3626/3625

Interval information

Ratio	3626/3625
Subgroup monzo	2.5.7.29.37 [1 -3 2 -1 1⟩
Size in cents	0.4775159¢
Name	ohsakisma
Color name	37o29uzzg33 thisotwenuzozotrigu 3rd
FJS name	[math]\text{d2}^{7,7,37}_{5,5,5,29}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	23.6479
Weil height (log2 max(n, d))	23.6483
Wilson height (sopfr(nd))	97
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20121 bits
Comma size	unnoticeable
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3626/3625, the ohsakisma, is a 37-limit superparticular comma of about 0.48 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 784/783 and 1000/999
• 1036/1035 and 1450/1449

It can be factored into the following superparticular ratios:

• 3751/3750 and 108780/108779
• 3876/3875 and 56203/56202
• 4641/4640 and 16576/16575
• 6076/6075 and 8991/8990

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament ohsakismic. Using the 2.5.7.29.37 subgroup leads to the rank-4 temperament ohsakic.

Ohsakic

Subgroup: 2.5.7.29.37

Comma list: 3626/3625

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.373, ~7/4 = 968.768, ~29/16 = 1029.663

Optimal ET sequence: 4l, 6, 10, 12j, 16, 19, 25, 37, 62, 99, 140, 177, 239, 373, 410, 472, 550, 612, 649, 1261, 3171, 4432, 4671, 5932

Badness (Sintel): 0.019

Etymology

This comma was named by Francium in 2025. It refers to 3626 Ohsaki, the asteroid, which in turn was named after Shoji Osaki, a Japanese astronomical historian.

See also

• Unnoticeable comma
• List of superparticular intervals