Survey of efficient temperaments by subgroup - Revision history

BudjarnLambeth: /* Other subgroups */ typo

2026-04-11T10:03:46Z

Other subgroups: typo

← Older revision		Revision as of 10:03, 11 April 2026
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	Subgroups ''without'' a "3" ''don't have'' multiple of 3 intervals (eg the 3/1 perfect twelfth, the 3/2 perfect fifth, the 5/3 major sixth).		Subgroups ''without'' a "3" ''don't have'' multiple of 3 intervals (eg the 3/1 perfect twelfth, the 3/2 perfect fifth, the 5/3 major sixth).

	Subgroups ''without'' a "5" ''don't have'' multiple of 3 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).		Subgroups ''without'' a "5" ''don't have'' multiple of 5 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).

	Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.		Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.

FloraC: Update link

2026-04-05T12:21:59Z

Update link

← Older revision		Revision as of 12:21, 5 April 2026
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	! 7-limit <br>(2.3.5.7)		! 7-limit <br>(2.3.5.7)
	\| [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]]		\| [[ennealimmal]], [[tertiaseptal]], [[hemififths]], [[quadritikleismic]], [[grendel]], [[unidec]]
	\| [[hendecatonic]]		\| [[hendecatonic (temperament)\|hendecatonic]]
	\| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]		\| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]
	\| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]		\| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]

FloraC: /* Table of temperaments (5 to 45 notes per equave) */ "meantoid"

2025-11-16T15:23:29Z

Table of temperaments (5 to 45 notes per equave): "meantoid"

← Older revision		Revision as of 15:23, 16 November 2025
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	\| [[lemba]]+, [[hedgehog]]+		\| [[lemba]]+, [[hedgehog]]+
	\| [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+		\| [[nusecond]]+, [[crepuscular]], [[winston]]+, [[pajara]], [[negroni]]+, [[sensis]]+, [[ringo]]+, [[pajarous]], [[augene]]+
	\| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[~~meantoid~~]], [[injera]], [[meanenneadecal]]		\| [[miraculous]], [[lupercalia]]+, [[mohajira]], [[superpyth]]+, [[fokkertone]]+, [[injera]], [[meanenneadecal]]
	\|-		\|-
	! 19-limit <br>(2.3.5.7.11.13.17.19)		! 19-limit <br>(2.3.5.7.11.13.17.19)
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	\| [[niner]]++		\| [[niner]]++
	\| [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++		\| [[wilsec]], [[winston]]++, [[augene]]++, [[sensis]]++
	\| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[~~meantoid~~]]		\| [[roman]]++, [[mohajira]], [[lupercalia]]++, [[superpyth]]++, [[negroni]]++, [[meanenneadecal]], [[ringo]]++, [[injera]], [[fokkertone]]++
	\|-		\|-
	! Higher prime limits		! Higher prime limits

BudjarnLambeth: /* Other subgroups */

2025-11-03T07:22:22Z

Other subgroups

← Older revision		Revision as of 07:22, 3 November 2025
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	=== Other subgroups ===		=== Other subgroups ===
	Subgroups ''without'' a "2" don't have ~~octaves~~ (~~similar to~~ the ~~[[Bohlen-Pierce scale]]~~).		Subgroups ''without'' a "2" ''don't have'' multiple of 2 intervals (eg the 2/1 octave, the 3/2 perfect fifth, the 5/4 major third).

	Subgroups ''without'' a "3" don't have perfect ~~fifths or~~ perfect ~~fourths~~.		Subgroups ''without'' a "3" ''don't have'' multiple of 3 intervals (eg the 3/1 perfect twelfth, the 3/2 perfect fifth, the 5/3 major sixth).

	Subgroups ''without'' a "5" don't have ~~conventional~~ major ~~and~~ minor ~~thirds or sixths~~.		Subgroups ''without'' a "5" ''don't have'' multiple of 3 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).

	Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.		Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.

BudjarnLambeth: /* Other subgroups */ Add explanation.

2025-11-03T07:18:38Z

Other subgroups: Add explanation.

← Older revision		Revision as of 07:18, 3 November 2025
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	=== Other subgroups ===		=== Other subgroups ===
			Subgroups ''without'' a "2" don't have octaves (similar to the [[Bohlen-Pierce scale]]).

			Subgroups ''without'' a "3" don't have perfect fifths or perfect fourths.

			Subgroups ''without'' a "5" don't have conventional major and minor thirds or sixths.

			Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-

BudjarnLambeth: /* Other subgroups */

2025-11-03T07:09:44Z

Other subgroups

← Older revision		Revision as of 07:09, 3 November 2025
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	\|-		\|-
	! JI subgroup		! JI subgroup
	! ~10 notes per equave~~<ref group="note">Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref>~~		! ~10 notes per equave
	! ~20 notes		! ~20 notes
	! ~30 notes		! ~30 notes

FloraC: /* Most linked-to rank-2 temperaments */ helmholtz was missing

2025-11-01T12:13:25Z

Most linked-to rank-2 temperaments: helmholtz was missing

← Older revision		Revision as of 12:13, 1 November 2025
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	== Most linked-to rank-2 temperaments ==		== Most linked-to rank-2 temperaments ==
	These are the top ~~104~~ rank-2 temperament pages with the most incoming links on the wiki as of 23 Oct 2025, about one year after this section was first written.		These are the top 105 rank-2 temperament pages with the most incoming links on the wiki as of 23 Oct 2025, about one year after this section was first written.

	# '''[[Meantone]] (479)'''		# '''[[Meantone]] (479)'''
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	# [[Archy]] (50)		# [[Archy]] (50)
	# [[Augmented (temperament)\|Augmented]] (50)		# [[Augmented (temperament)\|Augmented]] (50)
			# [[Helmholtz (temperament)\|Helmholtz]] (48)
	# [[Superkleismic]] (46)		# [[Superkleismic]] (46)
	# [[Augene]] (46)		# [[Augene]] (46)
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	# [[Escapade]] (36)		# [[Escapade]] (36)
	# [[Passion]] (35)		# [[Passion]] (35)
	# [[Schismic]] (35)		# [[Schismic]] (35) (already listed as ''helmholtz'')
	# [[Nautilus]] (34)		# [[Nautilus]] (34)
	# [[Bleu]] (34)		# [[Bleu]] (34)
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	# [[Wizard]] (33)		# [[Wizard]] (33)
	# [[Orson]] (32)		# [[Orson]] (32)
	# [[Schismatic]] (32) (already listed as ''~~schismic~~'')		# [[Schismatic]] (32) (already listed as ''helmholtz'')
	# [[Unidec]] (31)		# [[Unidec]] (31)
	# [[Muggles]] (30)		# [[Muggles]] (30)

FloraC: Linking

2025-10-27T13:14:57Z

Linking

← Older revision		Revision as of 13:14, 27 October 2025
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	\| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]		\| [[sesquiquartififths]], [[quinmite]], [[parakleismic]]
	\| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]		\| [[neptune]], [[gamera]], [[nessafof]], [[octoid]], [[septiquarter]]
	\| [[supermajor]], [[enneadecal]], [[term]]		\| [[supermajor (temperament)\|supermajor]], [[enneadecal]], [[term]]
	\|-		\|-
	! 11-limit <br>(2.3.5.7.11)		! 11-limit <br>(2.3.5.7.11)

BudjarnLambeth: /* Table of temperaments (5 to 45 notes per equave) */ Break into 2 tables to try to address others' complaints about messiness

2025-10-26T23:15:10Z

Table of temperaments (5 to 45 notes per equave): Break into 2 tables to try to address others' complaints about messiness

← Older revision		Revision as of 23:15, 26 October 2025
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	== Table of temperaments (5 to 45 notes per equave) ==		== Table of temperaments (5 to 45 notes per equave) ==
	The temperaments within each cell should be sorted by accuracy, with the lowest [[damage]] (highest accuracy) temperament listed first.		The temperaments within each cell should be sorted by accuracy, with the lowest [[damage]] (highest accuracy) temperament listed first.

	<!--		<!--
	If you see any temperaments listed in the wrong order, or see any temperaments in the wrong "approx. number of notes needed" category, please move them to the correct position.		If you see any temperaments listed in the wrong order, or see any temperaments in the wrong "approx. number of notes needed" category, please move them to the correct position.
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	-->		-->

			=== Full prime limits ===
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|-		\|-
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	\|		\|
	\| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+		\| [[lupercalia]]+++, [[nautilus]]+++, [[negroni]]+++, [[injera]]+
			\|}

			=== Other subgroups ===
			{\| class="wikitable center-all"
			\|-
			! JI subgroup
			! ~10 notes per equave<ref group="note">Number of notes per equave was estimated by multiplying the temperament’s [[graham complexity]] by 2.</ref>
			! ~20 notes
			! ~30 notes
			! ~40 notes
	\|-		\|-
	! 2.3.5.7.other ''n''		! 2.3.5.7.other ''n''

FloraC: /* Table of temperaments (5 to 45 notes per equave) */ correct misty's complexity

2025-10-26T10:34:55Z

Table of temperaments (5 to 45 notes per equave): correct misty's complexity

← Older revision		Revision as of 10:34, 26 October 2025
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	\|-		\|-
	! 5-limit <br>(2.3.5)		! 5-limit <br>(2.3.5)
	\| [[hanson~~]], [[misty~~]], [[magic]], [[meantone]], [[negri]], [[augmented (temperament)\|augmented]], [[porcupine]], [[diminished (temperament)\|diminished]], [[whitewood]], [[blackwood]], [[mavila]]		\| [[hanson]], [[magic]], [[meantone]], [[negri]], [[augmented (temperament)\|augmented]], [[porcupine]], [[diminished (temperament)\|diminished]], [[whitewood]], [[blackwood]], [[mavila]]
	\| [[helmholtz (temperament)\|helmholtz]], [[orson]], [[würschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]]		\| [[helmholtz (temperament)\|helmholtz]], [[orson]], [[würschmidt]], [[sensipent]], [[compton]], [[valentine]], [[diaschismic]], [[tetracot]], [[passion]], [[superpyth]], [[ripple]]
	\| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[gravity]], [[rodan]]		\| [[kwazy]], [[luna]], [[vishnu]], [[parakleismic]], [[escapade]], [[amity]], [[misty]], [[gravity]], [[rodan]]
	\| [[enneadecal]], [[gammic]], [[vulture]]		\| [[enneadecal]], [[gammic]], [[vulture]]
	\|-		\|-