Download The wave digital reed: A passive formulation
In this short paper, we address the numerical simulation of the single reed excitation mechanism. In particular, we discuss a formalism for approaching the lumped nonlinearity inherent in such a model using a circuit model and the application of wave digital filters (WDFs), which are of interest in that they allow simple stability verification, a property which is not generally guaranteed if one employs straightforward numerical methods. We present first a standard reed model, then its circuit representation, then finally the associated wave digital network. We then enter into some implementation issues, such as the solution of nonlinear algebraic equations, and the removal of delay-free loops, and present simulation results.
Download Modal-Type Synthesis Techniques for Nonlinear Strings with an Energy Conservation Property
There has recently been increased interest in the modelling of string vibration under large amplitude conditions, for sound synthesis purposes. A simple nonlinear model is given by the KirchhoffCarrier equation, which can be thought of as a generalization of the wave equation to the case for which the string tension is “modulated” by variations in the length of the string under deformation. Finite difference schemes are one means of approach for the simulation of nonlinear PDE systems; in this case, however, as the nonlinearity is spatially invariant, the solution may be broken down into sinusoidal components, much as in the linear case. More importantly, if time discretization is carried out in a particular way, it is possible to obtain a conserved energy in the numerical scheme, leading to a useful numerical stability guarantee, which can be difficult to obtain for strongly nonlinear systems. Numerical results are presented.
Download Sound Synthesis for Nonlinear Plates
In this paper, a simple finite difference scheme for a rectangular dynamic nonlinear plate, under free boundary conditions is presented. The algorithm is straightforward to program, and is capable of reproducing, to a first approximation, the behaviour of various percussion instruments whose timbre depends crucially on nonlinear effects (due to high-speed strikes), including transient pitch glides and the buildup of high-frequency energy. Though computationally intensive, algorithms such as that presented here promise more faithful sound synthesis and, as with all physical model inspired synthesis algorithms, require the specification of only a few, physically meaningful parameters. Full details of the algorithm, including the setting of boundary conditions and computational demands are provided. Numerical simulation results are presented.
Download Prepared Piano Sound Synthesis
A sound synthesis algorithm which simulates and extends the behaviour of the acoustic prepared piano is presented. The algorithm is based on a finite difference approximation to multiple stiff string vibration, including an excitation method (a hammer) as well as several connected preparation elements, modeled as lumped nonlinearities. Numerical issues and implementation details are discussed, and sound examples are presented.
Download Direct simulation for wind instrument synthesis
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.
Download A Modular Percussion Synthesis Environment
The construction of new virtual instruments is one long-term goal of physical modeling synthesis; a common strategy across various different physical modeling methodologies, including lumped network models, modal synthesis and scattering based methods, is to provide a canonical set of basic elements, and allow the user to build an instrument via certain specified connection rules. Such an environment may be described as modular. Percussion instruments form a good test-bed for the development of modular synthesis techniques—the basic components are bars and plates, and may be accompanied by connection elements, with a nonlinear character. Modular synthesis has been approached using all of the techniques mentioned above, but time domain finite difference schemes are an alternative, allowing many problems inherent in the above methods, including computability, large memory and precomputation requirements, and lack of extensibility to more complex systems, to be circumvented. One such network model is presented here along with the associated difference schemes, followed by a discussion of implementation details, the issues of excitation and output, and a description of various instrument configurations. The article concludes with a presentation of simulation results, generated in the Matlab prototyping language.
Download Spring Reverberation: A Physical Perspective
Spring-based artificial reverberation was one of the earliest attempts at compact replication of room-like reverberation for studio use. The popularity and unique sound of this effect have given it a status and desirability apart from its original use. Standard methods for modeling analog audio effects are not well suited to modeling spring reverberation, due to the complex and dispersive nature of its mechanical vibration. Therefore, new methods must be examined. A typical impulse responses of a spring used for reverberation is examined, and important perceptual parameters identified. Mathematical models of spring vibration are considered, with the purpose of drawing conclusions relevant to their application in an audio environment. These models are used to produce new results relevant to the design of digital systems for the emulation of spring reverberation units. The numerical solution of these models via the finite difference method is considered. A set of measurements of two typical spring reverberation units are presented.
Download More Modal Fun - “Forced Vibration” at One Point
The question, if a vibrating object can be forced to follow a given movement profile at one point forms a case of an inverse problem. It is shown that for the specific setting of an object described by modal data, this question may be solved by a newly developed method. The new technique has several strengths, such as allowing to compute modal data for the constrained scenario and forming a basis for precise and stable simulations. The latter potential is shown at a short example, a stiff string being hammered against a fixed board by a hammer of infinite mass.