Introduction

In this reader, we discuss methods for real-time synthesis of stringed instruments. Interest in this topic is wide and varying, as both studio and performance uses for realistic virtual stringed instruments are becoming increasingly possible with gains in computing power.

Having a high-fidelity physics-based virtual stringed instrument model is useful for many applications. Current sample-based synthesizers, which are based on audio recordings, do not allow fine control of the excitation of the strings of the instrument. Synthesizers based on physical models, in contrast, promise unlimited control over the expressive nuances of string excitation. The synthesis parameters are also more intuitive, since they have corresponding meanings in the physical world. Changing intuitive parameters can result in more realistic changes to the sound produced.

Another of many applications includes automatic transcription and resynthesis of old recordings. Given that there is a mechanism for processing old recordings and mapping them to how they were played on the instrument, with a high-fidelity synthesis model and the necessary performance parameters, resynthesis of old recordings can be made to sound like what they would, had they been made with today's technology. Figure 1 shows the block diagram of such a system. The focus of this reader is on the third circled block, the physical model of the plucked stringed instrument.

Figure 1: Block diagram of a performance parameter estimation and resynthesis of old recordings application.

The goal of this reader is to outline procedures for making a virtual stringed musical instrument based on a combination of physical theory and laboratory measurements from a real instrument. Since this topic is too large to be covered in the available space, we will make extensive use of pointers to supporting information. In addition to the traditional bibliographic citations, we will refer the reader to additional online books, related websites, and laboratory exercises covering elementary models and techniques used. Our goal is to make it possible to follow links in this reader in order to flesh out the complete details of the theory and practical techniques summarized here. For the advanced reader (such as a seasoned graduate student working in the area of virtual musical instrument design), this reader will hopefully prove sufficiently self-contained to be used as a laboratory guide.

In the following sections, we briefly review elementary components of stringed musical instruments and how they may be modeled efficiently for real-time digital synthesis applications. We then summarize practical measurement and calibration techniques for various instrument modeling components. Finally, we discuss methods specifically for estimating parameters of a plucked stringed instrument.

A useful abstraction that illustrates our modeling approach for virtual stringed instruments is shown in Figure 2. Not only is this decomposition useful for compartmentalizing from a modeling perspective, it is useful in performing measurements on the instrument as well as following the physical flow of how a stringed instrument is played: energy injected into the system to how energy reaches our ears by pressure waves created by the vibration of the instrument's body.