4992/4991

Interval information

Ratio	4992/4991
Factorization	27 × 3 × 7-1 × 13 × 23-1 × 31-1
Monzo	[7 1 0 -1 0 1 0 0 -1 0 -1⟩
Size in cents	0.3468364¢
Name	kalmanisma
Color name	31u23u3or1 thiwutwethuthoru unison
FJS name	[math]\displaystyle{ \text{d2}^{13}_{7,23,31} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	24.5705
Weil height (log2 max(n, d))	24.5708
Wilson height (sopfr(nd))	91
Comma size	unnoticeable
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4992/4991, the kalmanisma, is a 31-limit superparticular comma of about 0.35 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 156/155 and 161/160
• 208/207 and 217/216
• 576/575 and 651/650
• 806/805 and 961/960
• 1024/1023 and 1288/1287
• 1520/1519 and 2185/2184
• 1768/1767 and 2737/2736
• 2016/2015 and 3381/3380
• 2080/2079 and 3565/3564

It can be factored into the following superparticular ratios:

• 5083/5082 and 278784/278783
• 5104/5103 and 227448/227447
• 5643/5642 and 43264/43263
• 5888/5887 and 32799/32798
• 6480/6479 and 21736/21735
• 6656/6655 and 19965/19964
• 6728/6727 and 19344/19343
• 7936/7935 and 13455/13454
• 8464/8463 and 12168/12167
• 8960/8959 and 11271/11270

Temperaments

Tempering out this comma in the full 31-limit leads to the rank-10 temperament kalmanismic. Using the 2.3.7.13.23.31 subgroup leads to the rank-5 temperament kalmanic.

Kalmanismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 4992/4991

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.942, ~5/4 = 386.314, ~7/4 = 968.865, ~11/8 = 551.318, ~13/8 = 840.459, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.377, ~29/16 = 1029.577

Kalmanic

Subgroup: 2.3.7.13.23.31

Comma list: 4992/4991

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.942, ~7/4 = 968.865, ~13/8 = 840.459, ~23/16 = 628.377

Optimal ET sequence: 5fi, 5, 9k, 10, 14f, 17, 27, 36, 46, 63, 82, 84, 94, 113, 130, 311, 436, 441, 571, 1335, 1470, 1600, 1776, 1906, 2347k, 2477, 2954, 3525, 3853i, 3983i, 4554ik, 6330ik, 6460ik, 6901ikk, 7031ikk

Etymology

This comma was named by Francium in 2024. It refers to 4992 Kálmán, the asteroid, which in turn was named after Emmerich Kálmán, a Hungarian composer of operettas.

See also

• Unnoticeable comma
• List of superparticular intervals