741/740

Interval information

Ratio	741/740
Factorization	2-2 × 3 × 5-1 × 13 × 19 × 37-1
Monzo	[-2 1 -1 0 0 1 0 1 0 0 0 -1⟩
Size in cents	2.337926¢
Name	botolphisma
Color name	37u19o3og1 thisunothogu unison
FJS name	[math]\text{d2}^{13,19}_{5,37}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	19.0647
Weil height (log2 max(n, d))	19.0667
Wilson height (sopfr(nd))	81
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.25001 bits
Comma size	unnoticeable
S-expression	S38 × S39
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741/740, the botolphisma, is a 37-limit superparticular comma of about 2.3 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 171/170 and 222/221
• 260/259 and 400/399
• 297/296 and 495/494

It can be factored into the following superparticular intervals:

• 760/759 and 29601/29600
• 806/805 and 9177/9176
• 897/896 and 4256/4255
• 931/930 and 3627/3626
• 936/935 and 3553/3552
• 969/968 and 3146/3145
• 1001/1000 and 2850/2849
• 1296/1295 and 1729/1728
• 1444/1443 and 1521/1520

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament botolphismic. Using the 2.3.5.13.19.37 subgroup leads to the rank-5 temperament botolphic.

Botolphic

Subgroup: 2.3.5.13.19.37

Comma list: 741/740

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.867, ~5/4 = 386.502, ~13/8 = 840.048, ~19/16 = 296.881

Optimal ET sequence: 5, 5hl, 7h, 9l, 10, 12l, 15l, 19hl, 19, 24, 27, 34, 38fl, 41, 43, 46h, 50, 53, 164l, 183, 217l, 270, 323, 373, 426h, 537l, 590, 643

Etymology

This comma was named by Francium in 2025. It refers to 741 Botolphia, the asteroid, which in turn was named after Saint Botolph.

See also

• Unnoticeable comma
• List of superparticular intervals