Glacier comma - Revision history

FloraC: - duplicate data

2026-05-03T15:30:20Z

- duplicate data

← Older revision		Revision as of 15:30, 3 May 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).		The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n'' + 5)/''n'') / ((''n'' + 3)/(''n'' + 2))<sup>5</sup> = (S(''n'' + 1)⋅S(''n'' + 2)<sup>2</sup>) / (S(''n'' + 3)<sup>2</sup>⋅S(''n'' + 4)).

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 13~~-limit~~ leads to the [[glacier]] ~~family.~~		[[Tempering out]] this comma in the 2.3.13 subgroup leads to the [[glacier]] temperament.

	~~=== Glacier (2.3.13) ===~~
	~~[[Subgroup]]: 2.3.13~~

	~~[[Mapping]]: {{mapping\|1 1 3\|0 5 6}}~~

	~~: Mapping generators: ~2, ~13/12~~

	~~[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~13/12 = 140.3277~~

	~~{{Optimal ET sequence\|legend=1\|8, 9, 17, 26, 60, 77, 94, 111, 171}}~~

	~~[[Badness]]: 0~~.~~383 (Sintel)~~

	== See also ==		== See also ==

Eufalesio: Badness (Sintel)

2025-11-03T01:37:05Z

Badness (Sintel)

← Older revision		Revision as of 01:37, 3 November 2025
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	[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~13/12 = 140.3277		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~13/12 = 140.3277

	{{Optimal ET sequence\|legend=1\|8, 9, 17, 60, 77, 94, 171}}		{{Optimal ET sequence\|legend=1\|8, 9, 17, 26, 60, 77, 94, 111, 171}}

	[[Badness]]: 0.~~006431~~		[[Badness]]: 0.383 (Sintel)

	== See also ==		== See also ==

Xenllium: Quintic-particular is an idiosyncratic term

2025-05-23T12:46:26Z

Quintic-particular is an idiosyncratic term

← Older revision		Revision as of 12:46, 23 May 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).		The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).

	== Temperaments ==		== Temperaments ==

Xenllium at 12:24, 21 May 2025

2025-05-21T12:24:19Z

← Older revision		Revision as of 12:24, 21 May 2025
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	{{Infobox ~~Interval~~		{{Infobox interval
	\| Ratio = 373248/371293		\| Ratio = 373248/371293
	~~\| Monzo = 9 6 0 0 0 -5~~
	\| Name = glacier comma		\| Name = glacier comma
	\| Color name = 3u<sup>5</sup>-2, quinthu negative 2nd		\| Color name = 3u<sup>5</sup>-2, quinthu negative 2nd
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]).		The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 13-limit leads to the [[glacier]] family.		Tempering out this comma in the 13-limit leads to the [[glacier]] family.

			=== Glacier (2.3.13) ===
			[[Subgroup]]: 2.3.13

			[[Mapping]]: {{mapping\|1 1 3\|0 5 6}}

			: Mapping generators: ~2, ~13/12

			[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~13/12 = 140.3277

			{{Optimal ET sequence\|legend=1\|8, 9, 17, 60, 77, 94, 171}}

			[[Badness]]: 0.006431

			== See also ==
			* [[Quinticular comma]] – another example of quintic-particular comma

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

BudjarnLambeth at 02:24, 4 November 2024

2024-11-04T02:24:15Z

← Older revision		Revision as of 02:24, 4 November 2024
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	Tempering out this comma in the 13-limit leads to the [[glacier]] family.		Tempering out this comma in the 13-limit leads to the [[glacier]] family.

	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

BudjarnLambeth at 08:49, 3 November 2024

2024-11-03T08:49:11Z

← Older revision		Revision as of 08:49, 3 November 2024
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 13-limit leads to the [[glacier]] family.		Tempering out this comma in the 13-limit leads to the [[glacier]] family.

			[[Category:Commas named after individuals]]

ArrowHead294: —

2024-04-01T01:19:56Z

—

New page

{{Infobox Interval
| Ratio = 373248/371293
| Monzo = 9 6 0 0 0 -5
| Name = glacier comma
| Color name = 3u<sup>5</sup>-2, quinthu negative 2nd
| Comma = yes
}}
The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]).

== Temperaments ==
Tempering out this comma in the 13-limit leads to the [[glacier]] family.