833/832

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Interval information
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 [math]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~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

Optimal tunings:

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

Optimal ET sequence10, 21, 26, 36, 46, 47, 57, 93, 150, 207, 357, 704g, 854g, 911dg, 1061dg, 1268dg, 1418dgg

Horizmic

Subgroup: 2.3.5.7.11.13.17

Comma list: 833/832

Mapping:

[⟨ 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

Optimal tunings:

  • 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

Optimal ET sequence22f, 26, 31, 41, 46, 58, 72, 103, 130, 140, 171, 212g, 217, 243e, 289, 301, 311, 414, 460, 684g, 771, 1004dg, 1144degg, 1558cdegg, 1775ddgg

Etymology

The horizma was named by Jerdle in 2021.

See also