Consistency: Difference between revisions
m →Consistency to d copies: unify term to "number of copies" |
m Undo revision 63736 by Mike Battaglia (talk): "subgroup definition" meant consistent with the arithmetic of primes or some other subgroup basis elements, e.g. an nth power of a 3 is always approximated with n times the mapping of 3 in the chord. Tag: Undo |
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(If such an approximation exists, it must be the only such approximation, since changing one interval would make that interval go over the 50% error threshold.) | (If such an approximation exists, it must be the only such approximation, since changing one interval would make that interval go over the 50% error threshold.) | ||
In this formulation, 12edo represents the chord 1:3:5:7:9:17:19 consistently. | In this formulation, 12edo represents the chord 1:3:5:7:9:17:19 consistently. Note: The second definition disagrees with the first definition for some chords such as 1:3:81:243 in [[80edo]]. This is a feature, not a bug, as the distinction can be useful in some circumstances. | ||
The concept only makes sense for edos and not for non-edo rank-2 (or higher) temperaments, since for some choices of generator sizes in these temperaments, you can get any ratio you want to arbitary accuracy by piling up a lot of generators (assuming the generator is an irrational fraction of the octave). | The concept only makes sense for edos and not for non-edo rank-2 (or higher) temperaments, since for some choices of generator sizes in these temperaments, you can get any ratio you want to arbitary accuracy by piling up a lot of generators (assuming the generator is an irrational fraction of the octave). | ||