Acoustic e: Difference between revisions

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'''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. ~~It is close to~~ the JI intervals 8/3~~, 43/16,~~ and 11/4, 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.

{{Infobox Interval

| Ratio = e

| Cents = 1731.2340490667561

| Name = natave

}}

'''''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'', a.k.a. ''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 {{EDOs|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.

==Approximations==

== See also ==

* [[Ede|Ed''e'']], equal divisions of this interval

* [[Zetave]], the result of stacking 𝜏 nataves, of interest in regards to the [[zeta]] function

[[Category:Transcendental]]

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-'''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. It is close to the JI intervals 8/3, 43/16, and 11/4, 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.
+{{DISPLAYTITLE:Acoustic ''e''}}
+{{Infobox Interval
+| Ratio = e
+| Cents = 1731.2340490667561
+| Name = natave
+}}
+'''''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'', a.k.a. ''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 {{EDOs|2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253}}.
+==Approximations==
+{{interval edo approximation| interval = 271801/99990}}
+== See also ==
+* [[Ede|Ed''e'']], equal divisions of this interval
+* [[Zetave]], the result of stacking 𝜏 nataves, of interest in regards to the [[zeta]] function
+[[Category:Transcendental]]