Cloudy comma - Revision history

FloraC: - temp data (addressed in misc. 7-limit temps), thereby removing the 11-limit extension as there's no justification for it

2026-06-25T11:38:33Z

- temp data (addressed in misc. 7-limit temps), thereby removing the 11-limit extension as there's no justification for it

@@ Line 8: / Line 8: @@
 == Temperaments ==
-[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].
+[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. In the full 7-limit, this leads to the rank-3 [[cloudy]] temperament. For [[edo]]s ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].
 [[Category:Cloudy]]
 [[Category:Commas named for their regular temperament properties]]

FloraC: Rework

2026-06-25T10:53:44Z

Rework

← Older revision		Revision as of 10:53, 25 June 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
			'''16807/16384''', the '''cloudy comma''', or systematically the '''5-7-comma''', is a [[medium comma]] in the [[7-limit]] with a size of about 44.1 [[cent]]s. It is the amount by which five [[8/7]]'s fall short of an octave. In the [[2.5.7 subgroup]], it exceeds [[128/125]] by the [[rainy comma]].
	'''16807/16384''', the '''cloudy comma''', is a 7-limit ~~medium comma~~. It is the amount by which five [[8/7]]s fall short of ~~one~~ octave ~~and exceeds [[128/125]] by~~ the [[~~rainy comma]]~~. ~~For equal divisions ''N'' up to 65, the comma is tempered out if and only if~~ 5 ~~divides ''N''~~. ~~Examples are [[5edo~~]], [[~~10edo~~]], [[~~15edo]], [[50edo]], [[55edo]] and [[65edo~~]].

	== Temperaments ==		== Temperaments ==
	Tempering out ~~the cloudy~~ comma splits the octave into 5 equal parts and maps the harmonic 7 to 4\5. ~~It leads~~ to ~~a number of regular~~ temperaments ~~in the~~ [[~~cloudy clan~~]].		[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4\|harmonic seventh]] to [[5edo\|4\5]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].

	~~Cloudy~~ rank-3 temperament can be described as the 10&~~amp;~~15&~~amp;~~50 temperament, which ~~tempers~~ out 385/384 and 3087/3025 in the 11-limit; 105/104, 144/143, and 4459/4400 ~~in the 13-limit~~.		The cloudy rank-3 temperament can be described as the 10 & 15 & 50 temperament, which can be extended to the 11-limit by tempering out 385/384 and 3087/3025, and the 13-limit by tempering out 105/104, 144/143, and 4459/4400.

	=== Cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== Cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

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	{{Optimal ET sequence\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}

	=== 11-limit cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== 11-limit cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}

	=== 13-limit cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== 13-limit cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

BudjarnLambeth at 07:59, 3 November 2024

2024-11-03T07:59:08Z

← Older revision		Revision as of 07:59, 3 November 2024
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	[[Category:Cloudy]]		[[Category:Cloudy]]
			[[Category:Commas named for their regular temperament properties]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:24:32Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:24, 7 May 2023
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	[[POTE generator]]s: ~3/2 = 699.467, ~5/4 = 382.669		[[POTE generator]]s: ~3/2 = 699.467, ~5/4 = 382.669

	{{~~Val list~~\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}

	=== 11-limit cloudy (10&15&50) ===		=== 11-limit cloudy (10&15&50) ===
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	POTE generators: ~3/2 = 699.779, ~5/4 = 386.575		POTE generators: ~3/2 = 699.779, ~5/4 = 386.575

	~~Vals:~~ {{~~Val list~~\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}

	=== 13-limit cloudy (10&15&50) ===		=== 13-limit cloudy (10&15&50) ===
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	POTE generators: ~3/2 = 698.726, ~5/4 = 384.760		POTE generators: ~3/2 = 698.726, ~5/4 = 384.760

	~~Vals:~~ {{~~Val list~~\| 5, 10, 15, 40, 50, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 40, 50, 60, 65 }}

	[[Category:Cloudy]]		[[Category:Cloudy]]

Godtone: readability

2023-03-25T22:13:08Z

readability

← Older revision		Revision as of 22:13, 25 March 2023
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	}}		}}

	'''16807/16384''', the '''cloudy comma''', is a 7-limit medium comma. It is the amount by which five [[8/7]]s fall short of one octave and exceeds [[128/125]] by [[~~2100875/2097152~~]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]].		'''16807/16384''', the '''cloudy comma''', is a 7-limit medium comma. It is the amount by which five [[8/7]]s fall short of one octave and exceeds [[128/125]] by the [[rainy comma]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]].

	== Temperaments ==		== Temperaments ==

TallKite: added color name

2022-12-29T03:01:25Z

added color name

← Older revision		Revision as of 03:01, 29 December 2022
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	\| Ratio = 16807/16384		\| Ratio = 16807/16384
	\| Name = cloudy comma		\| Name = cloudy comma
			\| Color name = Lz<sup>5</sup>3, Laquinzo comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:33:12Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:33, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 16807/16384		\| Ratio = 16807/16384
	~~\| Monzo = -14 0 0 5~~
	~~\| Cents = 44.12953~~
	\| Name = cloudy comma		\| Name = cloudy comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name = d3<sup>7,7,7,7,7</sup>~~
	~~\| Sound~~ =
	}}		}}

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	Vals: {{Val list\| 5, 10, 15, 40, 50, 60, 65 }}		Vals: {{Val list\| 5, 10, 15, 40, 50, 60, 65 }}

	~~[[Category:7-limit]]~~
	~~[[Category:Medium commas]]~~
	[[Category:Cloudy]]		[[Category:Cloudy]]

Fredg999 category edits: Moving from Category:Medium comma to Category:Medium commas using Cat-a-lot

2022-03-20T21:53:42Z

Moving from Category:Medium comma to Category:Medium commas using Cat-a-lot

← Older revision		Revision as of 21:53, 20 March 2022
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	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Medium ~~comma~~]]		[[Category:Medium commas]]
	[[Category:Cloudy]]		[[Category:Cloudy]]

Fredg999: Misc. edits, categories

2022-01-22T05:24:49Z

Misc. edits, categories

← Older revision		Revision as of 05:24, 22 January 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 16807/16384		\| Ratio = 16807/16384
	\| Monzo = -14 0 0 5		\| Monzo = -14 0 0 5
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	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Medium comma]]		[[Category:Medium comma]]
	~~[[Category:Interval]]~~
	[[Category:Cloudy]]		[[Category:Cloudy]]

Xenllium at 14:09, 28 April 2021

2021-04-28T14:09:02Z

← Older revision		Revision as of 14:09, 28 April 2021
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	=== Cloudy (10&15&50) ===		=== Cloudy (10&15&50) ===

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

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	=== 11-limit cloudy (10&15&50) ===		=== 11-limit cloudy (10&15&50) ===

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	POTE generators: ~3/2 = 699.779, ~5/4 = 386.575		POTE generators: ~3/2 = 699.779, ~5/4 = 386.575

	{{Val list~~\|legend=1~~\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}		Vals: {{Val list\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}

	=== 13-limit cloudy (10&15&50) ===		=== 13-limit cloudy (10&15&50) ===

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	POTE generators: ~3/2 = 698.726, ~5/4 = 384.760		POTE generators: ~3/2 = 698.726, ~5/4 = 384.760

	{{Val list~~\|legend=1~~\| 5, 10, 15, 40, 50, 60, 65 }}		Vals: {{Val list\| 5, 10, 15, 40, 50, 60, 65 }}

	[[Category:7-limit]]		[[Category:7-limit]]