10th-octave temperaments - Revision history

FloraC: Update

2026-09-15T07:47:30Z

Update

← Older revision		Revision as of 07:47, 15 September 2026
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	[[10edo]] is notable for having close approximations of [[15/14]] to one step, the associated comma being the [[linus comma]] 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, the associated comma being the [[linus comma]] 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]], [[~~Quintile~~ family #Decile\|decile]], [[~~Metric~~ microtemperaments #Decimetra\|decimetra]], [[~~Stearnsmic clan~~ #Decistearn\|decistearn]], [[~~Vishnu~~ family #Decavish\|decavish]], and [[~~Kalismic~~ temperaments #Linus\|linus]] (the 15/14 relationship mentioned above).		Temperaments discussed elsewhere include: [[quintosec family #Decoid\|decoid]], [[quintile family #Decile\|decile]], [[metric microtemperaments #Decimetra\|decimetra]], [[trisedodge family #Decistearn\|decistearn]], [[vishnu family #Decavish\|decavish]], and [[kalismic temperaments #Linus\|linus]] (the 15/14 relationship mentioned above).

	== Neon ==		== Neon ==

FloraC: Do not name/catalog equal temps. Refer to them by 2.13-subgroup 10et, etc.

2026-08-02T08:31:38Z

Do not name/catalog equal temps. Refer to them by *2.13-subgroup 10et*, etc.

← Older revision		Revision as of 08:31, 2 August 2026
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	Temperaments discussed elsewhere include: [[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]] (the 15/14 relationship mentioned above).		Temperaments discussed elsewhere include: [[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]] (the 15/14 relationship mentioned above).

	~~== Valerismic (rank-1) ==~~
	~~Valerismic temperament tempers out the [[valerisma]], 137858491849/137438953472.~~

	~~Subgroup: 2.13~~

	~~Comma list: 2.13 {{monzo\|-37 10}}~~

	~~{{mapping\|legend=2\| 10 37 }}~~

	~~: mapping generators: ~2197/2048 = 1\10~~

	~~[[Support]]ing [[ET]]s: 10N, N = 1 to 113~~

	== Neon ==		== Neon ==

Eliora: /* Neon */ see also here is a tautology, a simple in-text link calling it neon comma suffices.

2026-08-01T20:07:20Z

Neon: see also here is a tautology, a simple in-text link calling it neon comma suffices.

← Older revision		Revision as of 20:07, 1 August 2026
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	== Neon ==		== Neon ==
	: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''		: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''
	~~{{See also\| Neon comma }}~~

	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 tempers out the [[neon comma]], {{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.

	Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]].		Extending neon with [[ragisma]], or equivalently with the linus comma, produces [[deca]].

Eliora: +valerisma is also of importance, 13/8 in 10edo. Adding in the same style as 37-11-comma is documented on 37th-octave temps.

2026-08-01T19:33:19Z

+valerisma is also of importance, 13/8 in 10edo. Adding in the same style as 37-11-comma is documented on 37th-octave temps.

← Older revision		Revision as of 19:33, 1 August 2026
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	{{Technical data page}}		{{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, the associated comma being the [[linus comma]] 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]], [[Quintile family #Decile\|decile]], [[Metric microtemperaments #Decimetra\|decimetra]], [[Stearnsmic clan #Decistearn\|decistearn]], [[Vishnu family #Decavish\|decavish]], and [[Kalismic temperaments #Linus\|linus]].		Temperaments discussed elsewhere include: [[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]] (the 15/14 relationship mentioned above).

			== Valerismic (rank-1) ==
			Valerismic temperament tempers out the [[valerisma]], 137858491849/137438953472.

			Subgroup: 2.13

			Comma list: 2.13 {{monzo\|-37 10}}

			{{mapping\|legend=2\| 10 37 }}

			: mapping generators: ~2197/2048 = 1\10

			[[Support]]ing [[ET]]s: 10N, N = 1 to 113

	== Neon ==		== Neon ==

Eliora: declutter miscellaneous 5-limit - neon is of importance to 10edo and fractional octave theory. see discord conversation

2026-08-01T19:06:45Z

declutter miscellaneous 5-limit - neon is of importance to 10edo and fractional octave theory. see discord conversation

@@ 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: [[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]].
+Temperaments discussed elsewhere include: [[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: - 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]]