Ennealimma - Revision history

FloraC: - data

2026-06-29T04:18:01Z

- data

@@ Line 8: / Line 8: @@
 == Temperament ==
-[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.
+[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts.
 == Etymology ==

FloraC: Cleanup

2026-06-29T04:14:34Z

Cleanup

← Older revision		Revision as of 04:14, 29 June 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = ~~7629394531250~~/~~7625597484987~~		\| Ratio = 7 629 394 531 250 / 7 625 597 484 987
	~~\| Monzo = 1 -27 18~~
	\| Name = ennealimma		\| Name = ennealimma
	\| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd		\| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo\| 1 -27 18 }}, is a [[5-limit]] [[~~unnoticeable~~ comma]] measuring about 0.86 [[cent]]s. It is the amount by which a stack of nine [[27/25\|large limmas]] falls short of the [[octave]].		The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo\| 1 -27 18 }}, is an [[unnoticeable comma\|unnoticeable]] [[5-limit]] [[comma]] measuring about 0.862 [[cent]]s. It is the amount by which a stack of nine [[27/25\|large limmas]] falls short of the [[octave]].

	== Temperament ==		== Temperament ==
	Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.		[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.

	=== Ennealimmal ===		=== Ennealimmal ===
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	== See also ==		== See also ==
	* [[Unnoticeable comma]]
	* [[Septimal ennealimma]]		* [[Septimal ennealimma]]

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

	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]

FloraC: - typo

2025-11-29T12:59:15Z

- typo

← Older revision		Revision as of 12:59, 29 November 2025
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	{{Mapping\|legend=1\| 9 1 1 \| 0 2 3 }}		{{Mapping\|legend=1\| 9 1 1 \| 0 2 3 }}
	: mapping generators: ~27/25, ~5/4		: mapping generators: ~27/25, ~5/3

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: + mapping generators

2025-11-29T12:59:03Z

+ mapping generators

← Older revision		Revision as of 12:59, 29 November 2025
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	{{Mapping\|legend=1\| 9 1 1 \| 0 2 3 }}		{{Mapping\|legend=1\| 9 1 1 \| 0 2 3 }}
			: mapping generators: ~27/25, ~5/4

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: Complete data

2025-11-29T12:58:30Z

Complete data

← Older revision		Revision as of 12:58, 29 November 2025
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	=== Ennealimmal ===		=== Ennealimmal ===
	''For the 7-limit temperament, see [[Septiennealimmal clan#Ennealimmal]].''		: ''For the 7-limit temperament, see [[Septiennealimmal clan #Ennealimmal]].''

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

	[[Comma list]]: ~~7629394531250/7625597484987~~		[[Comma list]]: {{monzo\| 1 -27 18 }}

	{{Mapping\|legend=1\|9 1 1\|0 2 3}}		{{Mapping\|legend=1\| 9 1 1 \| 0 2 3 }}

	[[Optimal tuning]] ([[~~CTE~~]]): ~27/25 = ~~1\9~~, ~5/3 = 884.~~319~~		[[Optimal tuning]]s:
			* [[WE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3190{{c}}
			: [[error map]]: {{val\| -0.000 +0.016 -0.023 }}
			* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3191{{c}}
			: error map: {{val\| 0.000 +0.017 -0.023 }}

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\|~~612~~, ~~171~~, ~~441~~, 99, ~~270~~, 72, 27, 45, ~~711~~, ~~18bc~~, ~~9bcc~~, ~~243~~, ~~369~~, ~~126~~ }}		{{Optimal ET sequence\|legend=1\| 27, 45, 72, 99, 171, 441, 612, 1665, 2277, 2889, 3501, 6390, 16281, 22671, 29061c }}

			[[Badness]] (Sintel): 0.403

	== Etymology ==		== Etymology ==

Lériendil: updated link

2025-03-18T14:29:12Z

updated link

← Older revision		Revision as of 14:29, 18 March 2025
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	=== Ennealimmal ===		=== Ennealimmal ===
	''For the 7-limit temperament, see [[~~Ragismic microtemperaments~~#Ennealimmal]].''		''For the 7-limit temperament, see [[Septiennealimmal clan#Ennealimmal]].''

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

BudjarnLambeth at 00:48, 4 November 2024

2024-11-04T00:48:20Z

← Older revision		Revision as of 00:48, 4 November 2024
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	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
	[[Category:Commas named for their periods per equave]]		[[Category:Commas named for their periods per equave]]
	~~[[Category:Commas named for the intervals they stack]]~~

BudjarnLambeth at 00:21, 4 November 2024

2024-11-04T00:21:03Z

← Older revision		Revision as of 00:21, 4 November 2024
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	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
	[[Category:Commas named for their ~~regular temperament properties~~]]		[[Category:Commas named for their periods per equave]]
			[[Category:Commas named for the intervals they stack]]

BudjarnLambeth at 13:36, 3 November 2024

2024-11-03T13:36:11Z

← Older revision		Revision as of 13:36, 3 November 2024
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	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
			[[Category:Commas named for their regular temperament properties]]

Lériendil: /* Temperament */

2024-08-26T07:11:52Z

Temperament

← Older revision		Revision as of 07:11, 26 August 2024
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	== Temperament ==		== Temperament ==
	Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the 7-limit temperament is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.		Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.

	=== Ennealimmal ===		=== Ennealimmal ===