Dee leap week: Difference between revisions
couldn't find which family to put this into, but also I think there's enough here for a full page |
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. |
||
| Line 20: | Line 20: | ||
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]] | |||
Revision as of 17:29, 15 November 2022
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
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