Horwell temperaments - Revision history

FloraC: More sorting

2026-06-22T15:19:33Z

More sorting

← Older revision		Revision as of 15:19, 22 June 2026
Line 3:		Line 3:

	Temperaments discussed elsewhere are		Temperaments discussed elsewhere are
	* ''[[~~Semabila~~]]'' (+49/48) → [[~~Mabila~~ family #~~Septimal mabila~~\|~~Mabila~~ family]]		* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac\|Schismatic family]]
			* ''[[Keen]]'' (+875/864) → [[Diaschismic family #Keen\|Diaschismic family]]
			* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #Paramity\|Amity family]]
			* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata\|Kleismic family]]
			* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt\|Würschmidt family]]
	* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]		* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]
	* ''[[~~Maquiloid~~]]'' (+~~686~~/~~675~~) → [[~~Maquila~~ family #~~Maquiloid~~\|~~Maquila~~ family]]		* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]
	* ''[[~~Keen~~]]'' (+~~875~~/~~864~~) → [[~~Diaschismic~~ family #~~Keen~~\|~~Diaschismic~~ family]]		* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu family]]
	* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds\|Hemimean clan]]		* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds\|Hemimean clan]]
	* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell\|Semicomma family]]
	* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal\|Breedsmic temperaments]]
	* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac\|Schismatic family]]
	* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata\|Kleismic family]]
	* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor\|Hemimage temperaments]]		* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor\|Hemimage temperaments]]
	* ''[[~~Eris~~]]'' (+~~16875~~/~~16807~~) → [[~~Mirkwai clan #Eris\|Mirkwai clan]]~~		* ''[[Maquiloid]]'' (+686/675) → [[Maquila family #Maquiloid\|Maquila family]]
	* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu family]]
	* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #~~Paramity~~\|~~Amity~~ family]]
	* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom\|Vavoom family]]		* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom\|Vavoom family]]
			* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal\|Breedsmic temperaments]]
			* ''[[Eris]]'' (+16875/16807) → [[Canopic clan #Eris\|Canopic clan]]
	* ''[[Soviet ferris wheel]]'' (+{{monzo\| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel\|20th-octave temperaments]]		* ''[[Soviet ferris wheel]]'' (+{{monzo\| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel\|20th-octave temperaments]]

FloraC: Sort by badness

2026-06-22T14:59:07Z

Sort by badness

Show changes

FloraC: Expand

2026-06-22T14:57:34Z

Expand

← Older revision		Revision as of 14:57, 22 June 2026
Line 22:		Line 22:
	== Mutt ==		== Mutt ==
	{{Main\| Mutt }}		{{Main\| Mutt }}
			: ''For the 5-limit version, see [[Father–3 equivalence continuum #Mutt (5-limit)]].''

			Mutt tempers out the [[landscape comma]] in addition to the horwell comma, and may be described as the {{nowrap\| 84 & 87 }} temperament.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 93:		Line 96:

	== Emkay ==		== Emkay ==
			: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Emka]].''

	[[File:Scale Tree Graph For Emkay.png\|thumb\|Scale tree graph for emkay.]]		[[File:Scale Tree Graph For Emkay.png\|thumb\|Scale tree graph for emkay.]]

Line 146:		Line 151:
	== Kastro ==		== Kastro ==
	: ''For the 5-limit version, see [[Very high accuracy temperaments #Astro]].''		: ''For the 5-limit version, see [[Very high accuracy temperaments #Astro]].''

			Kastro may be described as the {{nowrap\| 109 & 118 }} temperament, named by [[Petr Pařízek]] in 2011 as a variation of ''astro''<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 199:		Line 206:
	Oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the [[dimcomp comma]] (390625/388962). In this temperament, the [[5/4]] major third is mapped to 9\28.		Oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the [[dimcomp comma]] (390625/388962). In this temperament, the [[5/4]] major third is mapped to 9\28.

	The name ''oquatonic'' was given by [[Petr Pařízek]] in 2011 as an abbreviation of the Italian [[wiktionary: ottantaquatro\|''ottantaquatro'' ("eighty-four")]]<ref~~>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'~~']</~~ref~~>.		The name ''oquatonic'' was given by [[Petr Pařízek]] in 2011 as an abbreviation of the Italian [[wiktionary: ottantaquatro\|''ottantaquatro'' ("eighty-four")]]<ref name="petr's long post"/>.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 249:		Line 256:

	== Bezique ==		== Bezique ==
	Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. ~~The~~ card game of bezique is played with two packs of 32 cards~~, hence the name~~.		Bezique splits the octave into 32 equal parts and reaches 3/2, 8/5 and 11/8 in just one generator with the 64-tone mos. A notable edo tuning overshadowed by [[224edo]] is [[320edo]]. Bezique was named by [[Eliora]] in 2023 for the fact that the card game of bezique is played with two packs of 32 cards.

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

FloraC: /* Mutt */ - 5-limit (addressed in father-3 equivalence continuum)

2026-06-22T14:33:20Z

Mutt: - 5-limit (addressed in father-3 equivalence continuum)

← Older revision		Revision as of 14:33, 22 June 2026
Line 23:		Line 23:
	{{Main\| Mutt }}		{{Main\| Mutt }}

	~~[[Subgroup]]: 2.3.5~~

	~~[[Comma list]]: {{monzo\| -44 -3 21 }}~~

	~~{{Mapping\|legend=1\| 3 -2 6 \| 0 7 1 }}~~
	~~: mapping generators: ~98304/78125, ~5/4~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~98304/78125 = 400.0227{{c}}, ~5/4 = 386.0017{{c}} (~393216/390625 = 14.0210{{c}})
	~~: [[error map]]: {{val\| +0.068 +0.012 -0.176 }}~~
	* [[CWE]]: ~98304/78125 = 400.0000{{c}}, ~5/4 = 385.9858{{c}} (~393216/390625 = 14.0142{{c}})
	~~: error map: {{val\| 0.000 -0.055 -0.328 }}~~

	~~{{Optimal ET sequence\|legend=1\| 84, 87, 171, 771, 942, 1113, 1284, 1455, 4194cc, 5649cc }}~~

	~~[[Badness]] (Sintel): 3.81~~

	~~=== 7-limit ===~~
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Switch to Sintel's badness, WE & CWE tunings (2/2)

2026-06-22T12:02:09Z

Switch to Sintel's badness, WE & CWE tunings (2/2)

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings (1/)

2026-06-22T09:56:30Z

Switch to Sintel's badness, WE & CWE tunings (1/)

Show changes

FloraC: Units, misc. cleanup, - redundant category

2026-06-22T09:20:26Z

Units, misc. cleanup, - redundant category

Show changes

Overthink: /* Mutt */ update

2026-02-15T01:49:36Z

Mutt: update

← Older revision		Revision as of 01:49, 15 February 2026
Line 21:		Line 21:

	== Mutt ==		== Mutt ==
	{{Main\| Mutt ~~temperament~~ }}		{{Main\| Mutt }}

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

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

2025-11-27T12:31:14Z

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

← Older revision		Revision as of 12:31, 27 November 2025
Line 269:		Line 269:

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Horwell temperaments\| ]] <!-- main article -->		[[Category:Horwell temperaments\| ]] <!-- main article -->
	[[Category:Horwell\| ]] <!-- key article -->		[[Category:Horwell\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Overthink: /* Fifthplus */ note on restriction

2025-11-26T01:13:55Z

Fifthplus: note on restriction

← Older revision		Revision as of 01:13, 26 November 2025
Line 77:		Line 77:

	== Fifthplus ==		== Fifthplus ==
	Fifthplus (22 & 171) tempers out the sesesix comma, {{monzo\| -74 13 23 }} in the 5-limit. The name "fifthplus" means using a sharp fifth interval (such as [[superpyth]] fifth) as a generator.		Fifthplus (22 & 171) tempers out the sesesix comma, {{monzo\| -74 13 23 }} in the 5-limit. The name "fifthplus" means using a sharp fifth interval (such as [[superpyth]] fifth) as a generator. It is a restriction of [[24576/24565#2.3.5.7.17 subgroup (prime archagall)\|prime archagall]].

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

← Older revision		Revision as of 15:19, 22 June 2026
Line 3:		Line 3:

	Temperaments discussed elsewhere are		Temperaments discussed elsewhere are
	* ''[[~~Semabila~~]]'' (+49/48) → [[~~Mabila~~ family #~~Septimal mabila~~\|~~Mabila~~ family]]		* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac\|Schismatic family]]
			* ''[[Keen]]'' (+875/864) → [[Diaschismic family #Keen\|Diaschismic family]]
			* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #Paramity\|Amity family]]
			* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata\|Kleismic family]]
			* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+126/125) → [[Würschmidt family #Worschmidt\|Würschmidt family]]
	* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]		* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]
	* ''[[~~Maquiloid~~]]'' (+~~686~~/~~675~~) → [[~~Maquila~~ family #~~Maquiloid~~\|~~Maquila~~ family]]		* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]
	* ''[[~~Keen~~]]'' (+~~875~~/~~864~~) → [[~~Diaschismic~~ family #~~Keen~~\|~~Diaschismic~~ family]]		* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu family]]
	* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds\|Hemimean clan]]		* [[Hemithirds]] (+1029/1024) → [[Hemimean clan #Hemithirds\|Hemimean clan]]
	* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell\|Semicomma family]]
	* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal\|Breedsmic temperaments]]
	* [[Pontiac]] (+4375/4374) → [[Schismatic family #Pontiac\|Schismatic family]]
	* ''[[Countercata]]'' (+5120/5103) → [[Kleismic family #Countercata\|Kleismic family]]
	* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor\|Hemimage temperaments]]		* ''[[Bisupermajor]]'' (+10976/10935) → [[Hemimage temperaments #Bisupermajor\|Hemimage temperaments]]
	* ''[[~~Eris~~]]'' (+~~16875~~/~~16807~~) → [[~~Mirkwai clan #Eris\|Mirkwai clan]]~~		* ''[[Maquiloid]]'' (+686/675) → [[Maquila family #Maquiloid\|Maquila family]]
	* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu family]]
	* ''[[Paramity]]'' (+1600000/1594323) → [[Amity family #~~Paramity~~\|~~Amity~~ family]]
	* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom\|Vavoom family]]		* ''[[Kaboom]]'' (+4802000/4782969) → [[Vavoom family #Kaboom\|Vavoom family]]
			* [[Tertiaseptal]] (+2401/2400) → [[Breedsmic temperaments #Tertiaseptal\|Breedsmic temperaments]]
			* ''[[Eris]]'' (+16875/16807) → [[Canopic clan #Eris\|Canopic clan]]
	* ''[[Soviet ferris wheel]]'' (+{{monzo\| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel\|20th-octave temperaments]]		* ''[[Soviet ferris wheel]]'' (+{{monzo\| -5 -9 -5 11 }}) → [[20th-octave temperaments #Soviet ferris wheel\|20th-octave temperaments]]