Abstract
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 sound synthesis algorithm is designed, by simulating two-polarisation string motion, discretising the partial differential equations governing the string’s behaviour with 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. The dynamic input parameters allow for simulating a wide range of gestures; some typical bow and left hand gestures are presented, along with synthetic sound and video demonstrations.
Highlights
Sound synthesis techniques for string instruments have evolved, in the past few decades, from abstract synthesis [1] (wavetables, frequency-modulation (FM) synthesis . . . ) towards sampling synthesis, based on a library of pre-recorded sounds, and physical models, emulating the instruments themselves
The best synthesised sound quality is achieved by sampling techniques; the potentially very large storage requirements for these sound libraries are a major argument for using physical models
The use of a physical model allows for great flexibility for input parameters, as well as output parameters, usually the “listening conditions”, that can be changed freely and dynamically along a simulation, as opposed to the case of statically recorded samples
Summary
Sound synthesis techniques for string instruments have evolved, in the past few decades, from abstract synthesis [1] (wavetables, frequency-modulation (FM) synthesis . . . ) towards sampling synthesis, based on a library of pre-recorded sounds, and physical models, emulating the instruments themselves. The player shapes the sound and behaviour of his instrument throughout the whole production of a note Their gestures can be described with a handful of parameters, which must be perfectly coordinated at all times to allow a tone to be created and sustained; Schelleng [21], following the work of Raman [22] some decades earlier, was the first to analytically show that, under simplifying assumptions and for a certain bow velocity, only a relatively narrow triangular area (in logarithmic scale) in the downwards bow force versus bow-bridge distance parameter space gave rise to the characteristic stable Helmholtz motion desired by most musicians (his work was revised by Schoonderwaldt et al [23], introducing more refined elements of bowed string motion). Some sound and video examples from the computed simulations are available online [41]
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