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'' if its [[relative interval error|relative errors]] on odd harmonics up to and including ''q'' never exceed 25%. 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'''.  

|-

! Odd<br />limit !! Smallest<br />consistent edo&#42; !! Smallest distinctly<br />consistent edo !! Smallest ''purely<br />consistent''&#42;&#42; edo

| 135 || 70910024 || 70910024 || 93678217813

|- style="border-top: double; font-size: 0.75em;"

&#42;&#42;&#42;&thinsp;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.

[[Category:Consistency]]

[[Category:Odd limit]]