833/832

Interval information

Ratio	833/832
Factorization	2-6 × 72 × 13-1 × 17
Monzo	[-6 0 0 2 0 -1 1⟩
Size in cents	2.079561¢
Names	horizma, horizon comma
Color name	17o3uzz2, sothuzozo 2nd, Sothuzozo comma
FJS name	[math]\displaystyle{ \text{m2}^{7,7,17}_{13} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	19.4026
Weil height (log2 max(n, d))	19.4043
Wilson height (sopfr(nd))	56
Comma size	unnoticeable
S-expressions	S14 / S16, S49 × S50 × S51
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833/832, the horizma or horizon comma, is a 17-limit (also 2.7.13.17 subgroup) unnoticeable comma, the difference between 52/49 and 17/16. It is also the difference between 49/48 and 52/51.

Commatic relations

This comma identifies itself as the difference between the following superparticular pairs:

• 105/104 and 120/119
• 196/195 and 256/255
• 289/288 and 442/441
• 385/384 and 715/714
• 441/440 and 936/935
• 561/560 and 1716/1715
• 595/594 and 2080/2079
• 625/624 and 2500/2499
• 729/728 and 5832/5831

It factors into the following superparticular pairs:

• 1275/1274 and 2401/2400
• 1225/1224 and 2601/2600

It also factors into the product of the following ultraparticulars:

• 43904/43875 and 57375/57344.

Temperaments

Tempering out this comma in the 17-limit results in the rank-6 horizmic temperament, or in the 2.7.13.17 subgroup, the rank-3 horizon temperament.

Etymology

The horizma was named by Jerdle in 2021.

See also

• Unnoticeable comma
• List of superparticular intervals