4675/4674

Interval information

Ratio	4675/4674
Subgroup monzo	2.3.5.11.17.19.41 [-1 -1 2 1 1 -1 -1⟩
Size in cents	0.3703571 ¢
Name	ohbokisma
Color name	41u19u17o1oyy1 fowunusoloyoyo unison
FJS name	[math]\displaystyle{ \text{P1}^{5,5,11,17}_{19,41} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	24.3812
Weil norm (log2 max(n, d))	24.3815
Wilson norm (sopfr(nd))	103
Comma size	unnoticeable
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4675/4674, the ohbokisma, is a 41-limit superparticular comma of about 0.37 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 165/164 and 171/170
• 780/779 and 936/935
• 1600/1599 and 2432/2431

It can be factored into the following superparticular ratios:

• 4785/4784 and 203320/203319
• 4921/4920 and 93500/93499
• 4960/4959 and 81345/81344
• 5577/5576 and 28900/28899
• 5797/5796 and 24150/24149
• 5929/5928 and 22100/22099
• 6325/6324 and 17918/17917
• 6930/6929 and 14365/14364
• 7905/7904 and 11440/11439

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament ohbokismic. Using the 2.3.5.11.17.19.41 subgroup leads to the rank-6 temperament ohbokic.

Ohbokic

Subgroup 2.3.5.11.17.19.41

Comma list: 4675/4674

Mapping:

[⟨	1	1	2	3	4	4	5	],
⟨	0	1	0	0	0	0	-1	],
⟨	0	0	1	0	0	0	2	],
⟨	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 = 701.964, ~5/4 = 386.274, ~11/8 = 551.273, ~17/16 = 104.893, ~19/16 = 297.580

Optimal ET sequence: 5eghmm, 7ghm, 12e, 14cmm, 15, 15gm, 19, 22, 24, 31, 34h, 38m, 53, 56, 65m, 72m, 80, 87, 94m, 99em, 111, 118, 193, 205, 217, 255, 311, 342, 422, 460, 559, 677, 836, 1140, 1178, 1258, 1395, 1513, 2436, 2653, 3113, 3949, 4896, 6291m

Badness (Sintel): 0.100

Etymology

This comma was named by Francium in 2025. It refers to 4675 Ohboke, which in turn was named after the Oboke Gorge in Japan.

See also

• Unnoticeable comma
• List of superparticular intervals