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Formulas for the Schelleng diagram

$\displaystyle f_{\hbox{\small max}}=\frac{2Z v_{\hbox{\small b}}}{(\mu_{\hbox{\small
s}}-\mu_{\hbox{\small d}})\beta}
$

$\displaystyle f_{\hbox{\small min}}=\frac{Z^{2}}{2r_{\hbox{\small 1}}} \cdot
\frac{v_{\hbox{\small b}}}{(\mu_{\hbox{\small s}}-\mu_{\hbox{\small d}})\beta^{2}}
$

where $ \mu_{\hbox{\small s}}$ =coefficient of static friction
$ \mu_{\hbox{\small d}}$ =coefficient of dynamic friction
$ v_{\hbox{\small b}}$ =bow velocity
$ \beta$ =bow position
$ Z$ =characteristic impedance of the string,
$ Z=\sqrt{T \rho}$
$ r_{\hbox{\small 1}}$ =term that represents losses of the string


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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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