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Harmonic Filters calculation

We need two things to have audio parameters representing pitch: the frequency of each harmonic, and a bandwidth to compute a filter arround them.

harmonic frequencies $f_i$ are calculated as follow:

\begin{displaymath}f_i = (i+1)\left( f(a). e^{\alpha(pitch - p(a))}\right) \end{displaymath}

where:
$f(a)$ = 440Hz (A4 standard frequency)
$p(a)$ = 69 (jMax pitch value for A4)
$\alpha$ = 0,057762265

We choose to have a bandwidth of an half-tone arround each harmonic frequency. That means we will have:

\begin{displaymath}harmo\_filters[i][0] = f_i - (f_i.\delta_{halftone}) \end{displaymath}


\begin{displaymath}harmo\_filters[i][1] = f_i + (f_i.\delta_{halftone}) \end{displaymath}

With: $\delta_{halftone}$ = 0.0594631

The problem is that this model is instrument depending, and for each harmonic band will we have to determine a factor in order to have an harmonic filter that corresponds to the instrument which is playing.



Mathieu Gilles (Betr. soltau) 2003-08-25