851/850

Interval information

Ratio	851/850
Factorization	2-1 × 5-2 × 17-1 × 23 × 37
Monzo	[-1 0 -2 0 0 0 -1 0 1 0 0 1⟩
Size in cents	2.035549¢
Name	zeissisma
Color name	37o23o17ugg2 thisotwethosugugu 2nd
FJS name	[math]\text{m}{-2}^{23,37}_{5,5,17}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	19.4643
Weil height (log2 max(n, d))	19.466
Wilson height (sopfr(nd))	89
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.23768 bits
Comma size	unnoticeable
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851/850, the zeissisma, is a 37-limit superparticular comma of about 2.04 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 69/68 and 75/74
• 222/221 and 300/299
• 276/275 and 408/407

It can be factored into the following superparticular ratios:

• 868/867 and 43401/43400
• 897/896 and 16576/16575
• 925/924 and 10626/10625
• 936/935 and 9361/9360
• 1036/1035 and 4761/4760
• 1276/1275 and 2553/2552
• 1426/1425 and 2109/2108
• 1480/1479 and 2001/2000
• 1701/1700 and 1702/1701

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament zeissismic. Using the 2.5.17.23.37 subgroup leads to the rank-4 temperament zeissic.

Zeissic

Subgroup: 2.5.17.23.37

Comma list: 851/850

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.569, ~17/16 = 105.351, ~23/16 = 627.789

Optimal ET sequence: 4l, 5gl, 6g, 7gi, 9, 16, 25, 34, 59, 65, 80, 81, 90, 115, 124, 149, 239, 388, 627

Badness (Sintel): 0.026

Etymology

This comma was named by Francium in 2025. It refers to 851 Zeissia, the asteroid, which in turn was named after Zeiss, a German manufacturer of optical systems and optoelectronics.

See also

• Unnoticeable comma
• List of superparticular intervals