# 833/832

 Ratio 833/832 Factorization 2-6 × 72 × 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 $\text{m2}^{7,7,17}_{13}$ Special properties superparticular,reduced Tenney height (log2 nd) 19.4026 Weil height (log2 max(n, d)) 19.4043 Wilson height (sopfr (nd)) 56 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.23934 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:

It factors into the following superparticular pairs:

It also factors into the product of the following ultraparticulars:

## 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.

### Horizon

Subgroup: 2.7.13.17

Comma list: 833/832

Sval mapping[1 0 0 6], 0 1 0 -2], 0 0 1 1]]

sval mapping generators: ~2, ~7, ~11
• CTE: ~2 = 1\1, ~7/4 = 968.2966, ~13/8 = 840.9875
• CWE: ~2 = 1\1, ~7/4 = 968.1967, ~13/8 = 840.5950

### Horizmic

Subgroup: 2.3.5.7.11.13.17

Comma list: 833/832

 [⟨ 1 0 0 0 0 0 6 ], ⟨ 0 1 0 0 0 0 0 ], ⟨ 0 0 1 0 0 0 0 ], ⟨ 0 0 0 1 0 0 -2 ], ⟨ 0 0 0 0 1 0 0 ], ⟨ 0 0 0 0 0 1 1 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
• CTE: ~2 = 1\1, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875
• CWE: ~2 = 1\1, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950

## Etymology

The horizma was named by Jerdle in 2021.