Download On the Nonlinear Commuted Synthesis of the Piano In this paper a novel method is presented for the physics-based sound synthesis of the piano, based on digital waveguides. The approach combines the advantages of the commuted synthesis technique and the methods using a nonlinear hammer model. The interaction force of the hammer-string contact is computed by an auxiliary digital waveguide connected to a nonlinear hammer model. This force signal is used as a target impulse response for designing a low-order digital filter real-time. The piano sound is calculated by filtering the soundboard response with the hammer filter and feeding this signal to a synthesizer digital waveguide. A new method is presented for separating the contribution of the interaction force and the soundboard in measured piano tones. For modeling beating, a new technique is proposed based on a simplified pitch-shift effect. Considerations on modeling the effect of sustain pedal are also given. It is shown that the technique of designing the hammer filter real-time is not only useful for digital waveguide modeling, but it can be combined with sampling synthesis too.
Download A Piano Model Including Longitudinal String Vibrations In this paper a mixed-paradigm piano model is presented. The major development is the ability of modeling longitudinal string vibrations. Longitudinal string motion is the reason for the metallic sound of low piano notes, therefore its modeling greatly improves the perceptual quality of synthesized piano sound. In this novel approach the transversal displacement of the string is computed by a finite-difference string model and the longitudinal motion is calculated by a set of second-order resonators, which are nonlinearly excited by the transversal vibration. The soundboard is modeled by a multi-rate filter based on measurements of real pianos. The piano model is able to produce high-quality piano sounds in real-time with about 5–10 note polyphony on an average personal computer.
Download Nonlinear modeling of a guitar loudspeaker cabinet Distortion is a desirable effect for sound coloration in electric guitar amplifiers and effect processors. At high sound levels, particularly at low frequencies, the loudspeakers used in classic style cabinets are also a source of distortion. This paper presents a case study of measurements and digital modeling of a typical guitar loudspeaker as a real-time audio effect. It demonstrates the complexity of the driver behavior, which cannot be efficiently modeled in true physical detail. A model with linear transfer functions and static nonlinearity characteristics to approximate the measured behavior is derived based upon physical arguments. An efficient method to simulate radiation directivity is also proposed.
Download Simulation of piano sustain-pedal effect by parallel second-order filters This paper presents a sustain-pedal effect simulation algorithm for piano synthesis, by using parallel second-order filters. A robust two-step filter design procedure, based on frequency-zooming ARMA modeling and least squares fit, is applied to calibrate the algorithm from impulse responses of the soundboard and the string register. The model takes into account the differences in coupling between the various strings. The algorithm can be applied to both sample-based and physics-based piano synthesizers.
Download Energy-based synthesis of tension modulation in strings Above a certain amplitude, the string vibration becomes nonlinear due to the variation of tension. An important special case is when the tension varies with time but spatially uniform along the string. The most important effect of this tension modulation is the exponential decay of the pitch (pitch glide). In the case of nonrigid string termination, the generation of double frequency terms and the excitation of missing modes also occurs, but this is perceptually less relevant for most of the cases. Several modeling strategies have been developed for tension modulated strings. However, their computational complexity is significantly higher compared to linear string models. This paper proposes efficient techniques for modeling the quasistatic part (short-time average) of the tension variation that gives rise to the most relevant pitch glide effect. The modeling is based on the linear relationship between the energy of the string and quasistatic tension variation. When this feature is added to linear string models, the computational complexity is increased by a negligible amount, leading to significant savings compared to earlier tension modulated string models.
Download Passive Admittance Matrix Modeling for Guitar Synthesis In physics-based sound synthesis, it is generally possible to incorporate a mechanical or acoustical immittance (admittance or impedance) in the form of a digital filter. Examples include modeling of the termination of a string or a tube. However, when digital filters are fitted to measured immittance data, care has to be taken that the resulting filter corresponds to a passive mechanical or acoustical system, otherwise the stability of the instrument model is at risk. In previous work, we have presented a simple method for designing and realizing inherently passive scalar admittances, by composing the admittance as a linear combination of positive real (PR) functions with nonnegative weights. In this paper the method is extended to multidimensional admittances (admittance matrices). The admittance matrix is synthesized as a sum of PR scalar transfer functions (second-order filters) multiplied by positive semidefinite matrices. For wave-based modeling, such as digital waveguides (DWGs) or wave digital filters (WDFs), the admittance matrix is converted to a reflectance filter. The filter structure is retained during conversion, resulting in a numerically robust implementation. As an example, a dual-polarization guitar string model based on the DWG approach is connected to the reflectance model parameterized from guitar bridge admittance measurements.
Download Energy Based Synthesis of Tension Modulation in Membranes Above a certain amplitude, membrane vibration becomes nonlinear due to the variation of surface tension. This leads to audible pitch glides, which greatly contribute to the characteristic timbre of tom-tom drums of the classical drum set and many other percussion instruments. Therefore, there is a strong motivation to take the tension modulation effect into account in drum synthesis. Some models do already exist that model this phenomenon, however, their computational complexity is significantly higher compared to linear membrane models. This paper applies an efficient methodology previously developed for the string to model the quasistatic part (short-time average) of the surface tension. The efficient modeling is based on the linear relationship between the quasistatic tension and membrane energy, since the energy can be computed at a relatively low computational cost. When this energy-based tension modulation is added to linear membrane models, the perceptually most relevant pitch glides are accurately synthesized, while the increase in computational complexity is negligible.