Download Efficient simulation of the yaybahar using a modal approach 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.
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 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 Real-Time Modal Synthesis of Nonlinearly Interconnected Networks 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.
Download Efficient Simulation of the Bowed String in Modal Form The motion of a bowed string is a typical nonlinear phenomenon resulting from a friction force via interaction with the bow. The system can be described using suitable differential equations. Implicit numerical discretisation methods are known to yield energy consistent algorithms, essential to ensure stability of the timestepping schemes. However, reliance on iterative nonlinear root finders carries significant implementation issues. This paper explores a method recently developed which allows nonlinear systems of ordinary differential equations to be solved non-iteratively. Case studies of a mass-spring system and an ideal string coupled with a bow are investigated. Finally, a stiff string with loss is also considered. Combining semi-discretisation and a modal approach results in an algorithm yielding faster than real-time simulation of typical musical strings.
Download Non-Iterative Solvers For Nonlinear Problems: The Case of Collisions 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.
Download Sound morphologies due to non-linear interactions : towards a perceptive control of environmental sound-synthesis processes This paper is concerned with perceptual control strategies for physical modeling synthesis of vibrating resonant objects colliding nonlinearly with rigid obstacles. For this purpose, we investigate sound morphologies from samples synthesized using physical modeling for non-linear interactions. As a starting point, we study the effect of linear and non-linear springs and collisions on a single-degreeof-freedom system and on a stiff strings. We then synthesize realistic sounds of a stiff string colliding with a rigid obstacle. Numerical simulations allowed the definition of specific signal patterns characterizing the non linear behavior of the interaction according to the attributes of the obstacle. Finally, a global description of the sound morphology associated with this type of interaction is proposed. This study constitutes a first step towards further perceptual investigations geared towards the development of intuitive synthesis controls.
Download On the limits of real-time physical modelling synthesis with a modular environment One goal of physical modelling synthesis is the creation of new virtual instruments. Modular approaches, whereby a set of basic primitive elements can be connected to form a more complex instrument have a long history in audio synthesis. This paper examines such modular methods using finite difference schemes, within the constraints of real-time audio systems. Focusing on consumer hardware and the application of parallel programming techniques for CPU processors, useable combinations of 1D and 2D objects are demonstrated. These can form the basis for a modular synthesis environment that is implemented in a standard plug-in architecture such as an Audio Unit, and controllable via a MIDI keyboard. Optimisation techniques such as vectorization and multi-threading are examined in order to maximise the performance of these computationally demanding systems.
Download Real-Time Implementation of an Elasto-Plastic Friction Model using Finite-Difference Schemes The simulation of a bowed string is challenging due to the strongly non-linear relationship between the bow and the string. This relationship can be described through a model of friction. Several friction models in the literature have been proposed, from simple velocity dependent to more accurate ones. Similarly, a highly accurate technique to simulate a stiff string is the use of finitedifference time-domain (FDTD) methods. As these models are generally computationally heavy, implementation in real-time is challenging. This paper presents a real-time implementation of the combination of a complex friction model, namely the elastoplastic friction model, and a stiff string simulated using FDTD methods. We show that it is possible to keep the CPU usage of a single bowed string below 6 percent. For real-time control of the bowed string, the Sensel Morph is used.
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.