Decic - Revision history

Fredg999: Update link

2025-08-11T01:41:01Z

Update link

← Older revision		Revision as of 01:41, 11 August 2025
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	'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[~~15/14 equal-step tuning\|~~linus ~~temperaments~~]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.		'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[linus]] temperaments. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.

	There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendecic'' (10e&50) and ''prodecic'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments\|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendecic adds 4375/4376, and prodecic adds 441/440 to the 11-limit comma list.		There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendecic'' (10e&50) and ''prodecic'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments\|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendecic adds 4375/4376, and prodecic adds 441/440 to the 11-limit comma list.

FloraC: - parent category

2025-04-28T14:00:01Z

- parent category

← Older revision		Revision as of 14:00, 28 April 2025
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	* [[Decic50]] - [[10L 40s]] scale		* [[Decic50]] - [[10L 40s]] scale

	[[Category:~~Temperaments]]~~		[[Category:Decic\| ]] <!-- main article -->
	~~[[Category:Cloudy clan~~]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:~~Decic\|~~ ]]~~<!-- main article -->~~		[[Category:Cloudy clan]]

Lériendil at 23:03, 19 April 2025

2025-04-19T23:03:05Z

← Older revision		Revision as of 23:03, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Cloudy clan]]		[[Category:Cloudy clan]]
			[[Category:Rank-2 temperaments]]
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:Decic\| ]]<!-- main article -->		[[Category:Decic\| ]]<!-- main article -->

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T17:58:44Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 17:58, 7 May 2023
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	* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]		* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]

	[[Optimal ~~GPV~~ sequence]]s:		[[Optimal ET sequence]]s:
	* 7-limit: {{~~Vals~~\| 10, 30b, 40, 50, 60, 110d, 170cdd }}		* 7-limit: {{Optimal ET sequence\| 10, 30b, 40, 50, 60, 110d, 170cdd }}
	* 11 and 13-limit: {{~~Vals~~\| 10, 30be, 40, 50 }}		* 11 and 13-limit: {{Optimal ET sequence\| 10, 30be, 40, 50 }}
	* 17-limit: {{~~Vals~~\| 10, 30beg, 40, 50 }}		* 17-limit: {{Optimal ET sequence\| 10, 30beg, 40, 50 }}

	[[Badness]]:		[[Badness]]:
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	* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]		* 11, 13, 15, and 17-odd-limit: ~3/2 = [696.00000, 700.00000]

	[[Optimal ~~GPV~~ sequence]]s:		[[Optimal ET sequence]]s:
	* 11 and 13-limit: {{~~Vals~~\| 10e, 30bee, 40e, 50, 60e, 110de }}		* 11 and 13-limit: {{Optimal ET sequence\| 10e, 30bee, 40e, 50, 60e, 110de }}
	* 17-limit: {{~~Vals~~\| 10e, 30beeg, 40e, 50, 60e, 110deg }}		* 17-limit: {{Optimal ET sequence\| 10e, 30beeg, 40e, 50, 60e, 110deg }}

	[[Badness]]:		[[Badness]]:
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	* 11, 13, 15, and 17-odd-limit: ~3/2 = [700.00000, 702.85714]		* 11, 13, 15, and 17-odd-limit: ~3/2 = [700.00000, 702.85714]

	[[Optimal ~~GPV~~ sequence]]s:		[[Optimal ET sequence]]s:
	* 11, 13, and 17-limit: {{~~Vals~~\| 10, 40ee, 50e, 60e }}		* 11, 13, and 17-limit: {{Optimal ET sequence\| 10, 40ee, 50e, 60e }}

	[[Badness]]:		[[Badness]]:

Xenwolf: replace {{IoT}} by plain categorization

2022-03-01T21:02:13Z

replace {{IoT}} by plain categorization

← Older revision		Revision as of 21:02, 1 March 2022
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	* [[Decic50]] - [[10L 40s]] scale		* [[Decic50]] - [[10L 40s]] scale

			[[Category:Temperaments]]
	[[Category:Cloudy clan]]		[[Category:Cloudy clan]]
	[[Category:Marvel temperaments]]		[[Category:Marvel temperaments]]
	[[Category:Decic\| ]]<!-- main article -->		[[Category:Decic\| ]]<!-- main article -->
	~~{{IoT}}~~

Xenllium at 04:11, 20 February 2022

2022-02-20T04:11:08Z

← Older revision		Revision as of 04:11, 20 February 2022
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	* 17-limit: 0.025064		* 17-limit: 0.025064
	</div></div>		</div></div>


	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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	* 17-limit: 0.026050		* 17-limit: 0.026050
	</div></div>		</div></div>


	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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	<nowiki>*</nowiki> in 17-limit POTE tuning		<nowiki>*</nowiki> in 17-limit POTE tuning
	</div></div>		</div></div>


	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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	<nowiki>*</nowiki> in 17-limit POTE tuning		<nowiki>*</nowiki> in 17-limit POTE tuning
	</div></div>		</div></div>


	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">

Xenllium at 23:46, 11 February 2022

2022-02-11T23:46:08Z

← Older revision		Revision as of 23:46, 11 February 2022
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	'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning\|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.		'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning\|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.

	There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''~~splendic~~'' (10e&50) and ''~~prodigic~~'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments\|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, ~~splendic~~ adds 4375/4376, and ~~prodigic~~ adds 441/440 to the 11-limit comma list.		There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendecic'' (10e&50) and ''prodecic'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments\|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendecic adds 4375/4376, and prodecic adds 441/440 to the 11-limit comma list.

	== Temperament data ==		== Temperament data ==
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	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
	<div style="line-height:1.6;">'''~~Splendic~~ temperament (10e&50)'''</div>		<div style="line-height:1.6;">'''Splendecic temperament (10e&50)'''</div>
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17
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	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
	<div style="line-height:1.6;">'''~~Prodigic~~ temperament (10&50e)'''</div>		<div style="line-height:1.6;">'''Prodecic temperament (10&50e)'''</div>
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17
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	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
	<div style="line-height:1.6;">'''Intervals of ~~splendic~~ (10e&50)'''</div>		<div style="line-height:1.6;">'''Intervals of splendecic (10e&50)'''</div>
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	{\| class="wikitable"		{\| class="wikitable"
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	<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">		<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
	<div style="line-height:1.6;">'''Intervals of ~~prodigic~~ (10&50e)'''</div>		<div style="line-height:1.6;">'''Intervals of prodecic (10&50e)'''</div>
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	{\| class="wikitable"		{\| class="wikitable"
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	== Scales ==		== Scales ==
	* [[Decic50]] - [[10L 40s]] scale		* [[Decic50]] - [[10L 40s]] scale
	* [[Decic60]] - [[50L 10s]] scale

	[[Category:Cloudy clan]]		[[Category:Cloudy clan]]

Xenllium at 22:55, 11 February 2022

2022-02-11T22:55:39Z

← Older revision		Revision as of 22:55, 11 February 2022
Line 1:		Line 1:
	'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning\|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.		'''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit\|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning\|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.

	There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendic'' (10e&50) and ''prodigic'' (10&50e).		There are three mappings for 11, 13 and 17-limit that are comparable in complexity and error: ''decic'' (10&50), ''splendic'' (10e&50) and ''prodigic'' (10&50e). They share the comma list of the [[No-elevens subgroup temperaments\|no-elevens subgroups]], tempering out 105/104, 170/169, 196/195 and 289/288. Decic adds 385/384, splendic adds 4375/4376, and prodigic adds 441/440 to the 11-limit comma list.

	== Temperament data ==		== Temperament data ==
Line 524:		Line 524:
	== Scales ==		== Scales ==
	* [[Decic50]] - [[10L 40s]] scale		* [[Decic50]] - [[10L 40s]] scale
			* [[Decic60]] - [[50L 10s]] scale

	[[Category:Cloudy clan]]		[[Category:Cloudy clan]]

Xenllium at 01:45, 11 February 2022

2022-02-11T01:45:31Z

Show changes

Xenllium at 01:22, 11 February 2022

2022-02-11T01:22:25Z

@@ Line 1: / Line 1: @@
 '''Decic''' is a temperament for the 7, 11, 13, and 17 [[Harmonic limit|prime limits]]. It is a member of [[marvel temperaments]], [[cloudy clan]], and [[15/14 equal-step tuning|linus temperaments]]. It has a period of 1/10 octave and tempers out 225/224 and 16807/16384. The fifth of decic in size is a [[meantone]] fifth, but four of them are not used to reach the 5th harmonic. Instead, [[14/13]], [[15/14]] and [[16/15]] are equated to 1/10 of an octave, and from this it derives its name. Not only the meantone fifth (flat 3/2) or fourth (sharp 4/3), but also the [[magic]] major third (flat 5/4) can be used as a generator.
 == Temperament data ==
@@ Line 12: / Line 14: @@
 [[POTE generator]]s:
-* 7-limit: ~3/2 = 698.69596
+* 7-limit: ~15/14 = 120.00000, ~3/2 = 698.69596
-* 11-limit: ~3/2 = 696.79119
+* 11-limit: ~15/14 = 120.00000, ~3/2 = 696.79119
-* 13-limit: ~3/2 = 696.99342
+* 13-limit: ~14/13 = 120.00000, ~3/2 = 696.99342
-* 17-limit: ~3/2 = 697.08527
+* 17-limit: ~14/13 = 120.00000, ~3/2 = 697.08527
 [[TOP tuning|TOP generator]]s:
@@ Line 48: / Line 50: @@
 * 13-limit: 0.036880
 * 17-limit: 0.025064
 </div></div>
@@ Line 183: / Line 261: @@
 == Scales ==
-* [[Decic50]] - proper [[10L 40s]] scale
+* [[Decic50]] - [[10L 40s]] scale
 [[Category:Cloudy clan]]