Ed11/4

The equal division of 11/4 (ed11/4) is a tuning obtained by dividing the undecimal semi-augmented eleventh (11/4) in a certain number of equal steps.

Properties

Division of 11/4 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 11/4 as a base though, is apparent by being used at the base of so much 11-limit harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

Incidentally, one way to treat 11/4 as an equivalence in a temperament is the use of the 11:16:20 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone a stack of four 3/2's is equated with 5/1, here a stack of four 20/11's is equated with 16/11, tempering out the comma 161051/160000 in the 4.5.11 subgroup. Doing this yields 5-, 7-, 12-, and 17-note mos scales, coincidentally similar to Pythagorean tuning.