The simulating model and algorithm here discussed are based upon a
method quite different from the well know wave-guide approach – the
currently used model in musical research. Our approach is, at present,
more computationally complex, but the control of the various physical
parameters and of their meaning is very straightforward. Furthermore the
algorithm makes no assumption on the time invariance of the system, so
the variation of any parameter does not introduce artifacts.
Our model implements both the viscous friction of the string with the
air, and the internal friction – i.e. the energy dissipation due to
internal viscous-like behavior of the string. The friction of the bow is
represented by a discontinuous function, which simulates the thermal
behavior of the rosin by means of an hysteresis mechanism, and models
also the roughness of the bow by means of white noise.
The time-varying controllable parameters are
the tension/density ratio of the string, the two friction coefficients,
the speed and the pressure of the bow, and the (since now discrete)
point of bowing on the string. The computation algorithm here discussed
is an intermix of a method similar to the finite element one for what
concerns the integration over the space, and to the finite difference
method for what concerns the integration of the evolution of the system.
Our model can be used to play in extreme
parametric conditions, beyond the bowed strings performance tradition.
Although our model fully neglects twisting and longitudinal motions, as
well as the bridge admittance, it produces very likely sounds. One can
maybe infer that these characteristics are less important than one may
suspect. Using this model, the Italian composer Michelangelo Lupone
wrote the tape part of the string quartet "Corda di metallo"
("Metal string"), whose first world performance was held in
Rome in 1997 by the Kronos Quartet