Megumisma

Interval information

Ratio	3774/3773
Subgroup monzo	2.3.7.11.17.37 [1 1 -3 -1 1 1⟩
Size in cents	0.4587873¢
Name	megumisma
Color name	37o17o1ur31 thisosolutriru unison
FJS name	[math]\text{m}{-2}^{17,37}_{7,7,7,11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	23.7634
Weil height (log2 max(n, d))	23.7638
Wilson height (sopfr(nd))	91
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20105 bits
Comma size	unnoticeable
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3774/3773, the megumisma, is a 37-limit superparticular comma of about 0.46 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 148/147 and 154/153
• 925/924 and 1225/1224
• 1275/1274 and 1925/1924
• 1332/1331 and 2058/2057

It can be factored into the following superparticular ratios:

• 3876/3875 and 143375/143374
• 5083/5082 and 14652/14651
• 5832/5831 and 10693/10692

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament megumismic. Using the 2.3.7.11.17.37 subgroup leads to the rank-5 temperament megumic.

Megumismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 3774/3773

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.946, ~5/4 = 386.314, ~7/4 = 968.910, ~11/8 = 551.360, ~13/8 = 840.528, ~17/16 = 104.896, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Megumic

Subgroup: 2.3.7.11.17.37

Comma list: 3774/3773

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.946, ~7/4 = 968.910, ~11/8 = 551.360, ~17/16 = 104.896

Optimal ET sequence: 5, 9g, 10, 14l, 17g, 22, 31, 32, 36el, 46l, 53, 55gl, 58l, 63, 72, 121l, 135, 193l, 207, 328, 400, 535, 607, 629, 764, 836, 1371, 2000, 2207, 2607, 3443, 5650

Etymology

This comma was named by Francium in 2025. It refers to 3774 Megumi, the asteroid, which in turn was named after Megumi, the wife of Japanese astronomer Takuo Kojima who discovered the asteroid.

See also

• Unnoticeable comma
• List of superparticular intervals