This is the companion page for the article:
C. Desvages, S. Bilbao, Two-polarisation physical model of bowed strings with nonlinear contact and friction forces, and application to gesture-based sound synthesis, Appl. Sci. 2016, 6(5), 135.
A bowed string sound synthesis algorithm is designed, by simulating two-polarisation string motion, discretising the partial differential equations governing the string’s behaviour with the finite difference method. A globally energy balanced scheme is used, as a guarantee of numerical stability under highly nonlinear conditions. In one polarisation, a nonlinear contact model is used for the normal forces exerted by the dynamic bow hair, left hand fingers, and fingerboard. In the other polarisation, a force-velocity friction curve is used for the resulting tangential forces. The scheme update requires the solution of two nonlinear vector equations. The dynamic input parameters allow for simulating a wide range of gestures.
Here, we present a range of sound and video examples illustrating the synthesis capabilities of the model presented in the paper.
The gestural control of this model is defined by 2 sets of parameters (3 for the bow, 2 for the left hand finger), that can all be varied along the simulation:
- Bow parameters:
- bow position along the string, closer or further away from the bridge
- bow downwards force (usually called “bowing pressure” by musicians)
- bow tangential force, which will determine the bowing velocity
- Finger parameters:
- finger position along the string
- finger downwards force
Gesture-based sound synthesis
The presence of left hand fingers and a fingerboard allows for simulating a range of bowed string gestures. The initial transient of the bowing of a stopped note is shown below: the left hand finger (in blue) captures the string against the fingerboard (in grey), then the bow (pink) is lowered onto the string, and pushed across to set the string into motion.
Bowed string motion
For a given bow-bridge distance and bow velocity, if the player presses the bow too strongly for the returning Helmholtz corner to detach it from the string, the model produces raucous motion:
When the bow becomes too fast for a normal force too small, the static friction is not high enough for the bow to keep the string captured throughout a whole period, and multiple slipping occurs, resulting in surface sound:
Both the finger and bow can be moved along the simulation. If the finger slides or oscillates along the string, we can simulate glissando and vibrato gestures:
When the bow lands too fast on the string, it naturally bounces off. Refined control of this mechanism could allow for simulation of spiccato gestures.