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The figure below shows the results given by the algorithm, for a cello string (147 Hz) with $ B=3e-4$ .

\epsfig{file=eps/res1.eps,width=12cm}
Frequency error (in cent) after the allpass filter approximation, for a cello D string..

\epsfig{file=eps/Afreqerr.eps,width=12cm}
Frequency error (in cent) after the allpass filter approximation, for a violin A string, with $ B=4.8527e-5$ .

\epsfig{file=eps/modelbtorsinh.eps,width=15cm}

The friction models used in these simulations are:

\epsfig{file=eps/plasticres.eps,width=10cm}

$\displaystyle \mu=\frac{A k_{\hbox{\small y}}(T)}{N} \hbox{sgn}(v)
$

where

\begin{eqnarray*}
A&=&\hbox{contact area between the bow and the string}\\
N&=&\hbox{normal load}\\
k_{\hbox{\small y}}(T) &=&\hbox{ shear yield stress as a function of the bow-string contact temperature $T$.}
\end{eqnarray*}


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Download stiffbowed.pdf
Download stiffbowed_2up.pdf
Download stiffbowed_4up.pdf

``Impact of String Stiffness on Virtual Bowed Strings'', by Stefania Serafin<serafin@ccrma.stanford.edu>, (From CCRMA DSP Seminar Presentation, Music 423).
Copyright © 2014-03-24 by Stefania Serafin<serafin@ccrma.stanford.edu>
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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