1716/1715 - Revision history

FloraC: Expand for data

2026-03-04T08:09:22Z

Expand for data

← Older revision		Revision as of 08:09, 4 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''lummic comma''', '''1716/1715''', is a [[13-limit]] [[superparticular]] [[comma]] measuring about 1.0{{cent}}. It often arises as the difference between simpler commas: ([[176/175]])/([[196/195]]), ([[351/350]])/([[441/440]]), ([[1573/1568]])/([[385/384]]), ([[540/539]])/([[1575/1573]]), and ([[1001/1000]])/([[2401/2400]]). It factors into ([[2080/2079]])([[9801/9800]]).		The '''lummic comma''', '''1716/1715''', is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] [[superparticular]] [[comma]] measuring about 1.0{{cent}}. It often arises as the difference between simpler commas: ([[176/175]])/([[196/195]]), ([[351/350]])/([[441/440]]), ([[1573/1568]])/([[385/384]]), ([[540/539]])/([[1575/1573]]), and ([[1001/1000]])/([[2401/2400]]). It factors into ([[2080/2079]])⋅([[9801/9800]]).

	Tempering it out leads to the rank-5 '''lummic ~~temperament~~'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.		== Temperaments ==
			[[Tempering out]] this comma leads to the rank-5 '''lummic''' temperament. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.

			[[Subgroup]]: 2.3.5.7.11.13

			[[Mapping]]: <br>
			{\| class="right-all"
			\|-
			\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| -2 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 3 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| -1 \|\| ]]
			\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~11

			[[Optimal tuning]]s:
			: [[WE]]: ~2 = 1199.9814{{c}}, ~3/2 = 701.9502{{c}}, ~5/4 = 386.4011{{c}}, ~7/4 = 969.0830{{c}}, ~11/8 = 551.2624{{c}}
			: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9462{{c}}, ~5/4 = 386.3868{{c}}, ~7/4 = 969.0766{{c}}, ~11/8 = 551.2373{{c}}

			{{Optimal ET sequence\|legend=1\| 22f, 26, 27e, 31, 45ef, 46, 58, 72, 103, 121, 130, 193, 198, 224, 270, 494, 764, 1137, 1258, 1289, 1419, 1559, 1689, 2183d }}

			[[Badness]] (Sintel): 0.318

	== Etymology ==		== Etymology ==
	This comma was named after [[Carl Lumma]]. Perhaps interestingly, a ''lummisma'' was first proposed by [[Gene Ward Smith]] in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97947.html Yahoo! Tuning Group \| ''Short commas'']</ref>, which might ultimately led to this comma being named so.		This comma was named after [[Carl Lumma]]. Perhaps interestingly, a ''lummisma'' was first proposed by [[Gene Ward Smith]] in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97947.html Yahoo! Tuning Group \| ''Short commas'']</ref>, which might ultimately led to this comma being named so.

	== ~~Notes~~ ==		== References ==

	[[Category:Lummic]]		[[Category:Lummic]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: + etymology

2025-06-14T15:22:03Z

+ etymology

← Older revision		Revision as of 15:22, 14 June 2025
Line 7:		Line 7:

	Tempering it out leads to the rank-5 '''lummic temperament'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.		Tempering it out leads to the rank-5 '''lummic temperament'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.

			== Etymology ==
			This comma was named after [[Carl Lumma]]. Perhaps interestingly, a ''lummisma'' was first proposed by [[Gene Ward Smith]] in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97947.html Yahoo! Tuning Group \| ''Short commas'']</ref>, which might ultimately led to this comma being named so.

			== Notes ==

	[[Category:Lummic]]		[[Category:Lummic]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

BudjarnLambeth at 03:26, 4 November 2024

2024-11-04T03:26:53Z

← Older revision		Revision as of 03:26, 4 November 2024
Line 9:		Line 9:

	[[Category:Lummic]]		[[Category:Lummic]]
			[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

Francium at 13:13, 7 September 2023

2023-09-07T13:13:20Z

← Older revision		Revision as of 13:13, 7 September 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = lummic comma		\| Name = lummic comma
	\| Color name = 3o1or<sup>3</sup>g-2		\| Color name = 3o1or<sup>3</sup>g-2, tholotriru-agu negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}

Francium: Added color name

2023-09-07T13:12:22Z

Added color name

← Older revision		Revision as of 13:12, 7 September 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = lummic comma		\| Name = lummic comma
			\| Color name = 3o1or<sup>3</sup>g-2
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Rework

2023-06-20T07:15:46Z

Rework

← Older revision		Revision as of 07:15, 20 June 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~Lummic~~ comma		\| Name = lummic comma
	\| Comma = yes		\| Comma = yes
	}} The ~~Lummic~~ comma, 1716/1715, is a ~~superparticular 11~~-limit comma ~~which~~ is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. ~~It factors into the~~ [[~~cantonisma~~]].		}}
			The '''lummic comma''', '''1716/1715''', is a [[13-limit]] [[superparticular]] [[comma]] measuring about 1.0{{cent}}. It often arises as the difference between simpler commas: ([[176/175]])/([[196/195]]), ([[351/350]])/([[441/440]]), ([[1573/1568]])/([[385/384]]), ([[540/539]])/([[1575/1573]]), and ([[1001/1000]])/([[2401/2400]]). It factors into ([[2080/2079]])([[9801/9800]]).

			Tempering it out leads to the rank-5 '''lummic temperament'''. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others.

			[[Category:Lummic]]

BudjarnLambeth at 06:45, 18 June 2023

2023-06-18T06:45:31Z

← Older revision		Revision as of 06:45, 18 June 2023
Line 2:		Line 2:
	\| Name = Lummic comma		\| Name = Lummic comma
	\| Comma = yes		\| Comma = yes
	}} The Lummic comma, 1716/1715, is a superparticular 11-limit comma which is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. It factors into the [[~~Cantonisma~~]].		}} The Lummic comma, 1716/1715, is a superparticular 11-limit comma which is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. It factors into the [[cantonisma]].

BudjarnLambeth at 06:45, 18 June 2023

2023-06-18T06:45:16Z

← Older revision		Revision as of 06:45, 18 June 2023
Line 1:		Line 1:
	The Lummic comma, 1716/1715, is a superparticular 11-limit comma which is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. It factors into the [[Cantonisma]].
	{{Infobox Interval		{{Infobox Interval
	\| Name = Lummic comma		\| Name = Lummic comma
	\| Comma = yes		\| Comma = yes
	}}		}} The Lummic comma, 1716/1715, is a superparticular 11-limit comma which is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. It factors into the [[Cantonisma]].

BudjarnLambeth: Created wanted page

2023-06-18T06:44:57Z

Created wanted page

New page

The Lummic comma, 1716/1715, is a superparticular 11-limit comma which is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. It factors into the [[Cantonisma]].
{{Infobox Interval
| Name = Lummic comma
| Comma = yes
}}