Natave
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| Interval information |
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
e is a mathematical constant associated with the natural logarithm. Because pitch is logarithmic with respect to frequency, it might be of interest in xenharmony as well, where the name natave (a portmanteau of "natural" and "octave") is suggested for the interval e, aka e/1.
e lies between the JI intervals 8/3 and 11/4 and is well-approximated by 49/18 and 87/32, making it a rather sharp eleventh. Due to the limit definition of e, it also occurs as the limit of the following sequence: 2/1, two 3/2, three 4/3, four 5/4, five 6/5, etc. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.