Consistency: Difference between revisions
m clarify which definitions are being referred to |
m It turns out that the purported counterexample is not actually a counterexample |
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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. Question: Is using this formulation with a chord C equivalent to using the first formulation with S = the [[diamond function]] applied to C? | ||
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). | ||