2850/2849

Interval information

Ratio	2850/2849
Factorization	2 × 3 × 52 × 7-1 × 11-1 × 19 × 37-1
Monzo	[1 1 2 -1 -1 0 0 1 0 0 0 -1⟩
Size in cents	0.6075571 ¢
Name	mozhaiskisma
Color name	37u19o1uryy-2 thisunoluruyoyo negative 2nd
FJS name	[math]\displaystyle{ \text{A1}^{5,5,19}_{7,11,37} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	22.953
Weil norm (log2 max(n, d))	22.9535
Wilson norm (sopfr(nd))	89
Comma size	unnoticeable
S-expression	S75⋅S76
Open this interval in xen-calc

2850/2849, the mozhaiskisma, is a 37-limit superparticular comma of about 0.61 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 260/259 and 286/285
• 408/407 and 476/475
• 760/759 and 1036/1035
• 925/924 and 1369/1368
• 1000/999 and 1540/1539
• 1296/1295 and 2376/2375

It can be factored into the following superparticular intervals:

• 2945/2944 and 88320/88319
• 3025/3024 and 49248/49247
• 3060/3059 and 41515/41514
• 3220/3219 and 24795/24794
• 3249/3248 and 23200/23199
• 3553/3552 and 14400/14399
• 4256/4255 and 8625/8624
• 5292/5291 and 6175/6174
• 5440/5439 and 5985/5984
• 5625/5624 and 5776/5775

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament mozhaiskismic. Using the 2.3.5.7.11.19.37 subgroup leads to the rank-6 temperament mozhaiskic.

Mozhaiskic

Subgroup: 2.3.5.7.11.19.37

Comma list: 2850/2849

Mapping:

[⟨	1	1	2	2	3	4	5	],
⟨	0	1	0	0	0	0	1	],
⟨	0	0	1	0	0	0	2	],
⟨	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 = 701.938, ~5/4 = 386.240, ~7/4 = 968.880, ~11/8 = 551.400, ~19/16 = 297.390

Optimal ET sequence: 6hl, 7dh, 8d, 9, 12l, 14cl, 15l, 19eh, 19, 22l, 22h, 27e, 31h, 39dl, 41l, 50, 53, 72, 99e, 103hl, 118, 130, 152, 255, 270, 311, 400, 422l, 472, 581, 624, 684h, 783, 836, 1308, 1730l, 1889, 2041l, 2877, 3349l

Badness (Sintel): 0.177

Etymology

This comma was named by Francium in 2025. It refers to 2850 Mozhaiskij, the asteroid, which in turn was named after Alexander Mozhaysky, a Russian aviation pioneer.

See also

• Unnoticeable comma
• List of superparticular intervals