833/832
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Ratio | 833/832 |
Factorization | 2^{-6} × 7^{2} × 13^{-1} × 17 |
Monzo | [-6 0 0 2 0 -1 1⟩ |
Size in cents | 2.0795607¢ |
Names | horizma, horizon comma |
Color name | 17o3uzz2, sothuzozo 2nd, Sothuzozo comma |
FJS name | [math]\text{m2}^{7,7,17}_{13}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 19.4026 |
Weil height (log_{2} max(n, d)) | 19.4043 |
Wilson height (sopfr (nd)) | 56 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.41718 bits |
Comma size | unnoticeable |
S-expressions | S14 / S16, S49 × S50 × S51 |
open this interval in xen-calc |
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:
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.