10th-octave temperaments - Revision history

FloraC: - duplicate data (moved to misc)

2026-07-05T07:48:38Z

- duplicate data (moved to misc)

@@ Line 3: / Line 3: @@
 [[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.
-Temperaments discussed elsewhere include: [[Quintosec family #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnuzmic family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]].
+Temperaments discussed elsewhere include: [[Miscellaneous 5-limit temperaments #Neon|neon]]/[[Ragismic microtemperaments #Deca|deca]], [[Quintosec family #Decoid|decoid]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnu family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]].
 {{Navbox fractional-octave}}
 [[Category:10edo]]

FloraC: Review, switch to Sintel's badness, WE & CWE tunings

2026-07-05T07:34:13Z

Review, switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 07:34, 5 July 2026
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	== Neon ==		== Neon ==
	Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].		Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. It was named by [[Eliora]] in 2023 after the 10th element. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}		{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}

	: Mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}		: Mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}

	[[Optimal tuning]] ([[~~CTE~~]]): ~3125/2916 = 1\10, {{monzo\| 10 29 -24 }} = 284.~~3888~~		[[Optimal tuning]]s:
			* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo\| 10 29 -24 }} = 284.3890{{c}}
			: [[error map]]: {{val\| -0.001 -0.011 +0.019 }}
			* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo\| 10 29 -24 }} = 284.3891{{c}}
			: error map: {{val\| 0.000 -0.010 +0.021 }}

	{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}		{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}

	[[Badness]]: 0.~~206596~~		[[Badness]] (Sintel): 4.85

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

	[[Category:10edo]]		[[Category:10edo]]

Eliora: /* Neon */ explain what exactly makes this notable

2025-08-04T18:13:25Z

Neon: explain what exactly makes this notable

← Older revision		Revision as of 18:13, 4 August 2025
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	== Neon ==		== Neon ==
	Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].		Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].

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

Fredg999: Update links and temperament names (according to their respective pages)

2025-08-03T04:12:46Z

Update links and temperament names (according to their respective pages)

← Older revision		Revision as of 04:12, 3 August 2025
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	[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.		[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.

	Temperaments discussed elsewhere include: [[~~Breedsmic temperaments~~ #Decoid\|decoid]], [[Ragismic microtemperaments #Deca\|deca]], [[~~Pental~~ family #~~Decal~~\|~~decal~~]], [[Metric microtemperaments #Decimetra\|decimetra]], [[Stearnsmic clan #Decistearn\|decistearn]], [[Vishnuzmic family #Decavish\|decavish]], and [[Kalismic temperaments #Linus\|linus]].		Temperaments discussed elsewhere include: [[Quintosec family #Decoid\|decoid]], [[Ragismic microtemperaments #Deca\|deca]], [[Quintile family #Decile\|decile]], [[Metric microtemperaments #Decimetra\|decimetra]], [[Stearnsmic clan #Decistearn\|decistearn]], [[Vishnuzmic family #Decavish\|decavish]], and [[Kalismic temperaments #Linus\|linus]].

	== Neon ==		== Neon ==

Xenllium at 13:34, 13 April 2025

2025-04-13T13:34:14Z

← Older revision		Revision as of 13:34, 13 April 2025
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			{{Technical data page}}
	{{Infobox fractional-octave\|10}}		{{Infobox fractional-octave\|10}}
	[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.		[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.
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	{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}		{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}

	: ~~mapping~~ generators: ~3125/2916, {{monzo\| 10 29 -24 }}		: Mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}

	[[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo\| 10 29 -24 }} = 284.3888		[[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo\| 10 29 -24 }} = 284.3888
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	{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}		{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}

	[[Badness]]: 0.~~207~~		[[Badness]]: 0.206596

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

	[[Category:10edo]]		[[Category:10edo]]

ArrowHead294 at 03:43, 14 February 2025

2025-02-14T03:43:19Z

← Older revision		Revision as of 03:43, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|10}}		{{Infobox fractional-octave\|10}}
	[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.		[[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.

BudjarnLambeth: navbox

2024-12-05T07:17:17Z

navbox

← Older revision		Revision as of 07:17, 5 December 2024
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	[[Badness]]: 0.207		[[Badness]]: 0.207

			{{Navbox fractional-octave}}

	[[Category:10edo]]		[[Category:10edo]]
	~~[[Category:Temperament collections]]~~

FloraC: Review

2024-01-06T16:26:21Z

Review

← Older revision		Revision as of 16:26, 6 January 2024
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	== Neon ==		== Neon ==
	Neon tempers out ~~the~~ {{~~Monzo~~\|21 60 -50}} ~~comma~~ in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].		Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].

	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	Comma list: {{~~Monzo~~\|21 60 -50}}		[[Comma list]]: {{monzo\| 21 60 -50 }}

	{{Mapping\|10 4 9\|0 5 6~~\|legend=1~~}}		{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}

	: mapping generators: ~3125/2916 ~~= 1\10~~, {{~~Monzo~~\|1=10 29 -24}} ~~= 284.389~~		: mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}

	Optimal tuning (CTE): ~{{~~Monzo~~\|1=10 29 -24}} = 284.~~389~~		[[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo\| 10 29 -24 }} = 284.3888

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\|80, 190, 270, 460, 730, ~~1000~~, ~~1190~~, ~~1270~~, ~~1460, 2460~~}}		{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}

			[[Badness]]: 0.207

	[[Category:10edo]]		[[Category:10edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

FloraC: -linus (addressed in kalismic temperaments)

2024-01-06T16:20:40Z

-linus (addressed in kalismic temperaments)

@@ Line 2: / Line 2: @@
 [[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10.
-Temperaments discussed elsewhere include: [[Breedsmic temperaments #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Pental family #Decal|decal]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], and [[Vishnuzmic family #Decavish|decavish]].
+Temperaments discussed elsewhere include: [[Breedsmic temperaments #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Pental family #Decal|decal]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnuzmic family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]].
 == Neon ==

Eliora: /* Neon */

2023-11-25T01:40:47Z

Neon

← Older revision		Revision as of 01:40, 25 November 2023
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	{{Mapping\|10 4 9\|0 5 6\|legend=1}}		{{Mapping\|10 4 9\|0 5 6\|legend=1}}

	: mapping generators: ~3125/2916 = 1\10, ~~70277506421640192/59604644775390625~~ = 284.389		: mapping generators: ~3125/2916 = 1\10, {{Monzo\|1=10 29 -24}} = 284.389

	Optimal tuning (CTE): ~~~70277506421640192/59604644775390625~~ = 284.389		Optimal tuning (CTE): ~{{Monzo\|1=10 29 -24}} = 284.389

	[[Support]]ing [[ET]]s: {{EDOs\|80, 190, 270, 460, 730, 1000, 1190, 1270, 1460, 2460}}		[[Support]]ing [[ET]]s: {{EDOs\|80, 190, 270, 460, 730, 1000, 1190, 1270, 1460, 2460}}