Efficient Modeling Strategies for the Geometric Nonlinearities of Musical Instrument Strings

Sound synthesis algorithms modeling the linear behavior of strings are well developed. However, some musical instruments require the modeling of such nonlinear phenomena as the appearance of longitudinal string modes, phantom partials, or mode coupling and pitch glide due to tension variation. Accordingly, the effects of geometric nonlinearities in strings are gaining more and more interest in the sound synthesis community. These effects can be grouped into four different regimes, depending on the transverse slope and on the ratio of longitudinal and transverse fundamental frequencies. In some cases only the coupling from the transverse to the longitudinal polarization is significant, while in others both directions of coupling are important. Another question is whether the inertial effects of longitudinal modes have to be modeled or not. The four cases arising from the combinations of these factors are outlined in the paper. The most common string modeling approaches – finite difference modeling, digital waveguides and modal models – are investigated with respect to their ability to model the different effects of geometric nonlinearities. The paper proposes the combined use of different modeling approaches to reduce the computational cost required for modeling the aforementioned phenomena.