63edo: Difference between revisions
m →Subsets and supersets: note interesting structural uniqueness |
m →Subsets and supersets: link to temp |
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Its representation of the 2.3.5.7.13 subgroup (no-11's 13-limit) can uniquely be described in terms of accurate approximations contained in its main subsets of [[7edo]] and [[9edo]]: | Its representation of the 2.3.5.7.13 subgroup (no-11's 13-limit) can uniquely be described in terms of accurate approximations contained in its main subsets of [[7edo]] and [[9edo]]: | ||
* 1\9 = ~[[14/13]]~[[13/12]], implying (the much more accurate) 2\9 = ~[[7/6]] | * 1\9 = ~[[14/13]]~[[13/12]], implying (the much more accurate) 2\9 = ~[[7/6]] ([[septiennealic]]) | ||
* 2\7 = ~[[39/32]]~[[128/105]], via [[4096/4095]] and the [[akjaysma]] | * 2\7 = ~[[39/32]]~[[128/105]], via [[4096/4095]] and the [[akjaysma]] (which are naturally paired) | ||
If we avoid equating 14/13 and 13/12 (which is by far the highest damage equivalence) so that we achieve 7/6 = 2\9 directly, we get the 63 & 441 microtemperament in the same subgroup. | If we avoid equating 14/13 and 13/12 (which is by far the highest damage equivalence) so that we achieve 7/6 = 2\9 directly, we get the 63 & 441 microtemperament in the same subgroup. | ||