Mu badness: Difference between revisions
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Mu (μ) is a function for equal tuning badness provided by Vector Graphics, and in a slightly different form by [[User:Lériendil|Lériendil]]. | Mu (μ) is a function for equal tuning badness provided by Vector Graphics, and in a slightly different form by [[User:Lériendil|Lériendil]]. | ||
For a given edo x, it is defined as: | |||
<math>\mu\left(x\right)=\sum_{k=1}^{\infty}f\left(x,k\right)</math> | <math>\mu\left(x\right)=\sum_{k=1}^{\infty}f\left(x,k\right)</math> | ||
where | |||
<math>f\left(x,k\right)=\frac{\operatorname{abs}\left(\operatorname{mod}\left(2g\left(k\right)x,2\right)-1\right)}{k^{2}}</math> | <math>f\left(x,k\right)=\frac{\operatorname{abs}\left(\operatorname{mod}\left(2g\left(k\right)x,2\right)-1\right)}{k^{2}}</math> | ||
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and | and | ||
<math>g\left(k\right)=\log_{2}\left(k\right)</math> | <math>g\left(k\right)=\log_{2}\left(k\right)</math>. | ||
The function essentially sums up the relative error on all integer harmonics k, weighted by the inverse square of k in order to converge to a finite value. | |||
It is derived as follows: | It is derived as follows: | ||