2016edo: Difference between revisions

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Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here.  
Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here.  


2016 shares the mapping for 3 with [[224edo]], albeit with a 28 relative cent error. Using the 2016f val gives the same mapping for 13 as [[224edo]], and unleashes the full power of 224edo's 13 limit chords.
2016 shares the mapping for 3 with [[224edo]], albeit with a 28 relative cent error.  
 
2016edo has two reasonable mappings for 7. The 2016d val, {{Val|2016 3195 4681 5659}}, tempers out 5250987/5242880, 40353607/40310784 (tritrizo), and {{monzo|14, 11, -22, 7}}. As such, its circle of the interval 7/6 is the same as in [[9edo]]. The patent val, {{Val|2016 3195 4681 5658}} tempers out [[250047/250000]], along with {{monzo|7, 18, -2, -11}} and {{monzo|43, -1, -13, -4}}. This means that the symmetrical major third (400 cents, 1/3 of the octave) in 2016edo corresponds to [[63/50]].
 
In the 11-limit, 2016edo tempers out the {{monzo|0 0 -22 0 3 11}} comma, which equates a stack of 11 [[25/13]]<nowiki/>s with 3 [[11/1|hendecataves]].


== Regular temperament properties ==
== Regular temperament properties ==
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|0.050
|0.050
|8.4
|8.4
|-
|2.3.5.7
|250047/250000, {{monzo|7, 18, -2, -11}}, {{monzo|43, -1, -13, -4}}
|[{{Val|2016 3195 4681 5658}}]
|0.007
|0.066
|11.1
|-
|-
|2.3.5.7
|2.3.5.7
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|0.015
|0.015
|2.5
|2.5
|-
|2.5.11.13.19.41.47
|
|
|
|
|
|}
|}