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 Large-scale Real-time Modular Physical Modeling Sound Synthesis Due to recent increases in computational power, physical modeling synthesis is now possible in real time even for relatively complex models. We present here a modular physical modeling instrument design, intended as a construction framework for string- and bar- based instruments, alongside a mechanical network allowing for arbitrary nonlinear interconnection. When multiple nonlinearities are present in a feedback setting, there are two major concerns. One is ensuring numerical stability, which can be approached using an energy-based framework. The other is coping with the computational cost associated with nonlinear solvers—standard iterative methods, such as Newton-Raphson, quickly become a computational bottleneck. Here, such iterative methods are sidestepped using an alternative energy conserving method, allowing for great reduction in computational expense or, alternatively, to real-time performance for very large-scale nonlinear physical modeling synthesis. Simulation and benchmarking results are presented.
Download A Physical Model of the Trombone Using Dynamic Grids for Finite-Difference Schemes In this paper, a complete simulation of a trombone using finitedifference time-domain (FDTD) methods is proposed. In particular, we propose the use of a novel method to dynamically vary the
number of grid points associated to the FDTD method, to simulate
the fact that the physical dimension of the trombone’s resonator
dynamically varies over time. We describe the different elements
of the model and present the results of a real-time simulation.
Download Dynamic Grids for Finite-Difference Schemes in Musical Instrument Simulations For physical modelling sound synthesis, many techniques are available; time-stepping methods (e.g., finite-difference time-domain
(FDTD) methods) have an advantage of flexibility and generality
in terms of the type of systems they can model. These methods do,
however, lack the capability of easily handling smooth parameter
changes while retaining optimal simulation quality and stability,
something other techniques are better suited for. In this paper,
we propose an efficient method to smoothly add and remove grid
points from a FDTD simulation under sub-audio rate parameter
variations. This allows for dynamic parameter changes in physical models of musical instruments. An instrument such as the
trombone can now be modelled using FDTD methods, as well as
physically impossible instruments where parameters such as e.g.
material density or its geometry can be made time-varying. Results show that the method does not produce (visible) artifacts and
stability analysis is ongoing.
Download Learning Nonlinear Dynamics in Physical Modelling Synthesis Using Neural Ordinary Differential Equations Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are
possible in order to handle geometric nonlinearities. One such
case is the high-amplitude vibration of a string, where geometric nonlinear effects lead to perceptually important effects including pitch glides and a dependence of brightness on striking amplitude. A modal decomposition leads to a coupled nonlinear system of ordinary differential equations. Recent work in applied machine learning approaches (in particular neural ordinary differential equations) has been used to model lumped dynamic systems
such as electronic circuits automatically from data. In this work,
we examine how modal decomposition can be combined with neural ordinary differential equations for modelling distributed musical systems. The proposed model leverages the analytical solution
for linear vibration of system’s modes and employs a neural network to account for nonlinear dynamic behaviour. Physical parameters of a system remain easily accessible after the training without
the need for a parameter encoder in the network architecture. As
an initial proof of concept, we generate synthetic data for a nonlinear transverse string and show that the model can be trained to
reproduce the nonlinear dynamics of the system. Sound examples
are presented.
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 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 Real-time Gong Synthesis Physical modeling sound synthesis is notoriously computationally intensive. But recent advances in algorithm efficiency, accompanied by increases in available computing power have brought real-time performance within range for a variety of complex physical models. In this paper, the case of nonlinear plate vibration, used as a simple model for the synthesis of sounds from gongs is considered. Such a model, derived from that of Föppl and von Kármán, includes a strong geometric nonlinearity, leading to a variety of perceptually-salient effects, including pitch glides and crashes. Also discussed here are input excitation and scanned multichannel output. A numerical scheme is presented that mirrors the energetic and dissipative properties of a continuous model, allowing for control over numerical stability. Furthermore, the nonlinearity in the scheme can be solved explicitly, allowing for an efficient solution in real time. The solution relies on a quadratised expression for numerical energy, and is in line with recent work on invariant energy quadratisation and scalar auxiliary variable approaches to simulation. Implementation details, including appropriate perceptuallyrelevant choices for parameter settings are discussed. Numerical examples are presented, alongside timing results illustrating realtime performance on a typical CPU.
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 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.