Download Modeling Methods for the Highly Dispersive Slinky Spring: A Novel Musical Toy
The ’Slinky’ spring is a popular and beloved toy for many children. Like its smaller relatives, used in spring reverberation units, it can produce interesting sonic behaviors. We explore the behavior of the ’Slinky’ spring via measurement, and discover that its sonic characteristics are notably different to those of smaller springs. We discuss methods of modeling the behavior of a Slinky via the use of finite-difference techniques and digital waveguides. We then apply these models in different structures to build a number of interesting tools for computer-based music production.
Download Modelling of Brass Instrument Valves
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.
Download Binaural simulations using audio rate FDTD schemes and CUDA
Three dimensional finite difference time domain schemes can be used as an approach to spatial audio simulation. By embedding a model of the human head in a 3D computational space, such simulations can emulate binaural sound localisation. This approach normally relies on using high sample rates to give finely detailed models, and is computationally intensive. This paper examines the use of head models within audio rate FDTD schemes, ranging from 176.4 down to 44.1 kHz. Using GPU computing with Nvidia’s CUDA architecture, simulations can be accelerated many times over a serial computation in C. This allows efficient, dynamic simulations to be produced where sounds can be moved around during the runtime. Sound examples have been generated by placing a personalised head model inside an anechoic cube. At the lowest sample rate, 44.1 kHz, localisation is clear in the horizontal plane but much less so in the other dimensions. At 176.4, there is far greater three dimensional depth, with perceptible front to back, and some vertical movement.
Download Timpani Drum Synthesis in 3D on GPGPUs
Physical modeling sound synthesis for systems in 3D is a computationally intensive undertaking; the number of degrees of freedom is very large, even for systems and spaces of modest physical dimensions. The recent emergence into the mainstream of highly parallel multicore hardware, such as general purpose graphical processing units (GPGPUs) has opened an avenue of approach to synthesis for such systems in a reasonable amount of time, without severe model simplification. In this context, new programming and algorithm design considerations appear, especially the ease with which a given algorithm may be parallelized. To this end finite difference time domain methods operating over regular grids are explored, with regard to an interesting and non-trivial test problem, that of the timpani drum. The timpani is chosen here because its sounding mechanism relies on the coupling between a 2D resonator and a 3D acoustic space (an internal cavity). It is also of large physical dimensions, and thus simulation is of high computational cost. A timpani model is presented, followed by a brief presentation of finite difference time domain methods, followed by a discussion of parallelization on GPGPU, and simulation results.
Download A 3D Multi-Plate Environment for Sound Synthesis
In this paper, a physics-based sound synthesis environment is presented which is composed of several plates, under nonlinear conditions, coupled with the surrounding acoustic field. Equations governing the behaviour of the system are implemented numerically using finite difference time domain methods. The number of plates, their position relative to a 3D computational enclosure and their physical properties can all be specified by the user; simple control parameters allow the musician/composer to play the virtual instrument. Spatialised sound outputs may be sampled from the simulated acoustic field using several channels simultaneously. Implementation details and control strategies for this instrument will be discussed; simulations results and sound examples will be presented.
Download Numerical Simulation of Spring Reverberation
Virtual analog modeling of spring reverberation presents a challenging problem to the algorithm designer, regardless of the particular strategy employed. The difficulties lie in the behaviour of the helical spring, which, due to its inherent curvature, shows characteristics of both coherent and dispersive wave propagation. Though it is possible to emulate such effects in an efficient manner using audio signal processing constructs such as delay lines (for coherent wave propagation) and chains of allpass filters (for dispersive wave propagation), another approach is to make use of direct numerical simulation techniques, such as the finite difference time domain method (FDTD) in order to solve the equations of motion directly. Such an approach, though more computationally intensive, allows a closer link with the underlying model system— and yet, there are severe numerical difficulties associated with such designs, and in particular anomalous numerical dispersion, requiring some care at the design stage. In this paper, a complete model of helical spring vibration is presented; dispersion analysis from an audio perspective allows for model simplification. A detailed description of novel FDTD designs follows, with special attention is paid to issues such as numerical stability, loss modeling, numerical boundary conditions, and computational complexity. Simulation results are presented.
Download Fourth-Order and Optimised Finite Difference Schemes for the 2-D Wave Equation
This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one percent wave speed error up to some critical frequency. Simulation results are presented.
Download Revisiting Implicit Finite Difference Schemes for Three-Dimensional Room Acoustics Simulations on GPU
Implicit finite difference schemes for the 3-D wave equation using a 27-point stencil on the cubic grid are presented, for use in room acoustics modelling and artificial reverberation. The system of equations that arises from the implicit formulation is solved using the Jacobi iterative method. Numerical dispersion is analysed and computational efficiency is compared to second-order accurate 27-point explicit schemes. Timing results from GPU implementations demonstrate that the proposed algorithms scale over their explicit counterparts as expected: by a factor of M + 2, where M is a fixed number of Jacobi iterations (eight can be sufficient in single precision). Thus, the accuracy of the approximation can be improved over explicit counterparts with only a linear increase in computational costs, rather than the quartic (in operations) and cubic (in memory) increases incurred when oversampling the grid. These implicit schemes are advantageous in situations where less than 1% dispersion error is desired.
Download Numerical Simulation of String/Barrier Collisions: The Fretboard
Collisions play a major role in various models of musical instruments; one particularly interesting case is that of the guitar fretboard, the subject of this paper. Here, the string is modelled including effects of tension modulation, and the distributed collision both with the fretboard and individual frets, and including both effects of free string vibration, and under finger-stopped conditions, requiring an additional collision model. In order to handle multiple distributed nonlinearities simultaneously, a finite difference time domain method is developed, with a penalty potential allowing for a convenient model of collision within a Hamiltonian framework, allowing for the construction of stable energy-conserving methods. Implementation details are discussed, and simulation results are presented illustrating a variety of features of such a model.
Download An Energy Conserving Finite Difference Scheme for the Simulation of Collisions in Snare Drums
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.