Acoustic e: Difference between revisions

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{{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. 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. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.
'''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. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.



Revision as of 18:56, 27 October 2022

Interval information
Expression [math]\displaystyle{ e }[/math]
Size in cents 1731.234¢
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. 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. Edos that provide an increasingly close approximation to it are 2, 5, 7, 9, 34, 43, 52, 61, 131, 192, 253.

See also

  • EDN, equal divisions of this interval