Equal tuning accuracy functions

This is a technical or mathematical page. While the subject may be of some relevance to music, the page treats the subject in technical language.

There are a number of ways to quantify the tuning accuracy of equal temperaments.

Mu function

The mu function is defined as:

$\mu (x,\sigma )=\sum _{k=1}^{\mathrm{\infty }}f(x,k)$

for a given edo x and weight σ, where

$f(x,k)=\frac{|\mathrm{mod}(2gkx,2)-1|}{k^{\sigma }}$

and

$g\left(k\right)={\log }_2\left(k\right).$