Ed11/2

The equal division of 11/2 (ed11/2) is a tuning obtained by dividing the undecimal eighteenth (11/2) into a number of equal steps.

Properties

Division of 11/2 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.

Ed11/2s are a natural way to equalise and standardise any scale that repeats every 2940 to 2960 cents, or that happens to be finite and simply ends between 2940 and 2960 cents above the root. It is most likely to be empirical tunings that stumble into those properties, so a main use case for ed11/2 is approximating and deconstructing empirical tunings.

One example of this: aside from 31edo, ed11/2s are the next most natural way to approximate the McClain toy piano tuning, a finite empirical scale that ends 2950 cents above its root.