Computational Issues in Physically-based Sound Models

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Additional material

Chapter 3 - Single reed models

Clarinet-like sounds. 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 (see Sec. 3.2).
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.

Finite difference model (see Sec. 3.3). The reed is described as a clamped-free bar with non-constant cross-sectional area, subject to additional forces due to the interaction with the mouthpiece and the player's lip. This animated gif has been created from the Matlab simulations of the finite difference model.

Non-linear reed oscillator (see Sec. 3.4). 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.
Reed model with constant lumped parameters. You can hear 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.
Reed model with 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.

Chapter 4 - Source models for articulatory speech synthesis

The glottal models discussed in this chapter are based on lumped models of the vocal folds. These two animated gifs (which I downloaded from here) give an idea of how such models work.

One-mass model

Three-mass model

Identification and resynthesis (see Sec. 4.2). A voiced signal (radiated pressure) is inverse-filtered techniques, the vocal tract all-pole filter is identified and the glottal flow signal is reconstructed from the radiated pressure. The glottal model is identified using this glottal flow signal. Then the identified system can be used to resynthesize the signal, and even to perform physically-based transformations (e.g. changing the resonance frequency of the vocal fold oscillator affects the pitch). Here are some examples.

Glottal Flow Vowel /a/ Vowel /e/
Pitch shift
Ampl. modulation

The one-delayed-mass model (see Sec. 4.3) relies on the idea that the glottal system exhibits two main modes of oscillation. These mpeg files (which I downloaded from here) give a qualitative picture of these modes. The first one is the x10 mode, the second one is the x11 mode.

Chapter 5 - Contact models in multimodal environments

Hammer-resonator model (see Sec. 5.1). The resonator is modeled as a modal object, where the number of partials, the frequencies, and the quality factors can be controlled.
In this example you can hear a 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 the using only three partials produces veridical results.

Perceived material (see Sec. 5.2). Listening tests have been used to see whether the impact model can elicit perception of material. It turned out that the overall decay time of the resonator (i.e. the quality factor) is the most salient cue. These sounds provide examples of four materials.

Quality factor 7.2 30.8 584.4 3478
Pitch (Hz) 1189.2 1000 2000 1881.8

Perceived hammer hardness (see Sec. 5.3). 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.
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.
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.
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.