Consistency: Difference between revisions
m clarify |
Someone added some note about a "subgroup definition" of consistency which doesn't exist - an entire subgroup can't be consistent. I'm not sure what is meant but removing this |
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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. | ||
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). | ||