User:CompactStar/Ed11/4

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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. Many, though not all, ed11/4 scales have a perceptually important false octave, with various degrees of accuracy.

The structural utility of 11/4 is apparent by being central to much 11-limit harmony, as well as being a fairly trivial point to split the difference between the octave and the tritave.

One approach to ed11/4 tunings 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.