Methods for Modeling Realistic Playing in Acoustic Guitar Synthesis

Sound synthesis based on physical modeling of stringed instruments has been an active research field for the last decade. The most efficient synthesis models have been obtained using the theory of digital waveguides (Smith 1992). Commuted waveguide synthesis (Smith 1993; Karjalainen et al. 1993) is based on the linearity and time-invariance of the synthesis model and is an important method for developing a generic string instrument model. Recently, such a model has been presented including consolidated pluck and body wavetables, a pluck-shaping filter, a pluck-position comb filter, string models with loop filters and continuously variable delays, and sympathetic couplings between the strings (Karjalainen et al. 1998).

Our model is realized in a real-time software synthesizer called PWSynth. PWSynth is a user library for PatchWork (Laurson 1996) that attempts to effectively integrate computer-assisted composition and sound synthesis. PWSynth is a part of our project that investigates different control strategies for physical models of musical instruments. PatchWork is used also to generate control data from an extended score representation, the Expressive Notation Package (ENP) (Laurson et al. 1999; Kuuskankare and Laurson 2000; Laurson 2000).

Calibration of the synthesis model is based on the analysis of recorded guitar tones (Välimäki et al. 1996; Tolonen 1998). A recent article (Erkut et al. 2000) addressed the revision of the calibration process to improve efficiency and robustness. It also proposed extended methods to capture information about performance characteristics such as different pluck styles, vibrato, and dynamic variations of a professional player. In addition, the article presented basic techniques for simulation of the transients. Instead of using a detailed finger-string interaction model like that proposed by Cuzzucoli and Lombardo (1999), the simulation consolidates all the transient effects into the excitation signal and the update trajectories of the model parameters.

The current article summarizes our achievements in model-based sound synthesis of the acoustic guitar with improved realism. First, a simplified physical model of a string instrument realized in our work is described. The next section discusses the calibration of the synthesis model. Then, we address controlling the synthesizer using ENP. After this, we provide an overview of the real-time synthesizer PWSynth. The final section discusses how we simulate various playing styles used in the classical guitar repertoire. Musical excerpts related to this article will be included on the forthcoming Computer Music Journal 25:4 compact disc.

Structure of the Synthesizer

We have implemented a string instrument model that is based on the principle of commuted waveguide synthesis. We now present both the basic string model and a guitar string model that contains two basic models.

Basic String Model

A model for a vibrating string is the only part of the system that explicitly models a physical phenomenon. Our string model implementation is illustrated in Figure 1. It is a feedback loop that contains a delay line and two digital filters, as suggested previously in the literature (Jaffe and Smith 1983; Välimäki et al. 1996). The input signal x(n) of the system is obtained from a recorded guitar tone, as described later. The digital filter seen in Figure 1 inside a box drawn with a broken line is called the loop filter. Its output signal is computed as

y₁(n) = b(n)y(n) - a(n)y₁(n-1)         (1)

where n is the discrete time index, a(n) is the feedback coefficient, and b(n) = g(n)[1 + a(n)] is the gain coefficient of the loop filter. The magnitude of both g and a must be less than 1 to ensure that the feedback loop will be stable. Usually, g is slightly smaller than 1 and a is slightly smaller than 0, in which case the filter has a gentle lowpass characteristic. Note that the loop-filter coefficients a(n) and b(n...