Father family - Revision history

Xenllium: Fixed typo (CWE tuning of 11-limit 3&5, mother)

2026-03-08T02:20:39Z

Fixed typo (CWE tuning of 11-limit 3&5, mother)

← Older revision		Revision as of 02:20, 8 March 2026
Line 103:		Line 103:
	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}		* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~3/2 = ~~743~~.~~387~~{{c}}		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}

	{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}		{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}

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

2025-11-27T12:22:22Z

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

← Older revision		Revision as of 12:22, 27 November 2025
Line 142:		Line 142:

	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Father family\| ]] <!-- main article -->		[[Category:Father family\| ]] <!-- main article -->
	[[Category:Father\| ]] <!-- key article -->		[[Category:Father\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: - CTE & POTE tunings

2025-07-19T15:03:37Z

- CTE & POTE tunings

← Older revision		Revision as of 15:03, 19 July 2025
Line 18:		Line 18:
	* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.290{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.290{{c}}
	: error map: {{val\| 0.000 +40.335 +71.396 }}		: error map: {{val\| 0.000 +40.335 +71.396 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 737.469{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +35.514 +76.218 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 743.986{{c}}
	~~: error map: {{val\| 0.000 +42.031 +69.700 }} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 55:		Line 51:
	* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}
	: error map: {{val\| 0.000 +36.488 +75.244 +46.502 }}		: error map: {{val\| 0.000 +36.488 +75.244 +46.502 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 727.855{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +25.900 +85.831 +14.739 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.002{{c}}
	~~: error map: {{val\| 0.000 +40.047 +71.684 +57.180 }} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 80:		Line 72:
	* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}		* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 732.209{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~3/2 = 747.156{{c}} -->

	{{Optimal ET sequence\|legend=0\| 2de, 3de, 5, 8d }}		{{Optimal ET sequence\|legend=0\| 2de, 3de, 5, 8d }}
Line 99:		Line 89:
	* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}
	: error map: {{val\| 0.000 +20.911 +90.820 -14.559 }}		: error map: {{val\| 0.000 +20.911 +90.820 -14.559 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 727.290{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +25.335 +86.396 -23.406 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 721.569{{c}}
	~~: error map: {{val\| 0.000 +19.614 +92.118 -11.963 }} -->~~

	{{Optimal ET sequence\|legend=1\| 2, 3, 5 }}		{{Optimal ET sequence\|legend=1\| 2, 3, 5 }}
Line 118:		Line 104:
	* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}		* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~3/2 = 717.364{{c}} -->

	{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}		{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}
Line 137:		Line 121:
	* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}
	: error map: {{val\| 0.000 +53.201 +58.530 +55.392 }}		: error map: {{val\| 0.000 +53.201 +58.530 +55.392 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 761.765{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +59.810 +51.921 +22.348 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 753.113{{c}}
	~~: error map: {{val\| 0.000 +51.158 +60.574 +65.610 }} -->~~

	{{Optimal ET sequence\|legend=1\| 3, 5d, 8d, 27bbccdd }}		{{Optimal ET sequence\|legend=1\| 3, 5d, 8d, 27bbccdd }}
Line 156:		Line 136:
	* WE: ~2 = 1180.290{{c}}, ~3/2 = 739.054{{c}}		* WE: ~2 = 1180.290{{c}}, ~3/2 = 739.054{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~3/2 = 753.774{{c}}		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 753.774{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 761.872{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~3/2 = 751.396{{c}} -->

	{{Optimal ET sequence\|legend=0\| 3, 5de, 8d }}		{{Optimal ET sequence\|legend=0\| 3, 5de, 8d }}

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

2025-07-19T15:02:52Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

← Older revision		Revision as of 15:02, 19 July 2025
Line 14:		Line 14:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~3/2 = 737.469		* [[WE]]: ~2 = 1180.875{{c}}, ~3/2 = 732.129{{c}}
			: [[error map]]: {{val\| -19.125 +11.048 +24.181 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.290{{c}}
			: error map: {{val\| 0.000 +40.335 +71.396 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 737.469{{c}}
	: [[error map]]: {{val\| 0.000 +35.514 +76.218 }}		: [[error map]]: {{val\| 0.000 +35.514 +76.218 }}
	* [[POTE]]: ~2 = 1200.000, ~3/2 = 743.986		* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 743.986{{c}}
	: error map: {{val\| 0.000 +42.031 +69.700 }}		: error map: {{val\| 0.000 +42.031 +69.700 }} -->

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 25:		Line 29:
	{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}		{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}

	[[Badness]] (~~Smith~~): 0.~~014884~~		[[Badness]] (Sintel): 0.349

	=== Overview to extensions ===		=== Overview to extensions ===
Line 47:		Line 51:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~3/2 = 727.855		* [[WE]]: ~2 = 1180.634{{c}}, ~3/2 = 730.027{{c}}
			: [[error map]]: {{val\| -19.366 +8.706 +25.561 +1.890 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.443{{c}}
			: error map: {{val\| 0.000 +36.488 +75.244 +46.502 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 727.855{{c}}
	: [[error map]]: {{val\| 0.000 +25.900 +85.831 +14.739 }}		: [[error map]]: {{val\| 0.000 +25.900 +85.831 +14.739 }}
	* [[POTE]]: ~2 = 1200.000, ~3/2 = 742.002		* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 742.002{{c}}
	: error map: {{val\| 0.000 +40.047 +71.684 +57.180 }}		: error map: {{val\| 0.000 +40.047 +71.684 +57.180 }} -->

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 60:		Line 68:
	{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}		{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}

	[[Badness]] (~~Smith~~): 0.~~021312~~		[[Badness]] (Sintel): 0.539

	=== 11-limit ===		=== 11-limit ===
Line 70:		Line 78:

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~3/2 = 732.209		* WE: ~2 = 1180.894{{c}}, ~3/2 = 735.260{{c}}
	* POTE: ~2 = 1200.000, ~3/2 = 747.156		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 732.209{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~3/2 = 747.156{{c}} -->

	{{Optimal ET sequence\|legend=0\| 2de, 3de, 5, 8d }}		{{Optimal ET sequence\|legend=0\| 2de, 3de, 5, 8d }}

	Badness (~~Smith~~): 0.~~020589~~		Badness (Sintel): 0.681

	== Mother ==		== Mother ==
Line 85:		Line 95:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~3/2 = 727.290		* [[WE]]: ~2 = 1186.985{{c}}, ~3/2 = 713.743{{c}}
			: [[error map]]: {{val\| -13.015 -1.228 +60.898 -48.372 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 722.866{{c}}
			: error map: {{val\| 0.000 +20.911 +90.820 -14.559 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 727.290{{c}}
	: [[error map]]: {{val\| 0.000 +25.335 +86.396 -23.406 }}		: [[error map]]: {{val\| 0.000 +25.335 +86.396 -23.406 }}
	* [[POTE]]: ~2 = 1200.000, ~3/2 = 721.569		* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 721.569{{c}}
	: error map: {{val\| 0.000 +19.614 +92.118 -11.963 }}		: error map: {{val\| 0.000 +19.614 +92.118 -11.963 }} -->

	{{Optimal ET sequence\|legend=1\| 2, 3, 5 }}		{{Optimal ET sequence\|legend=1\| 2, 3, 5 }}

	[[Badness]] (~~Smith~~): 0.~~024152~~		[[Badness]] (Sintel): 0.611

	=== 11-limit ===		=== 11-limit ===
Line 101:		Line 115:
	Mapping: {{mapping\| 1 0 4 6 5 \| 0 1 -1 -2 -1 }}		Mapping: {{mapping\| 1 0 4 6 5 \| 0 1 -1 -2 -1 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~3/2 = ~~721~~.~~699~~		* WE: ~2 = 1192.016{{c}}, ~3/2 = 712.592{{c}}
	* POTE: ~2 = 1200.000, ~3/2 = 717.364		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 743.387{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 718.370{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~3/2 = 717.364{{c}} -->

	{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}		{{Optimal ET sequence\|legend=0\| 2, 3, 5 }}

	Badness (~~Smith~~): 0.~~021957~~		Badness (Sintel): 0.726

	== Pater ==		== Pater ==
Line 116:		Line 132:
	{{Mapping\|legend=1\| 1 0 4 11 \| 0 1 -1 -5 }}		{{Mapping\|legend=1\| 1 0 4 11 \| 0 1 -1 -5 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~3/2 = 761.765		* [[WE]]: ~2 = 1179.316{{c}}, ~3/2 = 740.132{{c}}
			: [[error map]]: {{val\| -20.684 +17.493 +11.503 +6.412 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 755.156{{c}}
			: error map: {{val\| 0.000 +53.201 +58.530 +55.392 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 761.765{{c}}
	: [[error map]]: {{val\| 0.000 +59.810 +51.921 +22.348 }}		: [[error map]]: {{val\| 0.000 +59.810 +51.921 +22.348 }}
	* [[POTE]]: ~2 = 1200.000, ~3/2 = 753.113		* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 753.113{{c}}
	: error map: {{val\| 0.000 +51.158 +60.574 +65.610 }}		: error map: {{val\| 0.000 +51.158 +60.574 +65.610 }} -->

	{{Optimal ET sequence\|legend=1\| 3, 5d, 8d, 27bbccdd }}		{{Optimal ET sequence\|legend=1\| 3, 5d, 8d, 27bbccdd }}

	[[Badness]] (~~Smith~~): 0.~~053001~~		[[Badness]] (Sintel): 1.34

	=== 11-limit ===		=== 11-limit ===
Line 133:		Line 153:
	Mapping: {{mapping\| 1 0 4 11 10 \| 0 1 -1 -5 -4 }}		Mapping: {{mapping\| 1 0 4 11 10 \| 0 1 -1 -5 -4 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~3/2 = 761.872		* WE: ~2 = 1180.290{{c}}, ~3/2 = 739.054{{c}}
	* POTE: ~2 = 1200.000, ~3/2 = 751.396		* CWE: ~2 = 1200.000{{c}}, ~3/2 = 753.774{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 761.872{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~3/2 = 751.396{{c}} -->

	{{Optimal ET sequence\|legend=0\| 3, 5de, 8d }}		{{Optimal ET sequence\|legend=0\| 3, 5de, 8d }}

	Badness (~~Smith~~): 0.~~035487~~		Badness (Sintel): 1.17

	[[Category:Temperament families]]		[[Category:Temperament families]]

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

2025-06-24T00:40:57Z

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

← Older revision		Revision as of 00:40, 24 June 2025
Line 142:		Line 142:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Father family\| ]] <!-- main article -->		[[Category:Father family\| ]] <!-- main article -->
	[[Category:Father\| ]] <!-- key article -->		[[Category:Father\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

2025-06-21T06:57:48Z

Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

← Older revision		Revision as of 06:57, 21 June 2025
Line 21:		Line 21:
	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[5-odd-limit]]: ~3/2 = {{monzo\| 1 1/2 -1/2 }}		* [[5-odd-limit]]: ~3/2 = {{monzo\| 1 1/2 -1/2 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5/3

	{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}		{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}
Line 54:		Line 54:
	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]]: ~3/2 = {{monzo\| 1/2 0 -1/4 1/4 }}		* [[7-odd-limit]]: ~3/2 = {{monzo\| 1/2 0 -1/4 1/4 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5
	* [[9-odd-limit]]: ~3/2 = {{monzo\| 1 -2 0 1 }} = 14/9		* [[9-odd-limit]]: ~3/2 = {{monzo\| 1 -2 0 1 }} = 14/9
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/7

	{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}		{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}

VectorGraphics at 04:40, 12 June 2025

2025-06-12T04:40:16Z

← Older revision		Revision as of 04:40, 12 June 2025
Line 45:		Line 45:

	{{Mapping\|legend=1\| 1 0 4 -2 \| 0 1 -1 3 }}		{{Mapping\|legend=1\| 1 0 4 -2 \| 0 1 -1 3 }}

	~~{{Multival\|legend=1\| 1 -1 3 -4 2 10 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
Line 85:		Line 83:

	{{Mapping\|legend=1\| 1 0 4 6 \| 0 1 -1 -2 }}		{{Mapping\|legend=1\| 1 0 4 6 \| 0 1 -1 -2 }}

	~~{{Multival\|legend=1\| 1 -1 -2 -4 -6 -2 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
Line 119:		Line 115:

	{{Mapping\|legend=1\| 1 0 4 11 \| 0 1 -1 -5 }}		{{Mapping\|legend=1\| 1 0 4 11 \| 0 1 -1 -5 }}

	~~{{Multival\|legend=1\| 1 -1 -5 -4 -11 -9 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

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

" to "{{Technical data page}}"

2025-04-13T13:41:11Z

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

← Older revision		Revision as of 13:41, 13 April 2025
Line 1:		Line 1:
	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''father family''' is a family of [[rank-2 temperament]]s which [[temper out]] the classic diatonic semitone, [[16/15]]. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].		The '''father family''' is a family of [[rank-2 temperament]]s which [[temper out]] the classic diatonic semitone, [[16/15]]. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].

BudjarnLambeth: {{Technical data page}}

+ edited first sentence of intro so the links had text in between instead of a whole blue sentence, to make it easy to tell where one link ends and one starts

2025-04-13T11:39:02Z

{{Technical data page}}<br><br> + edited first sentence of intro so the links had text in between instead of a whole blue sentence, to make it easy to tell where one link ends and one starts

← Older revision		Revision as of 11:39, 13 April 2025
Line 1:		Line 1:
	The '''father family''' of [[rank-2 ~~temperament\|rank-2]] [[~~temperament]]s [[~~tempering out\|tempers~~ out]] [[16/15]]~~, the classic diatonic semitone~~. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].		{{Technical data page}}<br><br>
			The '''father family''' is a family of [[rank-2 temperament]]s which [[temper out]] the classic diatonic semitone, [[16/15]]. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].

	== Father ==		== Father ==

FloraC: Cleanup

2025-01-17T16:59:51Z

Cleanup

← Older revision		Revision as of 16:59, 17 January 2025
Line 1:		Line 1:
	The '''father family''' of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempers out]] [[16/15]], the classic diatonic semitone. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].		The '''father family''' of [[rank-2 temperament\|rank-2]] [[temperament]]s [[tempering out\|tempers out]] [[16/15]], the classic diatonic semitone. This equates [[4/3]] with [[5/4]] and [[8/5]] with [[3/2]], so the generator is a "fourth-third" (or "fifth-sixth"), hence the name ''father''. In a sense, what father is all about is using [[semisixth]]s or [[subfourth]]s and pretending that these are 5-limit, and like any temperament which seems to involve a lot of "pretending", father is close to the edge of what can be sensibly called a temperament at all. In other words, it is an [[exotemperament]].

	== Father ==		== Father ==

← Older revision		Revision as of 06:57, 21 June 2025
Line 21:		Line 21:
	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[5-odd-limit]]: ~3/2 = {{monzo\| 1 1/2 -1/2 }}		* [[5-odd-limit]]: ~3/2 = {{monzo\| 1 1/2 -1/2 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5/3

	{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}		{{Optimal ET sequence\|legend=1\| 1, 2, 3, 5, 8, 13c, 21bcc }}
Line 54:		Line 54:
	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]]: ~3/2 = {{monzo\| 1/2 0 -1/4 1/4 }}		* [[7-odd-limit]]: ~3/2 = {{monzo\| 1/2 0 -1/4 1/4 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5
	* [[9-odd-limit]]: ~3/2 = {{monzo\| 1 -2 0 1 }} = 14/9		* [[9-odd-limit]]: ~3/2 = {{monzo\| 1 -2 0 1 }} = 14/9
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/7

	{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}		{{Optimal ET sequence\|legend=1\| 2d, 3d, 5, 8d, 13cd, 21bccdd }}