Paper Archive

The nodal DK method is a systematic way to derive a non-linear state-space system as a physical model for an electrical circuit. Unfortunately, calculating the system coefficients requires inversion of a relatively large matrix. This becomes a problem when the system changes over time, requiring continuous recomputation of the coefficients. In this paper, we present an extension of the DK method to more efficiently handle variable circuit elements. The method is exemplified with the Dunlop Crybaby wah-wah effect pedal, as the continuous change of the potentiometer position is an extremely important aspect of the wah-wah effect.

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This work takes place in the context of the development of an active control of instruments with geometrical nonlinearities. The study focuses on Chinese opera gongs that display a characteristic pitch glide in normal playing conditions. In the case of the xiaoluo gong, the fundamental mode of the instrument presents a softening behaviour (frequency glides upward when the amplitude decreases). Controlling the pitch glide requires a nonlinear model of the structure, which can be partially identified with experimental techniques that rely on the formalism of nonlinear normal modes. The fundamental nonlinear mode has been previously experimentally identified as a softening Duffing oscillator. This paper aims at performing a simulation of the control of the oscillator’s pitch glide. For this purpose, the study focuses on a single-degree-offreedom nonlinear mode described by a softening Duffing equation. This Duffing oscillator energy proves to be ill-posed - in particular, the energy becomes negative for large amplitudes of vibration, which is physically inconsistent. Then, the first step of the present study consists in redefining a new energetically well-posed model. In a second part, guaranteed-passive simulations using port-Hamiltonian formalism confirm that the new system is physically and energetically correct compared to the Duffing model. Third, the model is used for control issues in order to modify the softening or hardening behaviour of the fundamental pitch glide. Results are presented and prove the method to be relevant. Perspectives for experimental applications are finally exposed in the last section of the paper.

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Techniques for the simulation of the tanpura have advanced significantly in recent years allowing numerically stable inclusion of bridge contact. In this paper tension modulation is added to a tanpura model containing a stiff lossy string, distributed bridge contact and the thread. The model is proven to be unconditionally stable and the numerical solver used has a unique solution as a result of choices made in the discretisation process. Effects due to the distribution of the bridge contact forces by comparison to a single point bridge and of introducing the tension modulation are studied in simulations. This model is intended for use in furthering the understanding of the physics of the tanpura and for informing the development of algorithms for sound synthesis of the tanpura and similar stringed instruments.

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We present a computational model of the Hammond tonewheel organ vibrato/chorus, a musical audio effect comprising an LC ladder circuit and an electromechanical scanner. We model the LC ladder using the Wave Digital Filter (WDF) formalism, and introduce a new approach to resolving multiple nonadaptable linear elements at the root of a WDF tree. Additionally we formalize how to apply the well-known warped Bilinear Transform to WDF discretization of capacitors and inductors and review WDF polarity inverters. To model the scanner we propose a simplified and physically-informed approach. We discuss the time- and frequency-domain behavior of the model, emphasizing the spectral properties of interpolation between the taps of the LC ladder.

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The synthesis of sound textures, such as rain, wind, or crowds, is an important application for cinema, multimedia creation, games and installations. However, despite the clearly defined requirments of naturalness and flexibility, no automatic method has yet found widespread use. After clarifying the definition, terminology, and usages of sound texture synthesis, we will give an overview of the many existing methods and approaches, and the few available software implementations, and classify them by the synthesis model they are based on, such as subtractive or additive synthesis, granular synthesis, corpus-based concatenative synthesis, wavelets, or physical modeling. Additionally, an overview is given over analysis methods used for sound texture synthesis, such as segmentation, statistical modeling, timbral analysis, and modeling of transitions. 2

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In the design of real-time spring reverberation algorithms, a modal architecture offers several advantages, including computational efficiency and parametric control flexibility. Due to the complex, highly dispersive behavior of helical springs, computing physically accurate parameters for such a model presents specific challenges. In this paper these are addressed by applying an implicit higher-order-in-space finite difference scheme to a two-variable model of helical spring dynamics. A novel numerical boundary treatment is presented, which utilises multiple centered boundary expressions of different stencil width. The resulting scheme is unconditionally stable, and as such allows adjusting the numerical parameters independently of each other and of the physical parameters. The dispersion relation of the scheme is shown to be accurate in the audio range only for very high orders of accuracy in combination with a small temporal and spatial step. The frequency, amplitude, and decay rate of the system modes are extracted from a diagonalised form of this numerical model. After removing all modes with frequencies outside the audio range and applying a modal amplitude correction to compensate for omitting the magnetic transducers, a light-weight modal reverb algorithm is obtained. Comparison with a measured impulse response shows a reasonably good match across a wide frequency range in terms of echo density, decay characteristics, and diffusive nature.

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In this paper, a physics-based model for a snare drum will be discussed, along with its finite difference simulation. The interactions between a mallet and the membrane and between the snares and the membrane will be described as perfectly elastic collisions. A novel numerical scheme for the implementation of collisions will be presented, which allows a complete energy analysis for the whole system. Viscothermal losses will be added to the equation for the 3D wave propagation. Results from simulations and sound examples will be presented.

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Vactrols, which consist of a photoresistor and a light-emitting element that are optically coupled, are key components in optical dynamic compressors. Indeed, the photoresistor’s program-dependent dynamic characteristics make it advantageous for automatic gain control in audio applications. Vactrols are becoming more and more difficult to find, while the interest for optical compression in the audio community does not diminish. They are thus good candidates for virtual analog modeling. In this paper, a model of vactrols that is entirely physical, passive, with a program-dependent dynamic behavior, is proposed. The model is based on first principles that govern semi-conductors, as well as the port-Hamiltonian systems formalism, which allows the modeling of nonlinear, multiphysical behaviors. The proposed model is identified with a real vactrol, then connected to other components in order to simulate a simple optical compressor.

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Recently, energy quadratization and modal expansion have become popular methods for developing efficient physics-based sound synthesis algorithms. These methods have been primarily used to derive explicit schemes modeling the collision between a string and a fixed barrier. In this paper, these techniques are applied to a similar problem: modeling a distributed mouthpiece lay-reed-lip interaction in a woodwind instrument. The proposed model aims to provide a more accurate representation of how a musician’s embouchure affects the reed’s dynamics. The mouthpiece and lip are modeled as distributed static and dynamic viscoelastic barriers, respectively. The reed is modeled using an approximate modal expansion derived via the Rayleigh-Ritz method. The reed system is then acoustically coupled to a measured input impedance response of a saxophone. Numerical experiments are presented.

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Digital waveguide (DW) modeling techniques are typically associated with a traveling-wave decomposition of wave variables and a “reflection function” approach to simulating acoustic systems. As well, it is often assumed that inputs and outputs to/from these systems must be formulated in terms of traveling-wave variables. In this paper, we provide a tutorial review of DW modeling of acoustic structures to show that they can easily accommodate physical input and output variables. Under certain constraints, these formulations reduce to simple “Schroeder reverb-like” computational structures. We also present a stable single-reed filter model that allows an explicit solution at the reed / air column junction. A clarinet-like system is created by combining the reed filter with a DW impedance model of a cylindrical air column.

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