Algorithms and models for sound synthesis
Audio examples
Real-time physical model of the piano
- Polonaise
The model runs in real-time on medium-low cost platforms. The sound quality is still not fully satisfactory, due to the lack of an accurate soundboard model. Still, professional musicians who have played the model report that the instrument reacts in a realistic way to changes in touch and dynamics, and appears as less synthetic that usual wavetable instruments.
Single reed modeling
The reed is modeled as a one-mass system with constant parameters, and the bore is a single waveguide section with a low-pass filter modeling the bell termination. The system is discretized using the 1-step Weighted Sample method.
- Fundamental register. On the one hand,
the overall sound quality is clearly not satisfactory; this is mainly due
to poor modeling of the resonator, and can be noticed during steady state
oscillations. On the other hand, the accurate modeling of the excitation mechanism provides a realistic attack transient.
- Second (clarion) register, played without any register hole, by properly adjusting the reed parameters. Both the resonance and the damping coefficient are lowered, in particular the reed resonance matches the seventh harmonic of the bore. The transition to the clarion register can be clearly heard in the attack transient, and this behavior is qualitatively in agreement with experimental results on real clarinets.
- Reed regime ("squeaks"), obtained by giving the damping coefficient a very low value. Again, this behavior is qualitatively in agreement with experimental results. A similar effect can be produced on a real clarinet if the player presses the reed using his teeth instead of his lip, therefore providing little damping.
Non-linear reed oscillator: the reed is modeled as a one-mass system with non-constant parameters, in order to account properly for reed curling onto the mouthpiece and reed beating. In these two examples the mouth pressure was linearly increased from 1100 Pa to 2000 Pa, and then quickly decreased back to 1000 Pa. The resulting radiation pressure was calculated by high-pass filtering the pressure at the open end of the tube. Thanks to Maarten van Walstijn, who has synthesized these examples.
- Constant lumped parameters. You can hear the point when the reed suddenly enters the beating regime. The pitch is almost constant throughout the sample, it does not change significantly with increasing mouth pressure.
- Non-constant lumped parameters. The transition to the beating regime is much smoother than above, you can hear that the spectrum gradually opens up with increasing blowing pressure. There is an audible increase in the pitch, which is qualitatively in accordance with experimental results on real clarinets.
Contact sounds
A modal mechanical resonator is excited by a non-linear impact model.
The number of partials, the frequencies, and the quality factors of the resonator can be controlled.
- Double impact You can hear two impact sounds, the first synthesized using n=1 partials for the resonator, the second using n=3 partials. All the other parameters (hammer velocity, force parameters, etc.) have the same values in the two sounds. Note that using only three partials produces veridical results.
- Wood-like material
- Glass-like material In these two examples the decay time of the resonator is adjusted in such a way that the perceived material of the resonator can be controlled. Listening tests have velidated the model. The model can therefore synthesize "cartoon" sounds, to be used as auditory icons in human-computer interfaces.
Perceived hammer hardness: the contact time (i.e., the time after which the hammer separates from the resonator) can be controlled using the physical parameters of the contact force. The contact time is in turn related to the perceived hammer hardness. These three samples show examples of varying hardness.
- Varying mass. The hammer mass is increased throughout the sample. Correspondingly, the contact time increases and the hammer hardness decreases. You can hear the initial "bump" becoming more and more audible.
- Varying stiffness. The force stiffness is increased throughout the sample. Correspondingly, the contact time decreases and the hammer hardness increases. You can hear the attack becoming brighter and brighter.
- Varying dissipation. The force dissipative term is increased throughout the sample. This parameter does not affect the contact time significantly, and correspondingly you can hear little (if any) difference between the impacts.
Last modified: 05-31-2002