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 accurate{{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'''.  

{| class="wikitable center-all"

|+ Smallest consistent EDOs per odd limit

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

!Smallest<br />''accurate'' edo

!Smallest distinctly<br />''accurate'' edo

| 135 || 70910024 || 70910024 || 93678217813 ||  ||  

|}

<nowiki>*</nowiki> Apart from 0edo

<nowiki>**</nowiki> Purely consistent to the 137-odd-limit