# Natave

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Expression | [math]e[/math] |

Size in cents | 1731.234¢ |

Name | natave |

Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.55643 bits |

**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