Dee leap week - Revision history

FloraC: + basic norm-based tunings

2025-11-16T13:16:24Z

+ basic norm-based tunings

← Older revision		Revision as of 13:16, 16 November 2025
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	See [[Gamelismic clan #Dee leap week]] for technical data.		See [[Gamelismic clan #Dee leap week]] for technical data.

			== Tunings ==
			=== Norm-based tunings ===
			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~224/135 = 877.8770{{c}}
			\| CWE: ~224/135 = 877.8926{{c}}
			\| POTE: ~224/135 = 877.8969{{c}}
			\|}
			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~224/135 = 877.9026{{c}}
			\| CWE: ~224/135 = 877.8987{{c}}
			\| POTE: ~224/135 = 877.8976{{c}}
			\|}

	== Trivia ==		== Trivia ==

FloraC: Rework

2025-11-16T13:13:55Z

Rework

← Older revision		Revision as of 13:13, 16 November 2025
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	'''Dee leap week''' is a ~~rank-2~~ temperament with the ~~comma basis~~ 385/384, 441/440~~, and 2460375/2458624, making it a contraction of~~ [[~~portent~~]].		'''Dee leap week''' is a [[regular temperament\|temperament]] with a [[generator]] reprensenting [[135/112]], and three of them make a [[~]][[7/4]]. 135/112 is [[225/224]] sharp of [[6/5]]. In the 11-limit it tempers out [[385/384]] and [[441/440]] as is usual for temperaments in the [[gamelismic clan]].

	~~It is~~ derived from a 41 & 231 maximal evenness scale in a leap week version calendar proposed by John Dee, which features 8 leap days in 33 years in a [[1L 7s\|44444445 pattern]]. The leap week version would have ((365 + 8/33) / 7 - 52)*7 = (5+6/7)/33 = 41/231 week excess, and therefore represented by the 41 in 231 maximal evenness scale.		Dee leap week was named by [[Eliora]] in 2022, derived from a 41 & 231 [[maximal evenness]] scale in a leap week version calendar proposed by John Dee, which features 8 leap days in 33 years in a [[1L 7s\|44444445 pattern]]. The leap week version would have ((365 + 8/33) / 7 - 52)⋅7 = (5 + 6/7)/33 = 41/231 week excess, and therefore represented by the 41 in 231 maximal evenness scale.

	~~== Theory ==~~		See [[Gamelismic clan #Dee leap week]] for technical data.
	~~In this temperament, the generator corresponds to~~ [[~~135/112~~]]~~, and three of them make a [[7/4]]. 135/112 is 225/224 sharp of 6/5~~.

	~~In 231edo~~, ~~this corresponds to 62\~~231.		== Trivia ==
			According to the "Fixed Leap Cycle Finder" Excel widget provided on the Calendar Leap Cycles page, 231-year cycle is spread into 45 141 45 pattern, which results in an 8/7–32/21–8/7 chord. This can further be dissected into 45, 45, 6, 45, 45, which is the [[slendric pentad]]. As such, Dee leap week temperament provides chords which split both 3/2 and 7/4 into three parts.

	==~~= Chords =~~==		== External links ==
	~~One of the main chords of this temperament is 0-62-124-186, which divides 7/4 into three.~~		* [https://calendars.fandom.com/wiki/Dee_calendar Fandom \| Calendar Wiki \| ''Dee calendar'']
			* [http://individual.utoronto.ca/kalendis/leap/index.htm]{{dead link}}
	According to the "Fixed Leap Cycle Finder" Excel widget provided on the Calendar Leap Cycles page, 231-year cycle is spread into 45 141 45 pattern, which results in an 8/7 - 32/21 - 8/7 chord. This can further be dissected into 45-45-6-45-45, which is the [[~~slendric pentad]].~~

	~~As such, Dee leap week temperament provides chords which split both 3/2 and 7/4 into three parts.~~

	~~== Data ==~~
	~~See [[Gamelismic clan #Dee leap week]].~~

	~~== Links ==~~

	* https://calendars.fandom.com/wiki/Dee_calendar
	* http://individual.utoronto.ca/kalendis/leap/index.htm

	[[Category:Dee leap week\| ]] <!-- main article -->		[[Category:Dee leap week\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Gamelismic clan]]		[[Category:Gamelismic clan]]
	~~{{Todo\| cleanup }}~~

FloraC: Recategorize

2025-09-10T14:35:28Z

Recategorize

← Older revision		Revision as of 14:35, 10 September 2025
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	== Data ==		== Data ==
	See [[Gamelismic clan#Dee leap week]].		See [[Gamelismic clan #Dee leap week]].

	== Links ==		== Links ==
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	* http://individual.utoronto.ca/kalendis/leap/index.htm		* http://individual.utoronto.ca/kalendis/leap/index.htm

			[[Category:Dee leap week\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Gamelismic clan]]		[[Category:Gamelismic clan]]
	~~[[Category:Rank 2]]~~		{{Todo\| cleanup }}

Lériendil: moved data to gamelismic clan

2025-04-19T22:55:14Z

moved data to gamelismic clan

@@ Line 16: / Line 16: @@
 == Data ==
-Subgroup: 2.3.5.7
+See [[Gamelismic clan#Dee leap week]].
 == Links ==

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

2023-05-07T20:08:47Z

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

← Older revision		Revision as of 20:08, 7 May 2023
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	Optimal tuning (CTE): ~135/112 = 322.097		Optimal tuning (CTE): ~135/112 = 322.097

	~~Vals:~~ {{~~EDOs~~\|41, 149, 190, 231}}		{{Optimal ET sequence\|legend=1\|41, 149, 190, 231}}

	== Links ==		== Links ==

Eliora: /* Data */

2022-11-15T17:30:36Z

Data

← Older revision		Revision as of 17:30, 15 November 2022
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	Optimal tuning (CTE): ~135/112 = 322.097		Optimal tuning (CTE): ~135/112 = 322.097

	Vals: 41, 149, 190, 231		Vals: {{EDOs\|41, 149, 190, 231}}

	== Links ==		== Links ==

Eliora: apparently it's a member of the gamelismic clan, i'll leave the benefit of the doubt open but I think there's enough for a separate page.

2022-11-15T17:29:55Z

apparently it's a member of the gamelismic clan, i'll leave the benefit of the doubt open but I think there's enough for a separate page.

← Older revision		Revision as of 17:29, 15 November 2022
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	Comma list: 1029/1024, 2460375/2458624		Comma list: 1029/1024, 2460375/2458624

	Mapping: 1 4 -6 2, 0 -9 31 3		Mapping: [{{val\|1 4 -6 2}}, {{val\|0 -9 31 3}}]

	Optimal tuning (CTE): ~135/112 = 322.123		Optimal tuning (CTE): ~135/112 = 322.123
Line 29:		Line 29:
	Comma list: 385/384, 441/440, 2460375/2458624		Comma list: 385/384, 441/440, 2460375/2458624

	Mapping: 1 4 -6 2 15, 0 -9 31 3 43		Mapping: [{{val\|1 4 -6 2 15}}, {{val\|0 -9 31 3 43}}]

	Optimal tuning (CTE): ~135/112 = 322.097		Optimal tuning (CTE): ~135/112 = 322.097
Line 39:		Line 39:
	* https://calendars.fandom.com/wiki/Dee_calendar		* https://calendars.fandom.com/wiki/Dee_calendar
	* http://individual.utoronto.ca/kalendis/leap/index.htm		* http://individual.utoronto.ca/kalendis/leap/index.htm

			[[Category:Gamelismic clan]]
			[[Category:Rank 2]]

Eliora: couldn't find which family to put this into, but also I think there's enough here for a full page

2022-11-15T17:26:33Z

couldn't find which family to put this into, but also I think there's enough here for a full page

New page

'''Dee leap week''' is a rank-2 temperament with the comma basis 385/384, 441/440, and 2460375/2458624, making it a contraction of [[portent]].

It is derived from a 41 & 231 maximal evenness scale in a leap week version calendar proposed by John Dee, which features 8 leap days in 33 years in a [[1L 7s|44444445 pattern]]. The leap week version would have ((365 + 8/33) / 7 - 52)*7 = (5+6/7)/33 = 41/231 week excess, and therefore represented by the 41 in 231 maximal evenness scale.

== Theory ==
In this temperament, the generator corresponds to [[135/112]], and three of them make a [[7/4]]. 135/112 is 225/224 sharp of 6/5.

In 231edo, this corresponds to 62\231.

=== Chords ===
One of the main chords of this temperament is 0-62-124-186, which divides 7/4 into three.

According to the "Fixed Leap Cycle Finder" Excel widget provided on the Calendar Leap Cycles page, 231-year cycle is spread into 45 141 45 pattern, which results in an 8/7 - 32/21 - 8/7 chord. This can further be dissected into 45-45-6-45-45, which is the [[slendric pentad]].

As such, Dee leap week temperament provides chords which split both 3/2 and 7/4 into three parts.

== Data ==
Subgroup: 2.3.5.7

Comma list: 1029/1024, 2460375/2458624

Mapping: 1 4 -6 2, 0 -9 31 3

Optimal tuning (CTE): ~135/112 = 322.123

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 2460375/2458624

Mapping: 1 4 -6 2 15, 0 -9 31 3 43

Optimal tuning (CTE): ~135/112 = 322.097

Vals: 41, 149, 190, 231

== Links ==

* https://calendars.fandom.com/wiki/Dee_calendar
* http://individual.utoronto.ca/kalendis/leap/index.htm