Misty comma - Revision history

ArrowHead294 at 16:16, 10 December 2024

2024-12-10T16:16:16Z

← Older revision		Revision as of 16:16, 10 December 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents. It is the amount by which a stack of three [[512/405\|ptolemaic diminished fourths (512/405)]] exceed the [[octave]]. It can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[~~schismic-Pythagorean~~ equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents. It is the amount by which a stack of three [[512/405\|ptolemaic diminished fourths (512/405)]] exceed the [[octave]]. It can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic–Pythagorean equivalence continuum]], with ''n'' = 3.

	== Etymology ==		== Etymology ==

BudjarnLambeth at 12:32, 3 November 2024

2024-11-03T12:32:05Z

← Older revision		Revision as of 12:32, 3 November 2024
Line 13:		Line 13:

	[[Category:Misty]]		[[Category:Misty]]
	[[Category:Commas named ~~for other reasons~~]]		[[Category:Commas named following events]]

BudjarnLambeth at 12:00, 3 November 2024

2024-11-03T12:00:21Z

← Older revision		Revision as of 12:00, 3 November 2024
Line 13:		Line 13:

	[[Category:Misty]]		[[Category:Misty]]
			[[Category:Commas named for other reasons]]

FloraC: Review

2024-02-07T08:52:44Z

Review

← Older revision		Revision as of 08:52, 7 February 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]])~~. It is the amount by which 3 [[512/405]] major thirds exceed the octave~~. Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents. It is the amount by which a stack of three [[512/405\|ptolemaic diminished fourths (512/405)]] exceed the [[octave]]. It can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.

	== Etymology ==		== Etymology ==

CompactStar at 01:33, 7 February 2024

2024-02-07T01:33:14Z

← Older revision		Revision as of 01:33, 7 February 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). It is the amount by which 3 [[512/405]] major thirds exceed the octave. Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.

	== Etymology ==		== Etymology ==

FloraC: +naming

2023-05-14T06:52:27Z

+naming

← Older revision		Revision as of 06:52, 14 May 2023
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''misty comma''', '''67108864/66430125''' = {{monzo\|26 -12 -3}}, is ~~an interval~~ of 17.599 cents, ~~that~~ can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\| 26 -12 -3 }}, is a [[small comma]] of 17.599 cents, which can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.

			== Etymology ==
			The misty comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that [[Carl Lumma]] "missed" this comma in a 5-limit comma search<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group \| ''Ultimate 5-limit comma list'']</ref>.

			== Notes ==

	[[Category:Misty]]		[[Category:Misty]]

TallKite at 05:40, 19 January 2023

2023-01-19T05:40:40Z

← Older revision		Revision as of 05:40, 19 January 2023
Line 2:		Line 2:
	\| Ratio = 67108864/66430125		\| Ratio = 67108864/66430125
	\| Name = misty comma		\| Name = misty comma
			\|Color name = ssg<sup>3</sup>3, sasatrigu 3rd,<br>Sasatrigu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Infobox Interval added

2022-10-27T16:10:50Z

Infobox Interval added

← Older revision		Revision as of 16:10, 27 October 2022
Line 1:		Line 1:
			{{Infobox Interval
			\| Ratio = 67108864/66430125
			\| Name = misty comma
			\| Comma = yes
			}}
	The '''misty comma''', '''67108864/66430125''' = {{monzo\|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.

	~~[[Category:5-limit]]~~
	~~[[Category:Small commas]]~~
	[[Category:Misty]]		[[Category:Misty]]

FloraC: Restore the factorization

2022-05-15T12:32:30Z

Restore the factorization

← Older revision		Revision as of 12:32, 15 May 2022
Line 1:		Line 1:
	The '''misty comma''', '''67108864/66430125''' = {{monzo\|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. However, [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.		The '''misty comma''', '''67108864/66430125''' = {{monzo\|26 -12 -3}}, is an interval of 17.599 cents, that can be written as ([[81/80]])/([[32805/32768]])<sup>2</sup>, ([[2048/2025]])/([[32805/32768]]), ([[128/125]])/([[531441/524288]]). Since these are commas of [[12edo]], so is the misty comma. It factors into simpler commas as ([[393216/390625]])([[1600000/1594323]]). However, the [[misty]] temperament, the 5-limit temperament tempering out the misty comma, is much more accurate than 12 equal can provide, and is also a comma of [[87edo]] and [[99edo]]. This temperament is notably in the [[schismic-Pythagorean equivalence continuum]], with ''n'' = 3.

	[[Category:5-limit]]		[[Category:5-limit]]
	[[Category:Small commas]]		[[Category:Small commas]]
	[[Category:Misty]]		[[Category:Misty]]

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

2022-03-20T21:59:59Z

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

← Older revision		Revision as of 21:59, 20 March 2022
Line 2:		Line 2:

	[[Category:5-limit]]		[[Category:5-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Misty]]		[[Category:Misty]]