Recent Developments for Strings

The work of Laurson et al. [100,99] represents perhaps the best results to date in the area of classical guitar synthesis. A key factor in the quality of these results is the great attention to detail in the area of musical control when driving the model from a written score. Most of the sound examples in [162],¹³in contrast, were played in real time using physical controllers driving algorithms running in SynthBuilder on a NeXT Computer [121]. In general, it is much easier to ``voice'' a real-time algorithm driven by a physical controller than it is to synthesize a convincing performance from a written score. However, Laurson et al. show that the latter can be done very well.

In [172], Tolonen et al. developed a simplified extension to digital waveguide string models to incorporate nonlinear tension modulation. The first-order audible effect of nonlinearity in strings is an increase in pitch at high vibration amplitudes.¹⁴This occurs because the average tension is increased when the vibration amplitude is large (because the string must stretch to traverse the high-amplitude wave shape). Since tension waves travel much faster than transverse waves (more than ten times faster in piano strings [8]¹⁵), the tension increase is generally modeled as an instantaneous global effect as a function of instantaneous string length.

The 2002 thesis of Erkut [55] comprises nine publications covering analysis and synthesis of acoustic guitar, as well as other plucked-string instruments (tanbur, kantele, lute, and ud).

In [96], Krishnaswamy et al. proposed new, more physically accurate algorithms for simulating vibrating strings which strike against physical objects (for simulation of slap bass, tambura, sitar, etc.). Both a pure ``waveguide approach'' and a hybrid approach involving a ``mass-spring'' string model inside a digital waveguide are considered. The hybrid waveguide/finite-difference model enables maximally efficient simulation of freely vibrating string sections (``waveguide sections''), while also providing finite-difference sections for nonlinear interactions.¹⁶ A similar hybrid model was used by Pitteroff and Woodhouse to model a string bowed by a bow with finite with [119,120]. In [86], Karjalainen presented a systematic technique for mixing finite difference and digital waveguide simulations. More specifically, adaptors are given for converting modularly between traveling-wave components (used in digital waveguide simulations) and physical acoustic variables such as force and velocity (typical in finite difference schemes derived from differential equations).

Recent efforts to calibrate waveguide string models using a genetic algorithm are described by Riionheimo and Välimäki in [125]. The genetic algorithm was found to successfully automate parameter tunings that were formerly done by hand. The error measure is based on human perception of short-time spectra, similar to what is done in perceptual audio coding [27].