Xenharmonic Wiki:Things to do: Difference between revisions
| Line 153: | Line 153: | ||
I think the formulation "1:3:5:7:9:11 is consistent in 31edo" or "31edo is consistent with 1:3:5:7:9:11" is more obviously meaningful than "31edo is consistent in the 11-odd limit". A set of odd numbers such as an odd limit corresponds to a harmonic series chord independent of voicing. | I think the formulation "1:3:5:7:9:11 is consistent in 31edo" or "31edo is consistent with 1:3:5:7:9:11" is more obviously meaningful than "31edo is consistent in the 11-odd limit". A set of odd numbers such as an odd limit corresponds to a harmonic series chord independent of voicing. | ||
== Set a semi-objective standard for | == Set a semi-objective standard for classifying edos as subgroup temperaments == | ||
We need a criterion that's objective as possible for when an EDO should be said to be good for JI subgroups. Some suggestions: | We need a criterion that's objective as possible for when an EDO should be said to be good for JI subgroups. Some suggestions: | ||
# absolute error? (arbitrary since different people accept different amount of error) | # absolute error? (arbitrary since different people accept different amount of error) | ||
# [[consistent]]? (breaks for small edos; actual accuracy depends too much on the size of the edo) | # [[consistent]]? (breaks for small edos; actual accuracy depends too much on the size of the edo) | ||
# consistent to distance 1? (see new definition in [[Consistent]] page), The justification is that some small piece of the JI subgroup lattice (maybe to distance one of the "fundamental chord") should map "consistently" in the edo, in addition to the chord itself being consistent. | # consistent to distance 1? (see new definition in [[Consistent]] page), The justification is that some small piece of the JI subgroup lattice (maybe to distance one of the "fundamental chord") should map "consistently" in the edo, in addition to the chord itself being consistent. | ||