833/832: Difference between revisions

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| Comma = yes

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'''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]].

'''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 ==

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* [[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~~'''.

[[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 generators: ~2, ~7, ~13

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

[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1\1~~, ~7/4 = 968.~~2966~~, ~13/8 = 840.~~9875~~

* [[WE]]: ~2 = 1200.1274{{c}}, ~7/4 = 968.2363{{c}}, ~13/8 = 840.4362{{c}}

* [[CWE]]: ~2 = ~~1\1~~, ~7/4 = 968.1967, ~13/8 = 840.5950

* [[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

~~[[Comma list]]: 833/832~~

[[Mapping]]:<br>

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1\1~~, ~3/2 = 701.~~9550~~, ~5/4 = 386.~~3137~~, ~7/4 = 968.~~2966~~, ~11/8 = ~~551~~.~~3179~~, ~13/8 = 840.~~9875~~

* [[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 = ~~1\1~~, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950

* [[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 ==

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== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

[[Category:Horizmic]]

[[Category:Commas with unknown etymology]]

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 | Comma = yes
 }}
+'''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]].
-'''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 ==
@@ Line 22: / Line 21: @@
 * [[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'''.
+[[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 }}
+: mapping generators: ~2, ~7, ~13
-: sval mapping generators: ~2, ~7, ~11
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1\1, ~7/4 = 968.2966, ~13/8 = 840.9875
+* [[WE]]: ~2 = 1200.1274{{c}}, ~7/4 = 968.2363{{c}}, ~13/8 = 840.4362{{c}}
-* [[CWE]]: ~2 = 1\1, ~7/4 = 968.1967, ~13/8 = 840.5950
+* [[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
-[[Comma list]]: 833/832
 [[Mapping]]:<br>
@@ Line 67: / Line 63: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875
+* [[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 = 1\1, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950
+* [[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 ==
@@ Line 76: / Line 74: @@
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
 [[Category:Horizmic]]
+[[Category:Commas with unknown etymology]]