Consistency limits of small 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. Below is a table of every edo up to 99. "Consistent" gives its consistency limit, i.e. the highest odd limit to which the edo is consistent, and "Distinct" gives the distinct consistency limit, i.e. the highest odd limit to which the edo is distinctly consistent. The remaining columns give the [[Consistent #Consistency to distance d|consistency distance]] (also called ''consistency level''<ref group="note">This term was coined by [[Paul Hahn]] in 1996. See [https://yahootuninggroupsultimatebackup.github.io/mills-tuning-list/topicId_884.html Yahoo! Tuning Group | ''Consistency generalized'']. </ref>) for every odd limit from 3 to 23.

{| class="wikitable sortable mw-collapsible right-all"

! rowspan="2" | Edo

! colspan="2" | Consistency limit

! colspan="11" | Consistency distance

! Consistent

! Distinct

! 3-limit

! 5-limit

! 7-limit

! 9-limit

! 11-limit

! 13-limit

! 15-limit

! 17-limit

! 19-limit

! 21-limit

! 23-limit