Consistency: Difference between revisions

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In this formulation, 12edo represents the chord 1:3:5:7:9:17:19 consistently. Note: The chord definition disagrees with the subgroup 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 in these ~~tunings~~ 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).

The page ''[[Minimal consistent EDOs]]'' shows the smallest edo that is consistent or uniquely consistent in a given odd limit while the page ''[[Consistency levels of small EDOs]]'' shows the largest odd limit that a given edo is consistent or uniquely consistent in.

@@ Line 17: / Line 17: @@
 In this formulation, 12edo represents the chord 1:3:5:7:9:17:19 consistently. Note: The chord definition disagrees with the subgroup 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 in these tunings 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).
 The page ''[[Minimal consistent EDOs]]'' shows the smallest edo that is consistent or uniquely consistent in a given odd limit while the page ''[[Consistency levels of small EDOs]]'' shows the largest odd limit that a given edo is consistent or uniquely consistent in.