53edo: Difference between revisions
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|53}} | {{Harmonics in equal|53|columns=13}} | ||
There's also a cluster of usable higher primes starting at 71; even 89 (4.84{{cent}} flat), 97 (4.63{{cent}} sharp) and 101 (2.6{{cent}} sharp) are usable if placed in just the right context. | |||
{{Harmonics in equal|53|columns=4|start=20}} | |||
This make [[53edo]] excellent (for its size) in the 2.3.5.7.11.13.19.23.37.41.71.73.79.83 subgroup, although some higher error primes like 11 and 23 require the right context to be convincing. | |||
Note that the high primes, in rooted (/2<sup>n</sup>) position, essentially act as alternate interpretations of [[LCJI]] intervals, if you want to force a rooted interpretation; namely: | |||
[[71/64]] as ~[[10/9]], [[73/64]] as ~[[8/7]], [[79/64]] as ~[[16/13]], and perhaps most questionably in the context of [[53edo]], [[83/64]] as ~[[13/10]]. (Note that [[8edo]] offers a very good approximation of [[83/64]], so if you are working with a system that maps 13/10 to 3\8 = 450.000{{cent}} it makes more sense to think of 83/64 as the rooted approximation of 13/10 in that context.) | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
53edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | 53edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | ||