Trienstonic clan - Revision history

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:39:05Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:39, 30 September 2026
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	[[Comma list]]: 28/27		[[Comma list]]: 28/27

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

	{{Mapping\|legend=5\| 1 0 0 -2 \| 0 1 0 3 }}		{{Mapping\|legend=5\| 1 0 0 -2 \| 0 1 0 3 }}

FloraC: Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

2026-09-30T17:34:04Z

Text replacement - "{{Mapping|legend=3| " to "{{Mapping|legend=5| "

← Older revision		Revision as of 17:34, 30 September 2026
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	{{Mapping\|legend=2\| 1 0 -2 \| 0 1 3 }}		{{Mapping\|legend=2\| 1 0 -2 \| 0 1 3 }}

	{{Mapping\|legend=3\| 1 0 0 -2 \| 0 1 0 3 }}		{{Mapping\|legend=5\| 1 0 0 -2 \| 0 1 0 3 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:33:23Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:33, 24 September 2026
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	Comma list: 28/27, 50/49, 55/54		Comma list: 28/27, 50/49, 55/54

	~~Mapping:~~ {{~~mapping~~\| 2 0 -5 -4 7 \| 0 1 3 3 0 }}		{{Mapping\|legend=0\| 2 0 -5 -4 7 \| 0 1 3 3 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 28/27, 77/75, 245/242		Comma list: 28/27, 77/75, 245/242

	~~Mapping:~~ {{~~mapping~~\| 1 0 -3 -2 -4 \| 0 3 10 9 14 }}		{{Mapping\|legend=0\| 1 0 -3 -2 -4 \| 0 3 10 9 14 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 28/27, 40/39, 66/65, 147/143		Comma list: 28/27, 40/39, 66/65, 147/143

	~~Mapping:~~ {{~~mapping~~\| 1 0 -3 -2 -4 0 \| 0 3 10 9 14 7 }}		{{Mapping\|legend=0\| 1 0 -3 -2 -4 0 \| 0 3 10 9 14 7 }}

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-08-15T07:43:13Z

Recategorize

← Older revision		Revision as of 07:43, 15 August 2026
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	Badness (Sintel): 1.35		Badness (Sintel): 1.35

			[[Category:Trienstonic clan\| ]] <!-- main article -->
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:~~Trienstonic clan\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

FloraC: Update

2026-06-28T11:22:07Z

Update

← Older revision		Revision as of 11:22, 28 June 2026
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	* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]		* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]
	* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]		* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]
	* [[Blackwood]] (+49/48) → [[~~Limmic temperaments~~ #Blackwood\|~~Limmic temperaments~~]]		* [[Blackwood]] (+49/48) → [[Blackwood family #Blackwood\|Blackwood family]]
	* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]		* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]		* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]

Overthink: /* Octokaidecal */ anti-pajara

2026-05-16T01:45:21Z

Octokaidecal: anti-pajara

← Older revision		Revision as of 01:45, 16 May 2026
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	== Octokaidecal ==		== Octokaidecal ==
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].''
			Octokaidecal extends trienstonian by tempering out [[50/49]], thus splitting the octave in half. It generates the [[8L 2s]] (taric) mos scale, with tunings on the other side of [[10edo]] as [[2L 8s]] (jaric). Compared to [[pajara]], decatonic thirds ([[8/7]] and [[7/6]]) and fourths ([[6/5]] and [[5/4]]) have their mappings reversed, meaning octokaidecal can be considered what is to pajara as [[mavila]] is to [[meantone]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Xenllium at 04:55, 14 February 2026

2026-02-14T04:55:38Z

← Older revision		Revision as of 04:55, 14 February 2026
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	Members of the clan discussed elsewhere are:		Members of the clan discussed elsewhere are:
	* ''[[~~Wallaby~~]]'' (+35/32) → [[Very low accuracy temperaments #~~Wallaby~~\|Very low accuracy temperaments]]
			* [[Antonian]] (+10/9 or +15/14) → [[Very low accuracy temperaments #Septimal antonian\|Very low accuracy temperaments]]
			* [[Father]] (+16/15) → [[Father family #Septimal father\|Father family]]
			* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone\|Meantone family]]
	* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie\|Dicot family]]		* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie\|Dicot family]]
	* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]		* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]
			* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]
			* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]
			* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]		* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]
	* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]

	~~Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.~~

	~~== Father ==~~
	~~{{Main\| Father }}~~

	~~Father tempers out [[16/15]] and uses the generator for [[~]][[8/5]]. See [[Father family #Septimal father]].~~

	~~== Sharptone ==~~		Considered below are uncle, octokaidecal, and parakangaroo.
	~~Sharptone tempers out [[21/20]]~~ and ~~maps the interval class of 5 to four generator steps as in [[meantone]]. See [[Meantone family #Sharptone]]~~.

	== Uncle ==		== Uncle ==

Overthink: /* Trienstonian */ explain analogy further

2026-02-09T07:08:45Z

Trienstonian: explain analogy further

← Older revision		Revision as of 07:08, 9 February 2026
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	== Trienstonian ==		== Trienstonian ==
	This low-accuracy temperament is generated by a fifth, tuned very sharp such that a stack of three reach a ~7/4. [[5edo]] is the tuning that conflates 7/6~9/8 (+2 generator steps) with ~8/7 (-3 generator steps). If you do not care about the intervals of 9 in this temperament, you can tune the fifth sharper for the [[7-odd-limit]], leading to an [[5L 3s\|oneirotonic]] scale or otherwise a [[5L 2s\|diatonic]] scale with negative small steps. A tuning that prioritizes the 7-odd-limit also tunes the fifth sharper than the [[pentic]] range, instead generating an [[antipentic]] scale. Trienstonian can be considered the [[2.3.7 subgroup\|2.3.7]] analog of [[mavila]] temperament, with extremely sharp fifths rather than extremely flat ones.		This low-accuracy temperament is generated by a fifth, tuned very sharp such that a stack of three reach a ~7/4. [[5edo]] is the tuning that conflates 7/6~9/8 (+2 generator steps) with ~8/7 (-3 generator steps). If you do not care about the intervals of 9 in this temperament, you can tune the fifth sharper for the [[7-odd-limit]], leading to an [[5L 3s\|oneirotonic]] scale or otherwise a [[5L 2s\|diatonic]] scale with negative small steps. A tuning that prioritizes the 7-odd-limit also tunes the fifth sharper than the [[pentic]] range, instead generating an [[antipentic]] scale. Trienstonian can be considered the [[2.3.7 subgroup\|2.3.7]] analog of [[mavila]] temperament, with extremely sharp fifths rather than extremely flat ones, being on the other side of 3\5 from [[archy]] fifths, just like how mavila fifths are on the other side of 4\7 from [[meantone]] fifths.

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7
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	* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]		* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]

	Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.		Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.

	== Father ==		== Father ==

FloraC at 11:44, 30 November 2025

2025-11-30T11:44:39Z

← Older revision		Revision as of 11:44, 30 November 2025
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	{{Mapping\|legend=3\| 1 0 0 -2 \| 0 1 0 3 }}		{{Mapping\|legend=3\| 1 0 0 -2 \| 0 1 0 3 }}

	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	{{Main\| Father }}		{{Main\| Father }}

	See [[Father family #Septimal father]].		Father tempers out [[16/15]] and uses the generator for [[~]][[8/5]]. See [[Father family #Septimal father]].

	== Sharptone ==		== Sharptone ==
	See [[Meantone family #Sharptone]].		Sharptone tempers out [[21/20]] and maps the interval class of 5 to four generator steps as in [[meantone]]. See [[Meantone family #Sharptone]].

	== Uncle ==		== Uncle ==

FloraC: Consistency and - redundant category

2025-11-29T07:13:05Z

Consistency and - redundant category

← Older revision		Revision as of 07:13, 29 November 2025
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	== Octokaidecal ==		== Octokaidecal ==
	: ''For the 5-limit ~~versions~~, see [[Miscellaneous 5-limit temperaments #Supersharp]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Supersharp]].''

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Parakangaroo ==		== Parakangaroo ==
	: ''For the 5-limit version ~~of this temperament~~, see [[Miscellaneous 5-limit temperaments #Kangaroo]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Kangaroo]].''

	This temperament used to be known as ''kangaroo'', but was decanonicalized in 2024 in favor of a more accurate extension. It splits the perfect twelfth into three generators of ~10/7; its ploidacot is alpha-tricot. [[15edo]] shows us an obvious tuning.		This temperament used to be known as ''kangaroo'', but was decanonicalized in 2024 in favor of a more accurate extension. It splits the perfect twelfth into three generators of ~10/7; its ploidacot is alpha-tricot. [[15edo]] shows us an obvious tuning.
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Trienstonic clan\| ]] <!-- ~~Main article -->~~		[[Category:Trienstonic clan\| ]] <!-- main article -->
	~~[[Category:Trienstonic\| ]] <!-- Key~~ article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

← Older revision		Revision as of 11:22, 28 June 2026
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	* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]		* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]
	* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]		* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]
	* [[Blackwood]] (+49/48) → [[~~Limmic temperaments~~ #Blackwood\|~~Limmic temperaments~~]]		* [[Blackwood]] (+49/48) → [[Blackwood family #Blackwood\|Blackwood family]]
	* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]		* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]		* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]

← Older revision		Revision as of 04:55, 14 February 2026
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	Members of the clan discussed elsewhere are:		Members of the clan discussed elsewhere are:
	* ''[[~~Wallaby~~]]'' (+35/32) → [[Very low accuracy temperaments #~~Wallaby~~\|Very low accuracy temperaments]]
			* [[Antonian]] (+10/9 or +15/14) → [[Very low accuracy temperaments #Septimal antonian\|Very low accuracy temperaments]]
			* [[Father]] (+16/15) → [[Father family #Septimal father\|Father family]]
			* ''[[Sharptone]]'' (+21/20) → [[Meantone family #Sharptone\|Meantone family]]
	* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie\|Dicot family]]		* ''[[Sharpie]]'' (+25/24) → [[Dicot family #Sharpie\|Dicot family]]
	* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]		* ''[[Mite]]'' (+27/25) → [[Bug family #Mite\|Bug family]]
			* ''[[Wallaby]]'' (+35/32) → [[Very low accuracy temperaments #Wallaby\|Very low accuracy temperaments]]
			* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]
			* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]		* ''[[Inflated]]'' (+128/125) → [[Augmented family #Inflated\|Augmented family]]
	* ''[[Opossum]]'' (+126/125) → [[Porcupine family #Opossum\|Porcupine family]]
	* [[Blackwood]] (+49/48) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]

	~~Considered below are father, sharptone, uncle, octokaidecal, and parakangaroo.~~

	~~== Father ==~~
	~~{{Main\| Father }}~~

	~~Father tempers out [[16/15]] and uses the generator for [[~]][[8/5]]. See [[Father family #Septimal father]].~~

	~~== Sharptone ==~~		Considered below are uncle, octokaidecal, and parakangaroo.
	~~Sharptone tempers out [[21/20]]~~ and ~~maps the interval class of 5 to four generator steps as in [[meantone]]. See [[Meantone family #Sharptone]]~~.

	== Uncle ==		== Uncle ==