4225/4224 - Revision history

Squib at 01:50, 19 March 2026

2026-03-19T01:50:14Z

← Older revision		Revision as of 01:50, 19 March 2026
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	* [[169/168]] and [[176/175]]		* [[169/168]] and [[176/175]]
	* [[325/324]] and [[352/351]]		* [[325/324]] and [[352/351]]
			* [[385/384]] and [[847/845]]
	* [[2080/2079]] and [[4096/4095]]		* [[2080/2079]] and [[4096/4095]]
	* [[3025/3024]] and [[10648/10647]]		* [[3025/3024]] and [[10648/10647]]

	It factors into [[4375/4374]] and [[123201/123200]].		It factors into [[4375/4374]] and [[123201/123200]].

	== Temperaments ==		== Temperaments ==

FloraC: Complete data

2026-02-25T06:55:48Z

Complete data

← Older revision		Revision as of 06:55, 25 February 2026
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	\|}		\|}
	: mapping generators: ~2, ~3, ~5, ~7, ~65/48		: mapping generators: ~2, ~3, ~5, ~7, ~65/48

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.0205{{c}}, ~3/2 = 701.9418{{c}}, ~5/4 = 386.2411{{c}}, ~7/4 = 968.7849{{c}}, ~65/48 = 524.6851{{c}}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9442{{c}}, ~5/4 = 386.2465{{c}}, ~7/4 = 968.7910{{c}}, ~65/48 = 524.6866{{c}}

	{{Optimal ET sequence\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}		{{Optimal ET sequence\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}

			[[Badness]] (Sintel): 0.244

	== Etymology ==		== Etymology ==
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

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

	[[Category:Leprechaun]]		[[Category:Leprechaun]]
	[[Category:Commas named after mythology or literature]]		[[Category:Commas named after mythology or literature]]

BudjarnLambeth at 04:08, 11 April 2025

2025-04-11T04:08:22Z

← Older revision		Revision as of 04:08, 11 April 2025
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	[[Category:Leprechaun]]		[[Category:Leprechaun]]
	[[Category:Commas named ~~for other reasons~~]]		[[Category:Commas named after mythology or literature]]

FloraC: Misc. cleanup

2024-11-05T11:33:09Z

Misc. cleanup

← Older revision		Revision as of 11:33, 5 November 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. This comma is the difference between the following pairs:		'''4225/4224''', the '''leprechaun comma''', is an [[unnoticeable comma\|unnoticeable]] [[13-limit]] [[superparticular]] interval. This [[comma]] is the difference between the following pairs:
	* [[65/64]] and [[66/65]]		* [[65/64]] and [[66/65]]
	* [[169/168]] and [[176/175]]		* [[169/168]] and [[176/175]]
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.		[[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.

	[[Subgroup]]: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13
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	== Etymology ==		== Etymology ==
	~~The leprechaun~~ comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List \| ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>~~. It was named as a tribute to [[George Secor]]’s 2002 short story ''A Bit O’ Blarney''~~.		This comma was named by [[Margo Schulter]] in 2012 as a tribute to [[George Secor]]’s 2002 short story ''A Bit O' Blarney''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List \| ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>.

	== See also ==		== See also ==
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Unnoticeable comma]]

	== Notes ==		== Notes ==

BudjarnLambeth at 03:31, 4 November 2024

2024-11-04T03:31:50Z

← Older revision		Revision as of 03:31, 4 November 2024
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	== Etymology ==		== Etymology ==
	The leprechaun comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List \| ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>.		The leprechaun comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List \| ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>. It was named as a tribute to [[George Secor]]’s 2002 short story ''A Bit O’ Blarney''.

	== See also ==		== See also ==
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	[[Category:Leprechaun]]		[[Category:Leprechaun]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named for other reasons]]

BudjarnLambeth at 03:29, 4 November 2024

2024-11-04T03:29:27Z

← Older revision		Revision as of 03:29, 4 November 2024
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	[[Category:Leprechaun]]		[[Category:Leprechaun]]
			[[Category:Commas with unknown etymology]]

Francium: Added color name

2023-09-07T16:09:38Z

Added color name

← Older revision		Revision as of 16:09, 7 September 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = leprechaun comma		\| Name = leprechaun comma
			\| Color name = 3oo1uyy1, thotholuyoyo unison
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: /* Temperaments */ formatting

2023-07-19T12:30:29Z

Temperaments: formatting

← Older revision		Revision as of 12:30, 19 July 2023
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	[[Subgroup]]: 2.3.5.7.11.13		[[Subgroup]]: 2.3.5.7.11.13

	[[Mapping]]:		[[Mapping]]: <br>
	<br>[~~{{val~~\| 1 0 0 0 1 4 }}		{\| class="right-all"
	~~<br>{{val~~\| 0 1 0 0 1 1 }}		\|-
	~~<br>{{val~~\| 0 0 1 0 0 -1 }}		\| [⟨ \|\| 1 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 4 \|\| ],
	~~<br>{{val~~\| 0 0 0 1 0 0 }}		\|-
	~~<br>{{val~~\| 0 0 0 0 2 1 }}]		\| ⟨ \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| 1 \|\| 1 \|\| ],
			\|-
	~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~65/48		\| ⟨ \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| -1 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| 0 \|\| ],
			\|-
			\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 2 \|\| 1 \|\| ]]
			\|}
			: mapping generators: ~2, ~3, ~5, ~7, ~65/48

	{{Optimal ET sequence\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}		{{Optimal ET sequence\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}

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

2023-05-07T18:26:47Z

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

← Older revision		Revision as of 18:26, 7 May 2023
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	Mapping generators: ~2, ~3, ~5, ~7, ~65/48		Mapping generators: ~2, ~3, ~5, ~7, ~65/48

	{{~~Val list~~\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}		{{Optimal ET sequence\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}

	== Etymology ==		== Etymology ==

FloraC: +factorization; +etymology

2023-03-08T11:42:30Z

+factorization; +etymology

← Older revision		Revision as of 11:42, 8 March 2023
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. It is the difference between the following pairs:		'''4225/4224''', the '''leprechaun comma''', is an unnoticeable [[13-limit]] [[superparticular]] interval. This comma is the difference between the following pairs:
	* [[65/64]] and [[66/65]]		* [[65/64]] and [[66/65]]
	* [[169/168]] and [[176/175]]		* [[169/168]] and [[176/175]]
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	* [[2080/2079]] and [[4096/4095]]		* [[2080/2079]] and [[4096/4095]]
	* [[3025/3024]] and [[10648/10647]]		* [[3025/3024]] and [[10648/10647]]

			It factors into [[4375/4374]] and [[123201/123200]].

	== Temperaments ==		== Temperaments ==
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	{{Val list\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}		{{Val list\|legend=1\| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }}

			== Etymology ==
			The leprechaun comma was named by [[Margo Schulter]] in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105598.html Yahoo! Tuning List \| ''EDO alternatives, Leprechaun comma (4225/4224)'']</ref>.

	== See also ==		== See also ==
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

			== Notes ==

	[[Category:Leprechaun]]		[[Category:Leprechaun]]