Equal divisions of the natave, which is the mathematical constant e used as a musical interval. e is of particular interest because of its relationship with logarithms, the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic.
|1||173.12||e^(1/10)||11/10||flat whole tone|
|5||865.62||e^(1/2)||5/3||flat major sixth|
|8||1384.99||e^(4/5)||20/9||flat major ninth|
Beyond the natave, some particularly pleasant JI intervals can be found: 11\10 is only 2 cents sharp from 3/1; 13\10 is very close to 11/2; and 23\10 is very close to 10/1. This last approximation in particular makes this equal division almost equivalent to 23-ed(10/1).
10-EDN is similar to 7-EDO in that its step size is roughly 1/7 of an octave, therefore roughly corresponding to the diatonic scale, but with warped, equal-size steps. However, the octave is stretched, which simultaneously helps the extremely flat fifth of 7-EDO.
20-EDN is a doubling of 10-EDN with intervals closer to semitones.
17-EDN is very close to 12-EDO but with slightly sharp semitones (101.84 cents). This causes the octave to be far too sharp (1222 cents) and gives it a rather pleasant sharp fifth of 712 cents.