Minimal consistent EDOs: Difference between revisions

An [[edo]] ''N'' is ''[[consistent]]'' with respect to the [[Odd limit|''q''-odd-limit]] if the closest approximations of the odd harmonics of the q-odd-limit in that edo also give the closest approximations of all the differences between these odd harmonics. It is ''[[distinctly consistent]]'' if every one of those closest approximations is a distinct value, and ''purely consistent''{{idiosyncratic}} if its [[relative interval error|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. It is ''accurately consistent''{{idiosyncratic}} if the edo is consistent to [[Consistency #Generalization|distance 2]], or alternatively put, every ''q''-odd-limit interval in the edo has at most 25% relative error. Below is a table of the smallest consistent, and the smallest distinctly consistent, edo for every odd number up to 135. Odd limits of {{nowrap|2^''n'' − 1}} are '''highlighted'''.  

|+ style="font-size: 105%;" | Smallest consistent EDOs per odd limit

|-

| 13 || 26 || 87 || 46 || 270 || 270

|- style="font-weight: bold; background-color: #dddddd;"

|-

| 17 || 58 || 149 || 311 || 3395? || 3395?

| Purely consistent to the 137-odd-limit

}}

The last entry, 70910024edo, is consistent up to the 135-odd-limit. The next edo is [[5407372813edo|5407372813]], reported to be consistent to the 155-odd-limit.