Quince clan - Revision history

FloraC: + link to slendi

2026-03-13T11:19:16Z

+ link to slendi

← Older revision		Revision as of 11:19, 13 March 2026
Line 28:		Line 28:
	* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]		* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]
	* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]		* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
			* ''[[Slendi]]'' (+4000/3969) → [[Octagar temperaments #Slendi\|Octagar temperaments]]
	* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]		* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]
	* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]		* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]

FloraC: Improve intro to each temp

2026-02-06T11:08:00Z

Improve intro to each temp

← Older revision		Revision as of 11:08, 6 February 2026
Line 3:		Line 3:

	== Mercy ==		== Mercy ==
	Mercy is the no-3 version ~~of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup~~ of [[~~31edo~~]]. Two generators make an [[8/7]]; five generators make a [[7/5]].		Mercy is the no-3 version of [[miracle]]. Two generators make [[~]][[8/7]], five generators make ~[[7/5]], and seven make ~[[8/5]]. The [[ploidacot]] for this temperament is omega-heptaseph.

	[[Subgroup]]: 2.5.7		[[Subgroup]]: 2.5.7
Line 36:		Line 36:

	== Countermiracle ==		== Countermiracle ==
	The ''countermiracle'' temperament ({{nowrap\| 31 & 145 }}~~) tempers out~~ the ~~trimyna, 50421~~/~~50000 and~~ the [[~~quince comma~~]]~~, 823543/819200~~.		The countermiracle temperament tempers out the porwell comma ([[6144/6125]]), the trimyna comma ([[50421/50000]]) and the quince comma ([[823543/819200]]). It can be described as the {{nowrap\| 31 & 145 }} temperament, and finds the [[3/2\|perfect fifth]] -25 generators away (normalized for 2.5.7) as opposed to miracle's +6 generators. It has the [[ploidacot]] signature of 22-sheared 25-cot.

	~~{{Todo\|inline=1\|expand\|comment=Explain relationship to~~ miracle~~. There's clearly ''some'' relationship~~, ~~since the extensions are named~~ the ~~same way~~, but the ~~nature of that relationship isn't obvious from looking at this page~~.}}		Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
Line 209:		Line 209:
	== Subgroup extensions ==		== Subgroup extensions ==
	=== Mercy (2.5.7.13) ===		=== Mercy (2.5.7.13) ===
			This extension may be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]].

	Subgroup: 2.5.7.13		Subgroup: 2.5.7.13

FloraC: Re-organize

2026-02-06T10:51:44Z

Re-organize

← Older revision		Revision as of 10:51, 6 February 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	The '''quince clan''' [[Tempering out\|tempers out]] the [[quince comma]], {{monzo\| -15 0 -2 7 }} ~~= 823543/819200. Quince temperaments include:~~		The '''quince clan''' [[Tempering out\|tempers out]] the [[quince comma]] ({{monzo\|legend=1\| -15 0 -2 7 }}, [[ratio]]: 823543/819200).
	* ''[[~~Casablanca~~]]~~'' (+126~~/~~125~~) ~~→ [[Starling temperaments #Casablanca\|Starling temperaments]]~~
	* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
	* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]
	* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]
	* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]
	* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum\|Garischismic clan]]

	== Mercy ==		== Mercy ==
Line 16:		Line 10:

	{{Mapping\|legend=2\| 1 3 3 \| 0 -7 -2 }}		{{Mapping\|legend=2\| 1 3 3 \| 0 -7 -2 }}
	~~: mapping generators: ~2, ~343/320~~

	{{Mapping\|legend=3\| 1 0 3 3 \| 0 0 -7 -2 }}		{{Mapping\|legend=3\| 1 0 3 3 \| 0 0 -7 -2 }}
			: mapping generators: ~2, ~343/320

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
Line 29:		Line 23:

	[[Badness]] (Sintel): 0.428		[[Badness]] (Sintel): 0.428

			=== Overview to extensions ===
			Temperaments discussed elsewhere are:
			* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]
			* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
			* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]
			* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]
			* ''[[Octowerck]]'' (+321489/320000 or 420175/419904) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]
			* [[Cotoneum]] (+10976/10935) → [[Garischismic clan #Cotoneum\|Garischismic clan]]

			Discussed below is countermiracle.

	== Countermiracle ==		== Countermiracle ==
Line 256:		Line 261:
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Quince clan\| ]] <!-- main article -->		[[Category:Quince clan\| ]] <!-- main article -->
	~~[[Category:Quince\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - POTE tunings

2026-02-06T10:49:08Z

- POTE tunings

← Older revision		Revision as of 10:49, 6 February 2026
Line 25:		Line 25:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/320 = 116.2576{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/320 = 116.2576{{c}}
	: error map: {{val\| 0.000 -0.117 -1.341 }}		: error map: {{val\| 0.000 -0.117 -1.341 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~343/320 = 116.291{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}		{{Optimal ET sequence\|legend=1\| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
Line 48:		Line 47:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~625/336 = 1084.0787{{c}} (~343/320 = 115.9213{{c}})		* [[CWE]]: ~2 = 1200.0000{{c}}, ~625/336 = 1084.0787{{c}} (~343/320 = 115.9213{{c}})
	: error map: {{val\| 0.000 +0.013 +2.237 -0.669 }}		: error map: {{val\| 0.000 +0.013 +2.237 -0.669 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~343/320 = 115.9169{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 31, 114, 145, 176 }}		{{Optimal ET sequence\|legend=1\| 31, 114, 145, 176 }}
Line 64:		Line 62:
	* WE: ~2 = 1199.7942{{c}}, ~144/77 = 1083.8983{{c}} (~77/72 = 115.8959{{c}})		* WE: ~2 = 1199.7942{{c}}, ~144/77 = 1083.8983{{c}} (~77/72 = 115.8959{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0798{{c}} (~77/72 = 115.9202{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0798{{c}} (~77/72 = 115.9202{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.9158{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 114e, 145, 176 }}		{{Optimal ET sequence\|legend=0\| 31, 114e, 145, 176 }}
Line 80:		Line 77:
	* WE: ~2 = 1199.4465{{c}}, ~144/77 = 1083.6196{{c}} (~77/72 = 115.8268{{c}})		* WE: ~2 = 1199.4465{{c}}, ~144/77 = 1083.6196{{c}} (~77/72 = 115.8268{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1148{{c}} (~77/72 = 115.8852{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1148{{c}} (~77/72 = 115.8852{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.8803{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 83e, 114e, 145, 321ceff }}		{{Optimal ET sequence\|legend=0\| 31, 83e, 114e, 145, 321ceff }}
Line 96:		Line 92:
	* WE: ~2 = 1199.4013{{c}}, ~144/77 = 1083.5835{{c}} (~77/72 = 115.8178{{c}})		* WE: ~2 = 1199.4013{{c}}, ~144/77 = 1083.5835{{c}} (~77/72 = 115.8178{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1219{{c}} (~77/72 = 115.8781{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1219{{c}} (~77/72 = 115.8781{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.8756{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 83e, 114e, 145 }}		{{Optimal ET sequence\|legend=0\| 31, 83e, 114e, 145 }}
Line 112:		Line 107:
	* WE: ~2 = 1199.9460{{c}}, ~144/77 = 1084.0178{{c}} (~77/72 = 115.9283{{c}})		* WE: ~2 = 1199.9460{{c}}, ~144/77 = 1084.0178{{c}} (~77/72 = 115.9283{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0663{{c}} (~77/72 = 115.9337{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0663{{c}} (~77/72 = 115.9337{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.9335{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 145f, 176, 207 }}		{{Optimal ET sequence\|legend=0\| 31, 145f, 176, 207 }}
Line 128:		Line 122:
	* WE: ~2 = 1199.9950{{c}}, ~144/77 = 1084.0564{{c}} (~77/72 = 115.9386{{c}})		* WE: ~2 = 1199.9950{{c}}, ~144/77 = 1084.0564{{c}} (~77/72 = 115.9386{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0609{{c}} (~77/72 = 115.9391{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0609{{c}} (~77/72 = 115.9391{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.9391{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 176, 207 }}		{{Optimal ET sequence\|legend=0\| 31, 176, 207 }}
Line 144:		Line 137:
	* WE: ~2 = 1199.6687{{c}}, ~144/77 = 1083.8108{{c}} (~77/72 = 115.8578{{c}})		* WE: ~2 = 1199.6687{{c}}, ~144/77 = 1083.8108{{c}} (~77/72 = 115.8578{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1065{{c}} (~77/72 = 115.8935{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1065{{c}} (~77/72 = 115.8935{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.8898{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31f, 145, 176, 321ce }}		{{Optimal ET sequence\|legend=0\| 31f, 145, 176, 321ce }}
Line 160:		Line 152:
	* WE: ~2 = 1199.6458{{c}}, ~144/77 = 1083.7968{{c}} (~77/72 = 115.8490{{c}})		* WE: ~2 = 1199.6458{{c}}, ~144/77 = 1083.7968{{c}} (~77/72 = 115.8490{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1132{{c}} (~77/72 = 115.8868{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1132{{c}} (~77/72 = 115.8868{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~77/72 = 115.8832{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31fg, 145, 321ce }}		{{Optimal ET sequence\|legend=0\| 31fg, 145, 321ce }}
Line 176:		Line 167:
	* WE: ~2 = 1200.1897{{c}}, ~275/147 = 1084.2521{{c}} (~343/320 = 115.9375{{c}})		* WE: ~2 = 1200.1897{{c}}, ~275/147 = 1084.2521{{c}} (~343/320 = 115.9375{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~275/147 = 1084.0850{{c}} (~343/320 = 115.9150{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~275/147 = 1084.0850{{c}} (~343/320 = 115.9150{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~343/320 = 115.9192{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 114, 145e }}		{{Optimal ET sequence\|legend=0\| 31, 114, 145e }}
Line 192:		Line 182:
	* WE: ~2 = 1199.7651{{c}}, ~220/117 = 1083.9253{{c}} (~117/110 = 115.8398{{c}})		* WE: ~2 = 1199.7651{{c}}, ~220/117 = 1083.9253{{c}} (~117/110 = 115.8398{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~220/117 = 1084.1357{{c}} (~117/110 = 115.8643{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~220/117 = 1084.1357{{c}} (~117/110 = 115.8643{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~273/256 = 115.8624{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 83, 114 }}		{{Optimal ET sequence\|legend=0\| 31, 83, 114 }}
Line 208:		Line 197:
	* WE: ~2 = 1199.6935{{c}}, ~170/91 = 1083.8704{{c}} (~91/85 = 115.8231{{c}})		* WE: ~2 = 1199.6935{{c}}, ~170/91 = 1083.8704{{c}} (~91/85 = 115.8231{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~170/91 = 1084.1464{{c}} (~91/85 = 115.8536{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~170/91 = 1084.1464{{c}} (~91/85 = 115.8536{{c}})
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~91/85 = 115.8527{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 31, 83, 114 }}		{{Optimal ET sequence\|legend=0\| 31, 83, 114 }}
Line 227:		Line 215:
	* WE: ~2 = 1199.2166{{c}}, ~14/13 = 116.0181{{c}}		* WE: ~2 = 1199.2166{{c}}, ~14/13 = 116.0181{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 116.2099{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 116.2099{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~14/13 = 116.094{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 21, 31 }}		{{Optimal ET sequence\|legend=0\| 10, 21, 31 }}
Line 245:		Line 232:
	* WE: ~2 = 1198.5476{{c}}, ~14/13 = 115.6294{{c}}		* WE: ~2 = 1198.5476{{c}}, ~14/13 = 115.6294{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.9132{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.9132{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~14/13 = 115.769{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 21, 31, 83fg }}		{{Optimal ET sequence\|legend=0\| 10, 21, 31, 83fg }}
Line 263:		Line 249:
	* WE: ~2 = 1198.4839{{c}}, ~14/13 = 115.5700{{c}}		* WE: ~2 = 1198.4839{{c}}, ~14/13 = 115.5700{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.7299{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 115.7299{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~14/13 = 115.716{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10h, 21, 31, 52f, 83fg }}		{{Optimal ET sequence\|legend=0\| 10h, 21, 31, 52f, 83fg }}

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-02-06T10:47:59Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Sorting, units & misc. cleanup

2026-01-31T18:40:53Z

Sorting, units & misc. cleanup

Show changes

Lériendil: added countermiracle, which is the alternative mapping of 3 for quince on the other side of 31edo

2026-01-31T07:19:20Z

added countermiracle, which is the alternative mapping of 3 for quince on the other side of 31edo

Show changes

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

2025-11-27T12:21:48Z

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

← Older revision		Revision as of 12:21, 27 November 2025
Line 74:		Line 74:

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Quince clan\| ]] <!-- main article -->		[[Category:Quince clan\| ]] <!-- main article -->
	[[Category:Quince\| ]] <!-- key article -->		[[Category:Quince\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

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

2025-06-24T00:39:03Z

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

← Older revision		Revision as of 00:39, 24 June 2025
Line 74:		Line 74:

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Quince clan\| ]] <!-- main article -->		[[Category:Quince clan\| ]] <!-- main article -->
	[[Category:Quince\| ]] <!-- key article -->		[[Category:Quince\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:43:54Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:43, 13 April 2025
Line 1:		Line 1:
	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''quince clan''' [[Tempering out\|tempers out]] the [[quince comma]], {{monzo\| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:		The '''quince clan''' [[Tempering out\|tempers out]] the [[quince comma]], {{monzo\| -15 0 -2 7 }} = 823543/819200. Quince temperaments include:
	* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]		* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]

← Older revision		Revision as of 11:19, 13 March 2026
Line 28:		Line 28:
	* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]		* ''[[Casablanca]]'' (+126/125) → [[Starling temperaments #Casablanca\|Starling temperaments]]
	* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]		* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
			* ''[[Slendi]]'' (+4000/3969) → [[Octagar temperaments #Slendi\|Octagar temperaments]]
	* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]		* ''[[Quincy]]'' (+4375/4374) → [[Ragismic microtemperaments #Quincy\|Ragismic microtemperaments]]
	* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]		* ''[[Birds]]'' (+3136/3125) → [[31st-octave temperaments #Birds\|31st-octave temperaments]]

Quince clan - Revision history

FloraC: + link to slendi

FloraC: Improve intro to each temp

FloraC: Re-organize

FloraC: - POTE tunings

FloraC: Switch to Sintel's badness, WE & CWE tunings

FloraC: Sorting, units & misc. cleanup

Lériendil: added countermiracle, which is the alternative mapping of 3 for quince on the other side of 31edo

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

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

FloraC: Text replacement - "{{Technical data page}}" to "{{Technical data page}}"

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"