833/832 - Revision history

FloraC: /* Temperaments */ comma list is usually omitted here

2026-03-22T15:24:23Z

Temperaments: comma list is usually omitted here

← Older revision		Revision as of 15:24, 22 March 2026
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	=== Horizon ===		=== Horizon ===
	[[Subgroup]]: 2.7.13.17		[[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\|legend=2\| 1 0 0 6 \| 0 1 0 -2 \| 0 0 1 1 }}
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	=== Horizmic ===		=== Horizmic ===
	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

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

	[[Mapping]]:<br>		[[Mapping]]:<br>

FloraC: /* Temperaments */

2026-03-22T15:22:27Z

Temperaments

← Older revision		Revision as of 15:22, 22 March 2026
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	{{Mapping\|legend=2\| 1 0 0 6 \| 0 1 0 -2 \| 0 0 1 1 }}		{{Mapping\|legend=2\| 1 0 0 6 \| 0 1 0 -2 \| 0 0 1 1 }}
	: mapping generators: ~2, ~7, ~11		: mapping generators: ~2, ~7, ~13

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: Update data

2026-03-22T15:21:33Z

Update data

← Older revision		Revision as of 15:21, 22 March 2026
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	\| Comma = yes		\| 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 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 ==		== Commatic relations ==
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	== 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~~'''. In either case, it enables [[horizmic chords]].		[[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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	{{Mapping\|legend=2\| 1 0 0 6 \| 0 1 0 -2 \| 0 0 1 1 }}		{{Mapping\|legend=2\| 1 0 0 6 \| 0 1 0 -2 \| 0 0 1 1 }}
			: mapping generators: ~2, ~7, ~11
	: ~~sval~~ mapping generators: ~2, ~7, ~11

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.~~0000~~, ~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 = 1200.0000, ~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 }}		{{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 ===		=== Horizmic ===
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	[[Optimal tuning]]s:		[[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~~		* [[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, ~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 }}		{{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 ==		== Etymology ==

FloraC: Size in intro

2026-03-22T15:11:29Z

Size in intro

← Older revision		Revision as of 15:11, 22 March 2026
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	\| Comma = yes		\| 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 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 ==

FloraC: +an important identity. Misc. cleanup

2025-02-08T15:44:45Z

+an important identity. Misc. cleanup

← Older revision		Revision as of 15:44, 8 February 2025
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	}}		}}

	'''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]].		'''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 = ~~1\1~~, ~7/4 = 968.2966, ~13/8 = 840.9875		* [[CTE]]: ~2 = 1200.0000, ~7/4 = 968.2966, ~13/8 = 840.9875
	* [[CWE]]: ~2 = ~~1\1~~, ~7/4 = 968.1967, ~13/8 = 840.5950		* [[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 = ~~1\1~~, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875		* [[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 = ~~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, ~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 ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Horizmic]]		[[Category:Horizmic]]
	[[Category:Commas with unknown etymology]]		[[Category:Commas with unknown etymology]]

BudjarnLambeth at 01:53, 16 November 2024

2024-11-16T01:53:29Z

← Older revision		Revision as of 01:53, 16 November 2024
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	[[Category:Horizmic]]		[[Category:Horizmic]]
			[[Category:Commas with unknown etymology]]

FloraC: /* Temperaments */ +

2024-03-28T11:08:58Z

Temperaments: +

@@ Line 27: / Line 27: @@
 == 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'''.
 == Etymology ==

Jerdle: /* Commatic relations */ Added product of ultraparticulars

2023-06-05T00:16:06Z

Commatic relations: Added product of ultraparticulars

← Older revision		Revision as of 00:16, 5 June 2023
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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:

			* [[43904/43875]] and [[57375/57344]].

	== Temperaments ==		== Temperaments ==

FloraC: Expansion

2023-02-18T10:06:12Z

Expansion

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = horizon comma, horizma
+| Name = horizma, horizon comma
 | Color name = 17o3uzz2, sothuzozo 2nd,<br>Sothuzozo comma
 | Comma = yes
 }}
-'''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 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]].
 == See also ==
 * [[Unnoticeable comma]]
 * [[List of superparticular intervals]]

TallKite at 07:28, 14 January 2023

2023-01-14T07:28:59Z

← Older revision		Revision as of 07:28, 14 January 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = horizon comma, horizma		\| Name = horizon comma, horizma
	\| Color name = sothuzozo 2nd, ~~17o3uzz2~~		\| Color name = 17o3uzz2, sothuzozo 2nd,<br>Sothuzozo comma
	\| Comma = yes		\| Comma = yes
	}}		}}