Paper Archive

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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Finite difference time domain (FDTD) approaches to physical modeling sound synthesis, though more computationally intensive than other techniques (such as, e.g., digital waveguides), offer a great deal of flexibility in approaching some of the more interesting real-world features of musical instruments. One such case, that of brass instruments, including a set of time-varying valve components, will be approached here using such methods. After a full description of the model, including the resonator, and incorporating viscothermal loss, bell radiation, a simple lip model, and time varying valves, FDTD methods are introduced. Simulations of various characteristic features of valve instruments, including half-valve impedances, note transitions, and characteristic multiphonic timbres are presented, as are illustrative sound examples.

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Nonlinearity is a key feature in musical instruments and electronic circuits alike, and thus in simulation, for the purposes of physics-based modeling and virtual analog emulation, the numerical solution of nonlinear differential equations is unavoidable. Ensuring numerical stability is thus a major consideration. In general, one may construct implicit schemes using well-known discretisation methods such as the trapezoid rule, requiring computationally-costly iterative solvers at each time step. Here, a novel family of provably numerically stable time-stepping schemes is presented, avoiding the need for iterative solvers, and thus of greatly reduced computational cost. An application to the case of the collision interaction in musical instrument modeling is detailed.

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Recent bowed string sound synthesis has relied on physical modelling techniques; the achievable realism and flexibility of gestural control are appealing, and the heavier computational cost becomes less significant as technology improves. A bowed string is simulated in two polarisations by discretising the partial differential equations governing its behaviour, using 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.Sound examples and video demonstrations are presented.

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This paper presents a physical modelling sound synthesis environment for the production of valved brass instrument sounds. The governing equations of the system are solved using finite-difference time-domain (FDTD) methods and the environment is implemented in the C programming language. Users of the environment can create their own custom instruments and are able to control player parameters such as lip frequency, mouth pressure and valve openings through the use of instrument and score files. The algorithm for sound synthesis is presented in detail along with a discussion of optimisation methods used to reduce run time. Binaries for the environment are available for download online for multiple platforms.

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This work presents a physical model of the yaybahar, a recently invented acoustic instrument. Here, output from a bowed string is passed through a long spring, before being amplified and propagated in air via a membrane. The highly dispersive character of the spring is responsible for the typical synthetic tonal quality of this instrument. Building on previous literature, this work presents a modal discretisation of the full system, with fine control over frequency-dependent decay times, modal amplitudes and frequencies, all essential for an accurate simulation of the dispersive characteristics of reverberation. The string-bow-bridge system is also solved in the modal domain, using recently developed noniterative numerical methods allowing for efficient simulation.

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Modal methods are a long-established approach to physical modeling sound synthesis. Projecting the equation of motion of a linear, time-invariant system onto a basis of eigenfunctions yields a set of independent forced, lossy oscillators, which may be simulated efficiently and accurately by means of standard time-stepping methods. Extensions of modal techniques to nonlinear problems are possible, though often requiring the solution of densely coupled nonlinear time-dependent equations. Here, an application of recent results in numerical simulation design is employed, in which the nonlinear energy is first quadratised via a convenient auxiliary variable. The resulting equations may be updated in time explicitly, thus avoiding the need for expensive iterative solvers, dense linear system solutions, or matrix inversions. The case of a network of interconnected distributed elements is detailed, along with a real-time implementation as an audio plugin.

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The synthesis of guitar tones was one of the first uses of physical modeling synthesis, and many approaches (notably digital waveguides) have been employed. The dynamics of the string under playing conditions is complex, and includes nonlinearities, both inherent to the string itself, and due to various collisions with the fretboard, frets and a stopping finger. All lead to important perceptual effects, including pitch glides, rattling against frets, and the ability to play on the harmonics. Numerical simulation of these simultaneous strong nonlinearities is challenging, but recent advances in algorithm design due to invariant energy quadratisation and scalar auxiliary variable methods allow for very efficient and provably numerically stable simulation. A new design is presented here that does not employ costly iterative methods such as the Newton-Raphson method, and for which required linear system solutions are small. As such, this method is suitable for real-time implementation. Simulation and timing results are presented.

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There are now a number of methods available for generating synthetic sound based on physical models of wind instruments, including digital waveguides, wave digital filters, impedance-based methods and those involving impulse responses. Normally such methods are used to simulate the behaviour of the resonator, and the coupling to the excitation mechanism is carried out by making use of simple lumped finite difference schemes or digital filter structures. In almost all cases, a traveling wave, frequencydomain, or impulse response description of the resonator is used as a starting point—efficient structures may be arrived at when the bore is of a particularly simple form, such as a cylinder or cone. In recent years, however, due to the great computing power available, efficiency has become less of a concern—this is especially the case for musical instruments which may be well-modelled in 1D, such as wind instruments. In this paper, a fully time-space discrete algorithm for the simulation and synthesis of woodwind instrument sounds is presented; such a method, though somewhat more computationally intensive than an efficient waveguide structure, is still well within the realm of real-time performance. The main benefits of such a method are its generality (it is no longer necessary to make any assumptions about bore profile, which may be handled in an almost trivial manner), extensibility (i.e., the model may be generalized to handle nonlinear phenomena directly), ease of programming, and the possibility of direct proofs of numerical stability without invoking frequency domain concepts. Simulation results, sound examples and a graphical user interface, in the Matlab programming language are also presented.

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Efficient stable integration methods for nonlinear systems are of great importance for physical modeling sound synthesis. Specifically, a number of musical systems of interest, including vibrating strings, bars or plates may be written as port-Hamiltonian systems with quadratic kinetic energy and non-quadratic potential energy. Efficient schemes have been developed for such systems through the introduction of a scalar auxiliary variable. As a result, the stable real-time simulations of nonlinear musical systems of up to a few thousands of degrees of freedom is possible, even for nearly lossless systems. However, convergence rates can be slow and seem to be system-dependent. Specifically, at audio rates, they may suffer from numerical drift of the auxiliary variable, resulting in dramatic unwanted effects on audio output, such as pitch drifts after several impacts on the same resonator. In this paper, a novel method for mitigating this unwanted drift while preserving power balance is presented, based on a control approach. A set of modified equations is proposed to control the drift artefact by rerouting energy through the scalar auxiliary variable and potential energy state. Numerical experiments are run in order to check convergence on simulations in the case of a cubic nonlinear string. A real-time implementation is provided as a Max/MSP external. 60-note polyphony is achieved on a laptop, and some simple high level control parameters are provided, making the proposed implementation suitable for use in artistic contexts. All code is available in a public repository, along with compiled Max/MSP externals1.

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