Tero Tolonen

Modeling of tension modulation nonlinearity in plucked strings

A nonlinear discrete-time model that simulates a vibrating string exhibiting tension modulation nonlinearity is developed. The tension modulation phenomenon is caused by string elongation during transversal vibration. Fundamental frequency variation and coupling of harmonic modes are among the perceptually most important effects of this nonlinearity. The proposed model extends the linear bidirectional digital waveguide model of a string. It is also formulated as a computationally more efficient single-delay-loop structure. A method of reducing the computational load of the string elongation approximation is described, and a technique of obtaining the tension modulation parameter from recorded plucked string instrument tones is presented. The performance of the model is demonstrated with analysis/synthesis experiments and with examples of synthetic tones.

Plucked-string synthesis algorithms with tension modulation nonlinearity

Digital waveguide modeling of a nonlinear vibrating string is investigated when the nonlinearity is essentially caused by tension modulation. We derive synthesis models where the nonlinearity is implemented with a time-varying fractional delay filter. Also, conversion from a dual-delay-line physical model into a single-delay-loop model is explained. Realistic synthetic tones with nonlinear effects are obtained by introducing minor amendments to a linear string synthesis algorithm. It is shown how synthetic plucked-string tones are modified as a consequence of tension modulation.

New techniques and effects in model-based sound synthesis

Physical modeling and model-based sound synthesis have recently been among the most active topics of computer music and audio research. In the modeling approach one typically tries to simulate and duplicate the most prominent sound generation properties of the acoustic musical instrument under study. If desired, the models developed may then be modified in order to create sounds that are not common or even possible from physically realizable instruments. In addition to physically related principles it is possible to combine physical models with other synthesis and signal processing methods to realize hybrid modeling techniques. This article gives an overview of some recent results in model-based sound synthesis and related signal processing techniques. The focus is on modeling and synthesizing plucked string sounds, although the techniques may find much more widespread application. First, as a background, an advanced linear model of the acoustic guitar is discussed along with model control principles. Then the methodology to include inherent nonlinearities and time-varying features is introduced. Examples of nonlinearities are studied in the context of two string instruments, the kantele and the tanbur, which exhibit interesting nonlinear effects.