Dee leap week: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Data ==
== Data ==
Subgroup: 2.3.5.7
See [[Gamelismic clan#Dee leap week]].
 
Comma list: 1029/1024, 2460375/2458624
 
Mapping: [{{val|1 4 -6 2}}, {{val|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: [{{val|1 4 -6 2 15}}, {{val|0 -9 31 3 43}}]
 
Optimal tuning (CTE): ~135/112 = 322.097
 
{{Optimal ET sequence|legend=1|41, 149, 190, 231}}


== Links ==
== Links ==

Revision as of 22:55, 19 April 2025

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 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

See Gamelismic clan#Dee leap week.

Links