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.  
== 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


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[[Category:Rank-2 temperaments]]
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Revision as of 13:13, 16 November 2025

Dee leap week is a 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.

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 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.

See Gamelismic clan #Dee leap week for technical data.

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.

External links