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{{Infobox Interval | {{Infobox Interval | ||
| Name = horizma, horizon comma | |||
| Color name = 17o3uzz2, sothuzozo 2nd,<br>Sothuzozo comma | |||
| Comma = yes | |||
| Name = horizon comma | |||
| Color name = sothuzozo 2nd, | |||
}} | }} | ||
'''833/832''', the '''horizma''' or '''horizon comma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.7.13.17-[[subgroup]]) [[comma]] with a size of roughly 2.08 [[cent]]s. 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 | |||
{{Mapping|legend=2| 1 0 0 6 | 0 1 0 -2 | 0 0 1 1 }} | |||
: mapping generators: ~2, ~7, ~13 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.1274{{c}}, ~7/4 = 968.2363{{c}}, ~13/8 = 840.4362{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 968.1967{{c}}, ~13/8 = 840.5950{{c}} | |||
{{Optimal ET sequence|legend=1| 10, 21, 26, 36, 46, 47, 57, 93, 150, 207, 357, 704g, 854g, 911dg, 1061dg, 1268dg, 1418dgg }} | |||
[[Badness]] (Sintel): 0.0198 | |||
=== Horizmic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[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: | |||
* [[WE]]: ~2 = 1200.1274{{c}}, ~3/2 = 701.8276{{c}}, ~5/4 = 386.0589{{c}}, ~7/4 = 968.2363{{c}}, ~11/8 = 550.9357{{c}}, ~13/8 = 840.4362{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8313{{c}}, ~5/4 = 386.1324{{c}}, ~7/4 = 968.1967{{c}}, ~11/8 = 551.0479{{c}}, ~13/8 = 840.5950{{c}} | |||
{{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 }} | |||
[[Badness]] (Sintel): 1.14 | |||
== Etymology == | |||
The horizma was named by [[User:Jerdle|Jerdle]] in 2021. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category: | [[Category:Horizmic]] | ||
[[Category: | [[Category:Commas with unknown etymology]] | ||
Latest revision as of 15:24, 22 March 2026
| Interval information |
horizon comma
Sothuzozo comma
reduced
S49⋅S50⋅S51
833/832, the horizma or horizon comma, is an unnoticeable 17-limit (also 2.7.13.17-subgroup) comma with a size of roughly 2.08 cents. 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:
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
Subgroup-val mapping: [⟨1 0 0 6], ⟨0 1 0 -2], ⟨0 0 1 1]]
- mapping generators: ~2, ~7, ~13
- WE: ~2 = 1200.1274 ¢, ~7/4 = 968.2363 ¢, ~13/8 = 840.4362 ¢
- 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
Badness (Sintel): 0.0198
Horizmic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 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
- WE: ~2 = 1200.1274 ¢, ~3/2 = 701.8276 ¢, ~5/4 = 386.0589 ¢, ~7/4 = 968.2363 ¢, ~11/8 = 550.9357 ¢, ~13/8 = 840.4362 ¢
- 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
Badness (Sintel): 1.14
Etymology
The horizma was named by Jerdle in 2021.