 6138/6137 and 104329/104328
• 7106/7105 and 31465/31464
• 7905/7904 and 21736/21735
• 7936/7935 and 21505/21504
• 11271/11270 and 11935/11934

Temperaments

Tempering out this comma in the full 31-limit leads to the rank-10 temperament bivojismic. Using the 2.3.7.11.17.23.31 subgroup leads to the rank-6 temperament bivojic.

Bivojic

Subgroup: 2.3.7.11.17.23.31

Comma list: 5797/5796

Mapping:

[⟨	1	1	2	3	4	4	3	],
⟨	0	1	0	0	0	0	2	],
⟨	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 = 701.971, ~7/4 = 968.852, ~11/8 = 551.279, ~17/16 = 104.901, ~23/16 = 628.341

Optimal ET sequence: 5i, 5g, 7dgik, 7, 9gik, 10i, 12ik, 14, 22i, 24ik, 24, 26, 27egi, 31k, 32, 41g, 41i, 46, 75ei, 77, 82, 89, 121ik, 130, 135, 207k, 265, 311, 328, 342, 436, 518, 607, 653, 701, 764, 1029, 1043, 1371, 1417, 1807, 2118, 2460, 4532, 4578, 5949k, 7756k

Badness (Sintel): 0.058

Etymology

This comma was named by Francium in 2025. It refers to 5797 Bivoj, the asteroid, which in turn was named after a Bivoj, a mythological Bohemian hero.

See also

• Unnoticeable comma
• List of superparticular intervals