833/832: Difference between revisions
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'''833/832''', the '''horizma''' or '''horizon comma''', is | '''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 == | == Commatic relations == | ||
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* [[1275/1274]] and [[2401/2400]] | * [[1275/1274]] and [[2401/2400]] | ||
* [[1225/1224]] and [[2601/2600]] | * [[1225/1224]] and [[2601/2600]] | ||
It also factors into the product of the following ultraparticulars: | It also factors into the product of the following ultraparticulars: | ||
* [[43904/43875]] and [[57375/57344]]. | * [[43904/43875]] and [[57375/57344]]. | ||
== Temperaments == | == 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'''. | 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 === | === Horizon === | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[CTE]]: ~2 = 1200.0000, ~7/4 = 968.2966, ~13/8 = 840.9875 | ||
* [[CWE]]: ~2 = | * [[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 }} | {{Optimal ET sequence|legend=1| 10, 21, 26, 36, 46, 47, 57, 93, 150, 207, 357, 704g, 854g, 911dg, 1061dg, 1268dg, 1418dgg }} | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = | * [[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 = | * [[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 }} | {{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 }} | ||
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== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Horizmic]] | [[Category:Horizmic]] | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] | ||