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.

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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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Stencil operations are often a key component when performing acoustics simulations, for which the specific choice of implementation can have a significant effect on both accuracy and computational performance. This paper presents a detailed investigation of computational performance for GPU-based stencil operations in two-step finite difference schemes, using stencils of varying shape and size (ranging from seven to more than 450 points in size). Using an Nvidia K20 GPU, it is found that as the stencil size increases, compute times increase less than that naively expected by considering only the number of computational operations involved, because performance is instead determined by data transfer times throughout the GPU memory architecture. With regards to the effects of stencil shape, performance obtained with stencils that are compact in space is mainly due to efficient use of the read-only data (texture) cache on the K20, and performance obtained with standard high-order stencils is due to increased memory bandwidth usage, compensating for lower cache hit rates. Also in this study, a brief comparison is made with performance results from a related, recent study that used a shared memory approach on a GTX 670 GPU device. It is found that by making efficient use of a GTX 660Ti GPU—whose computational performance is generally lower than that of a GTX 670—similar or better performance to those results can be achieved without the use of shared memory.

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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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