Trienstonic clan - Revision history

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]]

FloraC: Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

2025-11-27T12:28:32Z

Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

← Older revision		Revision as of 12:28, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Trienstonic clan\| ]] <!-- Main article -->		[[Category:Trienstonic clan\| ]] <!-- Main article -->
	[[Category:Trienstonic\| ]] <!-- Key article -->		[[Category:Trienstonic\| ]] <!-- Key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - supersharp (address in the misc. page)

2025-11-16T14:44:58Z

- supersharp (address in the misc. page)

@@ Line 49: / Line 49: @@
 == Uncle ==
-: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum#Uncle_(5-limit)|Syntonic–diatonic equivalence continuum]].''
+: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Uncle (5-limit)]].''
 Uncle tempers out 256/245, mapping the interval class of 5 to -6 generator steps, as a major 2-step in oneirotonic or a diminished fifth in diatonic.
@@ Line 74: / Line 74: @@
 == Octokaidecal ==
-The 5-limit [[restriction]] of octokaidecal is supersharp, which tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.
+: ''For the 5-limit versions, see [[Miscellaneous 5-limit temperaments #Supersharp]].''
 [[Subgroup]]: 2.3.5.7

Fitzgerald Lee: /* Uncle */Got link to direct temp

2025-10-17T12:04:48Z

Uncle: Got link to direct temp

← Older revision		Revision as of 12:04, 17 October 2025
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	== Uncle ==		== Uncle ==
	: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum]].''		: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum#Uncle_(5-limit)\|Syntonic–diatonic equivalence continuum]].''

	Uncle tempers out 256/245, mapping the interval class of 5 to -6 generator steps, as a major 2-step in oneirotonic or a diminished fifth in diatonic.		Uncle tempers out 256/245, mapping the interval class of 5 to -6 generator steps, as a major 2-step in oneirotonic or a diminished fifth in diatonic.

Overthink: fixed typo

2025-09-21T19:25:48Z

fixed typo

← Older revision		Revision as of 19:25, 21 September 2025
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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 ~~fifth~~ 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.

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

← 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 ==