Ed11/5
The equal division of 11/5 (ed11/5) is a tuning obtained by dividing the neutral ninth (11/5) into a certain number of equal steps.
Division of 11/5 into equal parts does not necessarily imply directly using this interval as an equivalence. The question of equivalence has not even been posed yet. The utility of 11/5 as a base though is apparent by it being, beside the true high ninth of a just dominant 11th chord, the best option for "no-twos-or-threes" harmony after the extremely wide harmonic 5, and the awkwardly narrow small septimal tritone. It is also a relatively strong consonance. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
The simplest chord without 2's or 3's that sounds consonant and stable is 11:13:17, so it can be viewed as the fundamental sonority of no-twos-or-threes music. A neutral ninth-reduced stack of four 121/85's fall short of 17/13 by the small comma 2093663/2088025. Tempering out this comma together with the additional comma 54925/54043 results in catfish temperament, which can be viewed as an analog to meantone. It possesses mos scales of the families 2L 3s<11/5>, 2L 5s<11/5>, 2L 7s<11/5>, and 9L 2s<11/5>.
Ed11/5-edo correspondence
| Ed11/5 | Edo |
|---|---|
| 8ed11/5 | 7edo |
| 9ed11/5 | 8edo |
| 16ed11/5 | 14edo |
| 18ed11/5 | 16edo |
| 24ed11/5 | 21edo |
| 25ed11/5 | 22edo |
| 27ed11/5 | 24edo |
| 33ed11/5 | 29edo |
| 50ed11/5 | 44edo |