Equal tuning accuracy functions

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Revision as of 19:57, 18 May 2026 by Vector (talk | contribs) (Created page with "{{Technical}} There are a number of ways to quantify the tuning accuracy of equal temperaments. == Mu function == The mu function is defined as: $$ \mu \left( x, σ \right) = \sum_{k=1}^{\infty}f \left( x, k \right) $$ for a given edo x and weight σ, where <nowiki>$$ f \left( x, k \right) = \frac{\abs{\operatorname{mod} \left( 2g \left( k \right) x, 2 \right) - 1}}{k^{σ}} $$</nowiki> and $$ g \left( k \right) = \log_{2} \left( k \right) $$.")
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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:

$$ \mu \left( x, σ \right) = \sum_{k=1}^{\infty}f \left( x, k \right) $$

for a given edo x and weight σ, where

$$ f \left( x, k \right) = \frac{\abs{\operatorname{mod} \left( 2g \left( k \right) x, 2 \right) - 1}}{k^{σ}} $$

and

$$ g \left( k \right) = \log_{2} \left( k \right) $$.