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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = horizma, horizon comma
| Ratio = 833/832
| Color name = 17o3uzz2, sothuzozo 2nd,<br>Sothuzozo comma
| Monzo = -6 0 0 2 0 -1 1
| Comma = yes
| Cents = 2.07956
| Name = horizon comma, horizma
| Color name = sothuzozo 2nd, 17o3uzz2
| FJS name = m2<sup>7,7,17</sup><sub>13</sub>
<!--| Neutral FJS name = sd2<sup>7,7,17</sup><sub>13</sub>-->
}}
}}


'''833/832''', the '''horizon comma''', is a [[17-limit]] [[unnoticeable comma]], the difference between [[52/49]] and [[17/16]]. It is also the difference between [[49/48]] and [[52/51]].
'''833/832''', the '''horizma''' or '''horizon comma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.7.13.17 [[subgroup]]) [[comma]]. It is the difference between [[17/13]] and a stack of two [[8/7]]'s. It is also the difference between [[52/49]] and [[17/16]], and 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'''. In either case, it enables [[horizmic chords]].
 
=== Horizon ===
[[Subgroup]]: 2.7.13.17
 
[[Comma list]]: 833/832
 
{{Mapping|legend=2| 1 0 0 6 | 0 1 0 -2 | 0 0 1 1 }}
 
: sval mapping generators: ~2, ~7, ~11
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000, ~7/4 = 968.2966, ~13/8 = 840.9875
* [[CWE]]: ~2 = 1200.0000, ~7/4 = 968.1967, ~13/8 = 840.5950
 
{{Optimal ET sequence|legend=1| 10, 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]]:<br>
{| class="right-all"
|-
| [⟨ || 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 tuning]]s:
* [[CTE]]: ~2 = 1200.0000, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875
* [[CWE]]: ~2 = 1200.0000, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950
 
{{Optimal ET sequence|legend=1| 22f, 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 [[User:Jerdle|Jerdle]] in 2021.  


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:17-limit]]
[[Category:Horizmic]]
[[Category:Unnoticeable commas]]
[[Category:Commas with unknown etymology]]

Latest revision as of 15:44, 8 February 2025

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
Open this interval in xen-calc

833/832, the horizma or horizon comma, is an unnoticeable 17-limit (also 2.7.13.17 subgroup) comma. It is the difference between 17/13 and a stack of two 8/7's. It is also the difference between 52/49 and 17/16, and 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. In either case, it enables horizmic chords.

Horizon

Subgroup: 2.7.13.17

Comma list: 833/832

Subgroup-val mapping: [⟨1 0 0 6], ⟨0 1 0 -2], ⟨0 0 1 1]]

sval mapping generators: ~2, ~7, ~11

Optimal tunings:

  • CTE: ~2 = 1200.0000, ~7/4 = 968.2966, ~13/8 = 840.9875
  • CWE: ~2 = 1200.0000, ~7/4 = 968.1967, ~13/8 = 840.5950

Optimal ET sequence: 10, 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 = 1200.0000, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875
  • CWE: ~2 = 1200.0000, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950

Optimal ET sequence: 22f, 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

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