View source for EDe

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.

== 10-EDN ==
{| class="wikitable"
|+Intervals of 10-EDN
!Step
!Cents
!Ratio
!JI approximation(s)
!Interval
|-
|0
|0.0
|1/1
|1/1
|unison
|-
|1
|173.12
|e^(1/10)
|11/10
|flat whole tone
|-
|2
|346.25
|e^(1/5)
|11/9
|neutral third
|-
|3
|519.37
|e^(3/10)
|43/32
|sharp fourth
|-
|4
|692.49
|e^(2/5)
|3/2
|flat fifth
|-
|5
|865.62
|e^(1/2)
|5/3
|flat major sixth
|-
|6
|1038.74
|e^(3/5)
|117/64
|neutral seventh
|-
|7
|1211.86
|e^(7/10)
|2/1
|stretched octave
|-
|8
|1384.99
|e^(4/5)
|20/9
|flat major ninth
|-
|9
|1558.11
|e^(9/10)
|22/9
|neutral tenth
|-
|10
|1731.23
|e/1
|43/16
|natave
|}
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 ==
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.