Trisedodge family - Revision history

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

2025-11-27T12:18:33Z

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

← Older revision		Revision as of 12:18, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Trisedodge family\| ]] <!-- main article -->		[[Category:Trisedodge family\| ]] <!-- main article -->
	[[Category:Trisedodge\| ]] <!-- key article -->		[[Category:Trisedodge\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Septimal blackwood is now canon

2025-09-11T15:14:06Z

Septimal blackwood is now canon

← Older revision		Revision as of 15:14, 11 September 2025
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	{{See also\| Cloudy clan #Coblack }}		{{See also\| Cloudy clan #Coblack }}

	In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[~~blacksmith~~]]<ref name="naming"/>.		In addition to 126/125, the coblack temperament tempers out the [[cloudy comma]], 16807/16384, which is the amount by which five septimal supermajor seconds ([[8/7]]) fall short of an octave. Coblack was also named by Petr Pařízek, who considered it a counterpart of [[blackwood]]<ref name="naming"/>.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Badness: 0.045070		Badness: 0.045070

	== ~~Notes~~ ==		== References ==

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

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

2025-06-24T00:40:44Z

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

VectorGraphics: wedgie

2025-06-12T04:16:20Z

wedgie

← Older revision		Revision as of 04:16, 12 June 2025
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	{{Mapping\|legend=1\| 5 1 7 21 \| 0 3 2 -3 }}		{{Mapping\|legend=1\| 5 1 7 21 \| 0 3 2 -3 }}

	~~Wedgie: {{multival\| 15 10 -15 -19 -66 -63}}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 5 1 7 14 \| 0 3 2 0 }}		{{Mapping\|legend=1\| 5 1 7 14 \| 0 3 2 0 }}

	~~{{Multival\|legend=1\| 15 10 0 -19 -42 -28 }}~~

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

FloraC: Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

2025-06-06T16:38:19Z

Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

← Older revision		Revision as of 16:38, 6 June 2025
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	Badness: ?		Badness: ?

	Badness (~~Dirichlet~~): 1.609		Badness (Sintel): 1.609

	==== 19-limit ====		==== 19-limit ====
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	Badness: ?		Badness: ?

	Badness (~~Dirichlet~~): 1.542		Badness (Sintel): 1.542

	==== 23-limit ====		==== 23-limit ====
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	Badness: ?		Badness: ?

	Badness (~~Dirichlet~~): 1.463		Badness (Sintel): 1.463

	==== 29-limit ====		==== 29-limit ====
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	Badness: ?		Badness: ?

	Badness (~~Dirichlet~~): 1.380		Badness (Sintel): 1.380

	==== Trisey ====		==== Trisey ====

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

" to "{{Technical data page}}"

2025-04-13T13:43:18Z

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

← Older revision		Revision as of 13:43, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo\| 19 10 -15 }}.		The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo\| 19 10 -15 }}.

BudjarnLambeth: {{Technical data page}}

2025-04-13T09:14:32Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 09:14, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo\| 19 10 -15 }}.		The '''trisedodge family''' tempers out the [[trisedodge comma]], 30958682112/30517578125 = {{monzo\| 19 10 -15 }}.

Lériendil at 05:03, 14 February 2025

2025-02-14T05:03:21Z

← Older revision		Revision as of 05:03, 14 February 2025
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	Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>.		Named by [[Petr Pařízek]] in 2011, ''trisedodge'' (originally spelt ''trisedoge'') means that three semidiminished [[octave]]s add up to [[7/1]], and that an octave is made of 5 [[period]]s<ref name="naming">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>.

	Temperaments discussed elsewhere include [[~~Trienstonic clan~~ #Quindecic\|quindecic]] and [[Stearnsmic clan #Decistearn\|decistearn]]. Considered below are trisedodge and coblack.		Temperaments discussed elsewhere include [[15th-octave temperaments #Quindecic\|quindecic]] and [[Stearnsmic clan #Decistearn\|decistearn]]. Considered below are trisedodge and coblack.

	== Trisedodge ==		== Trisedodge ==

Godtone: /* Trisedodge */ note 29-limit

2024-12-01T20:26:13Z

Trisedodge: note 29-limit

← Older revision		Revision as of 20:26, 1 December 2024
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	In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens.		In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens.

			Remarkably, trisedodge admits an extension to the full [[29-limit]] which, except for prime 13, is surprisingly obvious/simple a way to extend the 11-limit representation.

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

Godtone: /* 29-limit */ consistency

2024-12-01T18:50:48Z

29-limit: consistency

← Older revision		Revision as of 18:50, 1 December 2024
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	Optimal tunings:		Optimal tunings:
	* CTE: ~55/48 = 1\5, ~11/8 = 554.673 (~25/24 = 74.673)		* CTE: ~23/20 = 1\5, ~11/8 = 554.673 (~24/23 = 74.673)
	* CWE: ~55/48 = 1\5, ~11/8 = 554.684 (~25/24 = 74.684)		* CWE: ~23/20 = 1\5, ~11/8 = 554.684 (~24/23 = 74.684)

	Optimal ET sequence: {{Optimal ET sequence\| 15f, 65d, 80 }}		Optimal ET sequence: {{Optimal ET sequence\| 15f, 65d, 80 }}