2146/2145

2146/2145, the stentorisma, is a 37-limit superparticular comma of about 0.81 cents.

Interval information

Ratio	2146/2145
Factorization	2 × 3-1 × 5-1 × 11-1 × 13-1 × 29 × 37
Monzo	[1 -1 -1 0 -1 -1 0 0 0 1 0 1⟩
Size in cents	0.806914¢
Name	stentorisma
Color name	37o29o3u1ug2 thisotwenothulugu 2nd
FJS name	[math]\displaystyle{ \text{P1}^{29,37}_{5,11,13} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	22.1342
Weil norm (log2 max(n, d))	22.1349
Wilson norm (sopfr(nd))	100
Comma size	unnoticeable
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Commatic relationships

This comma is the difference between the following superparticular pairs:

• 111/110 and 117/116
• 232/231 and 260/259
• 261/260 and 297/296
• 703/702 and 1045/1044
• 925/924 and 1625/1624
• 1015/1014 and 1925/1924
• 1036/1035 and 2002/2001

It can be factored into the following superparticular ratios:

• 2176/2175 and 155585/155584
• 2185/2184 and 120176/120175
• 2233/2232 and 55056/55055
• 2432/2431 and 18241/18240
• 2465/2464 and 16576/16575
• 2553/2552 and 13456/13455
• 2784/2783 and 9361/9360
• 3256/3255 and 6293/6292
• 3367/3366 and 5916/5915

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament stentorismic. Using the 2.3.5.11.13.29.37 subgroup leads to the rank-6 temperament stentoric.

Stentorismic

Subgroup 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 2146/2145

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.979, ~5/4 = 386.365, ~7/4 = 968.826, ~11/8 = 551.432, ~13/8 = 840.659, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.351, ~31/16 = 1145.036

Stentoric

Subgroup: 2.3.5.11.13.29.37

Comma list: 2146/2145

Mapping:

[⟨	1	1	2	3	3	4	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 = 701.979, ~5/4 = 386.365, ~11/8 = 551.432, ~13/8 = 840.659, ~29/16 = 1029.351

Optimal ET sequence: 5ejl, 7fjj, 7, 12el, 12fj, 14cfjjl, 15l, 19el, 19, 24, 31fj, 34j, 38fjl, 41, 43, 50, 53, 65, 80, 87, 118, 121l, 130, 140, 145jl, 159, 183, 224, 304, 311, 407, 916, 1012, 1099, 1323, 1730

Etymology

This comma was named by Francium in 2024. It refers to 2146 Stentor, the asteroid, which in turn was named after Stentor, a Greek warrior.

See also

• Unnoticeable comma
• List of superparticular intervals