Equal tuning accuracy functions: Difference between revisions
From Xenharmonic Reference
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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The mu function is defined as: | The mu function is defined as: | ||
<math> \mu( x, \sigma) = \sum_{k=1}^{\infty}f \left( x, k \right) </math> | |||
for a given edo x and weight σ, where | for a given edo x and weight σ, where | ||
< | <math>f(x, k) = \frac{|\operatorname{mod}(2gkx, 2) - 1|}{k^{\sigma}}</math> | ||
and | and | ||
<math>g \left( k \right) = \log_{2} \left( k \right).</math> | |||
Revision as of 20:04, 18 May 2026
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:
for a given edo x and weight σ, where
and
