3146/3145

Interval information

Ratio	3146/3145
Subgroup monzo	2.5.11.13.17.37 [1 -1 2 1 -1 -1⟩
Size in cents	0.5503844 ¢
Name	datonisma
Color name	37u17u3o1oog-2 thisusutholologu negative 2nd
FJS name	[math]\displaystyle{ \text{d1}^{11,11,13}_{5,17,37} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	23.2381
Weil norm (log2 max(n, d))	23.2386
Wilson norm (sopfr(nd))	96
Comma size	unnoticeable
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3146/3145, the datonisma, is a 37-limit superparticular comma of about 0.55 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 715/714 and 925/924
• 936/935 and 1332/1331
• 1089/1088 and 1665/1664
• 1276/1275 and 2146/2145

It can be factored into the following superparticular ratios:

• 3220/3219 and 136851/136850
• 3256/3255 and 93093/93092
• 3367/3366 and 47916/47915
• 3520/3519 and 29601/29600
• 3553/3552 and 27456/27455
• 3627/3626 and 23716/23715
• 3751/3750 and 19500/19499

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament datonismic. Using the 2.5.11.13.17.37 subgroup leads to the rank-5 temperament datonic.

Datonic

Subgroup: 2.5.11.13.17.37

Comma list: 3146/3145

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.340, ~11/8 = 551.199, ~13/8 = 840.460, ~17/16 = 105.038

Optimal ET sequence: 5egl, 6, 7, 8cefgl, 8, 12, 12fg, 13, 16, 21l, 28g, 34l, 35f, 37, 43, 56, 59, 80, 81, 87, 96, 100, 103l, 108g, 116, 124, 196, 261, 320, 444, 764, 1025, 1041, 1165, 1485, 1826l, 1842, 1966, 2286, 2867, 2991l

Badness (Sintel): 0.039

Etymology

This comma was named by Francium in 2025. It refers to 3146 Dato, the asteroid, which in turn was named after Dato Kratsashvili, a Georgian painter.

See also

• Unnoticeable comma
• List of superparticular intervals