Horwell temperaments - Revision history

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
Line 90:		Line 90:
	Comma list: 441/440, 4375/4356, 16384/16335		Comma list: 441/440, 4375/4356, 16384/16335

	~~Mapping:~~ {{~~mapping~~\| 3 -2 6 20 21 \| 0 7 1 -12 -11 }}		{{Mapping\|legend=0\| 3 -2 6 20 21 \| 0 7 1 -12 -11 }}

	Optimal tunings:		Optimal tunings:
Line 105:		Line 105:
	Comma list: 364/363, 441/440, 625/624, 2200/2197		Comma list: 364/363, 441/440, 625/624, 2200/2197

	~~Mapping:~~ {{~~mapping~~\| 3 -2 6 20 21 14 \| 0 7 1 -12 -11 -3 }}		{{Mapping\|legend=0\| 3 -2 6 20 21 14 \| 0 7 1 -12 -11 -3 }}

	Optimal tunings:		Optimal tunings:
Line 144:		Line 144:
	Comma list: 1375/1372, 6250/6237, 65625/65536		Comma list: 1375/1372, 6250/6237, 65625/65536

	~~Mapping:~~ {{~~mapping~~\| 28 0 65 123 230 \| 0 1 0 -1 -3 }}		{{Mapping\|legend=0\| 28 0 65 123 230 \| 0 1 0 -1 -3 }}

	Optimal tunings:		Optimal tunings:
Line 159:		Line 159:
	Comma list: 625/624, 1375/1372, 2080/2079, 2200/2197		Comma list: 625/624, 1375/1372, 2080/2079, 2200/2197

	~~Mapping:~~ {{~~mapping~~\| 28 0 65 123 230 148 \| 0 1 0 -1 -3 -1 }}		{{Mapping\|legend=0\| 28 0 65 123 230 148 \| 0 1 0 -1 -3 -1 }}

	Optimal tunings:		Optimal tunings:
Line 198:		Line 198:
	Comma list: 3025/3024, 4000/3993, 65625/65536		Comma list: 3025/3024, 4000/3993, 65625/65536

	~~Mapping:~~ {{~~mapping~~\| 1 -13 -2 39 4 \| 0 27 8 -67 -1 }}		{{Mapping\|legend=0\| 1 -13 -2 39 4 \| 0 27 8 -67 -1 }}

	Optimal tunings:		Optimal tunings:
Line 213:		Line 213:
	Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197		Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197

	~~Mapping:~~ {{~~mapping~~\| 1 -13 -2 39 4 1 \| 0 27 8 -67 -1 5 }}		{{Mapping\|legend=0\| 1 -13 -2 39 4 1 \| 0 27 8 -67 -1 5 }}

	Optimal tunings:		Optimal tunings:
Line 250:		Line 250:
	Comma list: 385/384, 3388/3375, 12005/11979		Comma list: 385/384, 3388/3375, 12005/11979

	~~Mapping:~~ {{~~mapping~~\| 1 -26 13 -23 -9 \| 0 31 -12 29 14 }}		{{Mapping\|legend=0\| 1 -26 13 -23 -9 \| 0 31 -12 29 14 }}

	Optimal tunings:		Optimal tunings:
Line 265:		Line 265:
	Comma list: 169/168, 364/363, 385/384, 3388/3375		Comma list: 169/168, 364/363, 385/384, 3388/3375

	~~Mapping:~~ {{~~mapping~~\| 1 -26 13 -23 -9 -23 \| 0 31 -12 29 14 30 }}		{{Mapping\|legend=0\| 1 -26 13 -23 -9 -23 \| 0 31 -12 29 14 30 }}

	Optimal tunings:		Optimal tunings:
Line 300:		Line 300:
	Comma list: 9801/9800, 46656/46585, 65625/65536		Comma list: 9801/9800, 46656/46585, 65625/65536

	~~Mapping:~~ {{~~mapping~~\| 32 0 125 -113 60 \| 0 1 -1 4 1 }}		{{Mapping\|legend=0\| 32 0 125 -113 60 \| 0 1 -1 4 1 }}

	Optimal tunings:		Optimal tunings:
Line 315:		Line 315:
	Comma list: 729/728, 1575/1573, 4225/4224, 6656/6655		Comma list: 729/728, 1575/1573, 4225/4224, 6656/6655

	~~Mapping:~~ {{~~mapping~~\| 32 0 125 -113 60 17 \| 0 1 -1 4 1 2 }}		{{Mapping\|legend=0\| 32 0 125 -113 60 17 \| 0 1 -1 4 1 2 }}

	Optimal tunings:		Optimal tunings:

FloraC: + link to counterpara

2026-08-20T08:53:29Z

+ link to counterpara

← Older revision		Revision as of 08:53, 20 August 2026
Line 11:		Line 11:
	* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]		* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]
	* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]		* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]
			* ''[[Counterpara]]'' (+100442349/100000000) → [[Parakleismic family #Counterpara\|Parakleismic family]]
	* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu 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]]

FloraC: Recategorize

2026-08-15T07:55:39Z

Recategorize

← Older revision		Revision as of 07:55, 15 August 2026
Line 326:		Line 326:
	== References ==		== References ==

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

FloraC: /* Fifthplus */ move prime archagall here, descriptions adapted for this temp

2026-07-22T16:03:38Z

Fifthplus: move prime archagall here, descriptions adapted for this temp

← Older revision		Revision as of 16:03, 22 July 2026
Line 25:		Line 25:
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sesesix]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sesesix]].''

	Fifthplus tempers out the [[wizma]] in addition to the horwell comma, and may be described as the {{nowrap\| 22 & 171 }}. The name ''fifthplus'' means using a sharp fifth interval (such as a [[superpyth]] fifth) as a generator. ~~It is a restriction of [[24576/24565 #~~2.3.5.7.17 subgroup (prime archagall)~~\|prime archagall~~]].		Fifthplus tempers out the [[wizma]] in addition to the horwell comma, and may be described as the {{nowrap\| 22 & 171 }} temperament. The name ''fifthplus'' means using a sharp fifth interval (such as a [[superpyth]] fifth) as a generator.

			Fifthplus may be extended to the 2.3.5.7.17 subgroup, called prime archagall, derived from the fact that it is an extension of [[archagall]] to a prime subgroup. In either the 7-limit or the add-17 subgroup, [[171edo]] is exceptionally efficient and accurate, but in the latter case 171edo is the tuning where [[2401/2400]] (S49), [[2500/2499]] (S50), and [[1701/1700]] (S18/S20) all vanish, which is natural because this temperament tempers out [[1225/1224]] (S35, S49⋅S50) and [[5832/5831]] ((S18/S20)/S49) while not tempering out any of above individually.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 40:		Line 42:
	: error map: {{val\| 0.000 -0.126 -0.391 -0.268 }}		: error map: {{val\| 0.000 -0.126 -0.391 -0.268 }}

	{{Optimal ET sequence\|legend=1\| 22, 149, 171, 1903c, 2074c, …, 3613ccd }}		{{Optimal ET sequence\|legend=1\| 22, 105d, 127d, 149, 171, 1903c, 2074c, …, 3613ccd }}

	[[Badness]] (Sintel): 0.654		[[Badness]] (Sintel): 0.654

			=== Prime archagall ===
			Subgroup: 2.3.5.7.17

			Comma list: 1225/1224, 24576/24565, 57375/57344

			Subgroup-val mapping: {{mapping\| 1 -12 10 -22 -3 \| 0 23 -13 42 12 }}

			Optimal tunings:
			* WE: ~2 = 1200.0516{{c}}, ~128/85 = 708.8057{{cent}}
			* CWE: ~2 = 1200.0000{{c}}, ~128/85 = 708.7758{{cent}}

			{{Optimal ET sequence\|legend=0\| 22, 105d, 127d, 149, 171, 1219, 1390 }}

			Badness (Sintel): 0.421

	== Mutt ==		== Mutt ==

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

← Older revision		Revision as of 08:53, 20 August 2026
Line 11:		Line 11:
	* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]		* ''[[Escaped]]'' (+245/243) → [[Escapade family #Escaped\|Escapade family]]
	* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]		* ''[[Semabila]]'' (+49/48) → [[Mabila family #Septimal mabila\|Mabila family]]
			* ''[[Counterpara]]'' (+100442349/100000000) → [[Parakleismic family #Counterpara\|Parakleismic family]]
	* ''[[Narayana]]'' (+321489/320000) → [[Vishnu family #Narayana\|Vishnu 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]]

← 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]]