Bug family - Revision history

FloraC: Distinguish note

2026-03-04T10:11:40Z

Distinguish note

← Older revision		Revision as of 10:11, 4 March 2026
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	=== Pento ===		=== Pento ===
			{{Distinguish\| Penta }}

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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

2025-11-27T12:28:43Z

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

← Older revision		Revision as of 12:28, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Bug family\| ]] <!-- Main article -->		[[Category:Bug family\| ]] <!-- Main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Update

2025-11-19T11:07:13Z

Update

← Older revision		Revision as of 11:07, 19 November 2025
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	== Bug ==		== Bug ==
			{{Main\| Bug and beep }}
	The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the {{nowrap\| 4 & 5 }} temperament, and its [[ploidacot]] is alpha-dicot. [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it. Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.		The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the {{nowrap\| 4 & 5 }} temperament, and its [[ploidacot]] is alpha-dicot. [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it. Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.

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	== Beep ==		== Beep ==
	{{Main\| ~~Beep~~ }}		{{Main\| Bug and beep }}
	{{See also\| Semaphoresmic clan }}		{{See also\| Semaphoresmic clan }}

FloraC at 13:42, 2 November 2025

2025-11-02T13:42:44Z

← Older revision		Revision as of 13:42, 2 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Bug family]] <!-- Main article -->		[[Category:Bug family\| ]] <!-- Main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Rework for an overview to extensions

2025-07-20T09:30:18Z

Rework for an overview to extensions

← Older revision		Revision as of 09:30, 20 July 2025
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	{{Technical data page}}		{{Technical data page}}
	The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[9edo]]. The monzo for 27/25 is {{monzo\| 0 3 -2 }}. The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the 4 & 5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it.		The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[9edo]]. The monzo for 27/25 is {{monzo\| 0 3 -2 }}.

	Bug has a 7-limit extension, [[#Beep\|beep]], via the normal comma list {27/25, 36/35} which can also be obtained by adding [[21/20]]. Beep has the curious property that if we know both the beep tempering and the [[Ragismic microtemperaments #Ennealimmal\|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.

	~~Bug divides [[3/1]] in half so it may be viewed as a less accurate version of [[semaphore and godzilla\|semaphore]] (with beep combining the two).~~

	~~Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino\|ugolino]] and [[Very low accuracy temperaments #Codex\|codex]]~~.

	== Bug ==		== Bug ==
	Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.		The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the {{nowrap\| 4 & 5 }} temperament, and its [[ploidacot]] is alpha-dicot. [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it. Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	[[Badness]] (Sintel): 0.769		[[Badness]] (Sintel): 0.769

			=== Overview to extensions ===
			Bug has an obvious 7-limit extension, [[#Beep\|beep]], via the normal comma list {27/25, 36/35} which can also be obtained by adding [[21/20]]. There is an alternative, [[#Mite\|mite]], which adds [[28/25]] instead.

			Temperaments discussed elsewhere include [[Very low accuracy temperaments #Ugolino\|ugolino]] and [[Very low accuracy temperaments #Codex\|codex]]. Considered below are beep and mite.

	== Beep ==		== Beep ==
	{{Main\| Beep }}		{{Main\| Beep }}
	{{See also\| Semaphoresmic clan }}		{{See also\| Semaphoresmic clan }}

			As bug divides [[3/1]] in half for 5/3~9/5, it only makes sense to also equate this interval with 7/4~12/7, joining the temperament with [[semaphore and godzilla\|semaphore]].

			Beep has the curious property that if we know both the beep tempering and the [[ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.

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

FloraC: - CTE & POTE tunings, but leave a note to 5-limit bug's TE, CTE & POTE tunings

2025-07-20T09:17:01Z

- CTE & POTE tunings, but leave a note to 5-limit bug's TE, CTE & POTE tunings

← Older revision		Revision as of 09:17, 20 July 2025
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	== Bug ==		== Bug ==
			Another notable tuning of bug is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 939.612{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.

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

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	* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}
	: error map: {{val\| 0.000 -22.993 +32.129 }}		: error map: {{val\| 0.000 -22.993 +32.129 }}
	~~<!-- * [[TE]], [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.612{{c}}~~
	~~: [[error map]]: {{val\| 0.000 -22.731 +32.523 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 14 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 14 }}
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	* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}
	: error map: {{val\| 0.000 -25.734 +28.018 -30.715 }}		: error map: {{val\| 0.000 -25.734 +28.018 -30.715 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 940.706{{c}}~~
	~~: [[error map]]: {{val\| 0.000 -20.543 +35.804 -28.120 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 936.605{{c}}
	~~: error map: {{val\| 0.000 -28.744 +23.502 -32.221 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 5, 9 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9 }}
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	* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}		* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.237{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~5/3 = 935.688{{c}} -->

	{{Optimal ET sequence\|legend=0\| 4, 5, 9 }}		{{Optimal ET sequence\|legend=0\| 4, 5, 9 }}
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	* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}		* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.589{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.065{{c}} -->

	Optimal ET sequence: {{Optimal ET sequence\| 4f, 5, 9 }}		Optimal ET sequence: {{Optimal ET sequence\| 4f, 5, 9 }}
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	* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}		* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 938.078{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.153{{c}} -->

	Optimal ET sequence: {{Optimal ET sequence\| 4e, 5e, 9 }}		Optimal ET sequence: {{Optimal ET sequence\| 4e, 5e, 9 }}
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	* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}		* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}
	: error map: {{val\| 0.000 +9.766 +81.268 -33.663 }}		: error map: {{val\| 0.000 +9.766 +81.268 -33.663 }}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 952.365{{c}}~~
	~~: [[error map]]: {{val\| 0.000 +2.775 +70.781 -54.637 }}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 959.288{{c}}
	~~: error map: {{val\| 0.000 +16.622 +91.552 -13.095 }} -->~~

	{{Optimal ET sequence\|legend=1\| 1cdd, 4dd, 5 }}		{{Optimal ET sequence\|legend=1\| 1cdd, 4dd, 5 }}

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

2025-07-20T09:12:07Z

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

← Older revision		Revision as of 09:12, 20 July 2025
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	: mapping generators: ~2, ~5/3		: mapping generators: ~2, ~5/3

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]] and [[POTE]]: ~2 = 1200.000, ~5/3 = 939.612		* [[WE]]: ~2 = 1199.665{{c}}, ~5/3 = 939.350{{c}}
	: [[error map]]: {{val\| 0.000 -22.731 +32.523 }}		: [[error map]]: {{val\| -0.335 -23.255 +31.736 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.481{{c}}
			: error map: {{val\| 0.000 -22.993 +32.129 }}
			<!-- * [[TE]], [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 939.612{{c}}
			: [[error map]]: {{val\| 0.000 -22.731 +32.523 }} -->

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 14 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 14 }}

	[[Badness]] (~~Smith~~): 0.~~032801~~		[[Badness]] (Sintel): 0.769

	== Beep ==		== Beep ==
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~5/3 = 940.706		* [[WE]]: ~2 = 1204.399{{c}}, ~5/3 = 940.039{{c}}
			: [[error map]]: {{val\| +4.399 -21.877 +33.803 -19.988 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 938.111{{c}}
			: error map: {{val\| 0.000 -25.734 +28.018 -30.715 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 940.706{{c}}
	: [[error map]]: {{val\| 0.000 -20.543 +35.804 -28.120 }}		: [[error map]]: {{val\| 0.000 -20.543 +35.804 -28.120 }}
	* [[POTE]]: ~2 = 1200.000, ~5/3 = 936.605		* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 936.605{{c}}
	: error map: {{val\| 0.000 -28.744 +23.502 -32.221 }}		: error map: {{val\| 0.000 -28.744 +23.502 -32.221 }} -->

	{{Optimal ET sequence\|legend=1\| 4, 5, 9 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9 }}

	[[Badness]] (~~Smith~~): 0.~~018638~~		[[Badness]] (Sintel): 0.472

	=== Pentoid ===		=== Pentoid ===
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	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~5/3 = 939.237		* WE: ~2 = 1205.296{{c}}, ~5/3 = 939.817{{c}}
	* POTE: ~2 = 1200.000, ~5/3 = 935.688		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.415{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.237{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~5/3 = 935.688{{c}} -->

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 4, 5, 9 }}		{{Optimal ET sequence\|legend=0\| 4, 5, 9 }}

	Badness (~~Smith~~): 0.~~022649~~		Badness (Sintel): 0.749

	==== 13-limit ====		==== 13-limit ====
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	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~5/3 = 939.589		* WE: ~2 = 1205.291{{c}}, ~5/3 = 940.192{{c}}
	* POTE: ~2 = 1200.000, ~5/3 = 934.065		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 936.788{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 939.589{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.065{{c}} -->

	Optimal ET sequence: {{Optimal ET sequence\| 4f, 5, 9 }}		Optimal ET sequence: {{Optimal ET sequence\| 4f, 5, 9 }}

	Badness (~~Smith~~): 0.~~021159~~		Badness (Sintel): 0.874

	=== Pento ===		=== Pento ===
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	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000, ~5/3 = 938.078		* WE: ~2 = 1205.575{{c}}, ~5/3 = 938.493{{c}}
	* POTE: ~2 = 1200.000, ~5/3 = 934.153		* CWE: ~2 = 1200.000{{c}}, ~5/3 = 935.485{{c}}
			<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 938.078{{c}}
			* POTE: ~2 = 1200.000{{c}}, ~5/3 = 934.153{{c}} -->

	Optimal ET sequence: {{Optimal ET sequence\| 4e, 5e, 9 }}		Optimal ET sequence: {{Optimal ET sequence\| 4e, 5e, 9 }}

	Badness (~~Smith~~): 0.~~022799~~		Badness (Sintel): 0.754

	== Mite ==		== Mite ==
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, ~5/3 = 952.365		* [[WE]]: ~2 = 1187.604{{c}}, ~5/3 = 949.379{{c}}
			: [[error map]]: {{val\| -12.396 -3.196 +61.824 -47.759 }}
			* [[CWE]]: ~2 = 1200.000{{c}}, ~5/3 = 955.861{{c}}
			: error map: {{val\| 0.000 +9.766 +81.268 -33.663 }}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 952.365{{c}}
	: [[error map]]: {{val\| 0.000 +2.775 +70.781 -54.637 }}		: [[error map]]: {{val\| 0.000 +2.775 +70.781 -54.637 }}
	* [[POTE]]: ~2 = 1200.000, ~5/3 = 959.288		* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 959.288{{c}}
	: error map: {{val\| 0.000 +16.622 +91.552 -13.095 }}		: error map: {{val\| 0.000 +16.622 +91.552 -13.095 }} -->

	{{Optimal ET sequence\|legend=1\| 1cdd, 4dd, 5 }}		{{Optimal ET sequence\|legend=1\| 1cdd, 4dd, 5 }}

	[[Badness]] (~~Smith~~): 0.~~054770~~		[[Badness]] (Sintel): 1.39

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

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

2025-06-24T00:37:12Z

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

← Older revision		Revision as of 00:37, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Bug family]] <!-- Main article -->		[[Category:Bug family]] <!-- Main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:13, 12 June 2025

2025-06-12T05:13:57Z

← Older revision		Revision as of 05:13, 12 June 2025
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[9edo]]. The monzo for 27/25 is {{monzo\| 0 3 -2 ~~}}, the dual of which is {{multival\| 2 3 0~~ }}. The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the 4 & 5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it.		The 5-limit parent of the '''bug family''' is bug, a temperament of sorts (that is, an [[exotemperament]]) which tempers out [[27/25]], the large limma, approximately one step of [[9edo]]. The monzo for 27/25 is {{monzo\| 0 3 -2 }}. The generator for bug is ~5/3, two of which give the ~3, and three of which give the ~5. Bug may be described as the 4 & 5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4-, 5-, or 9-note [[mos]] are a place to start with it.

	Bug has a 7-limit extension, [[#Beep\|beep]], via the normal comma list {27/25, 36/35} which can also be obtained by adding [[21/20]]. Beep has the curious property that if we know both the beep tempering and the [[Ragismic microtemperaments #Ennealimmal\|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.		Bug has a 7-limit extension, [[#Beep\|beep]], via the normal comma list {27/25, 36/35} which can also be obtained by adding [[21/20]]. Beep has the curious property that if we know both the beep tempering and the [[Ragismic microtemperaments #Ennealimmal\|ennealimmal]] tempering of a given 7-limit interval ''x'', that is enough to know what JI ratio ''x'' is.

VectorGraphics at 04:39, 12 June 2025

2025-06-12T04:39:30Z

← Older revision		Revision as of 04:39, 12 June 2025
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	{{Mapping\|legend=1\| 1 0 0 2 \| 0 2 3 1 }}		{{Mapping\|legend=1\| 1 0 0 2 \| 0 2 3 1 }}

	~~{{Multival\|legend=1\| 2 3 1 0 -4 -6 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 1 0 0 -2 \| 0 2 3 6 }}		{{Mapping\|legend=1\| 1 0 0 -2 \| 0 2 3 6 }}

	~~{{Multival\|legend=1\| 2 3 6 0 4 6 }}~~

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