Dee leap week: Difference between revisions

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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~~.

== 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}}

|}

==~~= Chords =~~==

== Trivia ==

~~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.

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]].

== External links ==

* [https://calendars.fandom.com/wiki/Dee_calendar Fandom | Calendar Wiki | ''Dee calendar'']

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

* [http://individual.utoronto.ca/kalendis/leap/index.htm]{{dead link}}

== ~~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| ]]

[[Category:Rank-2 temperaments]]

[[Category:Gamelismic clan]]

~~{{Todo| cleanup }}~~

@@ Line 1: / Line 1: @@
-'''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.
+== 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}}
+|}
-=== Chords ===
+== Trivia ==
-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.
-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]].
+== External links ==
+* [https://calendars.fandom.com/wiki/Dee_calendar Fandom | Calendar Wiki | ''Dee calendar'']
-As such, Dee leap week temperament provides chords which split both 3/2 and 7/4 into three parts.
+* [http://individual.utoronto.ca/kalendis/leap/index.htm]{{dead link}}
-== 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:Rank-2 temperaments]]
 [[Category:Gamelismic clan]]
-{{Todo| cleanup }}