Introduction

The ``virtualization'' of traditional musical instruments is well under way.<sup>2</sup> For many instrument families (such as plucked strings), it is possible to devise real-time computer algorithms which produce sound so realistic that most people cannot distinguish the synthesized sound from real recordings, under normal listening conditions.<sup>3</sup> This development enables a fork in the future evolution of traditional musical instruments. Down one fork is the continued refinement of traditional instrument making. Down the other lies a potentially large variety of new realizations in terms of sensitive physical controllers coupled to sound rendering engines. In ``traditional mode,'' a sound rendering engine may implement a virtual acoustic sound synthesis algorithm; alternatively, there is no limit to the range of new sounds controllable by the player. A schematic depiction for the case of bowed strings is shown in Fig. 1. While controllers may continue to resemble traditional musical instruments, due to player preference, they will be freed of the responsibility for quality sound production. Instrument makers will be able to focus instead on the playability of the controller [202], without compromising ease of play for better sound. As an example, the body of the double-bass can be made closer to that of the cello, or eliminated entirely, leaving only the strings, fingerboard, and suitable bracing, as in Chris Chafe's celletto, shown in Fig. 2. In summary, it is now possible to factor traditional musical instruments into the ideal controller for that instrument, together with a matched synthesis engine.

Figure 1: Virtual bowed string instrument (from [145]). A bow with embedded sensors (developed by Diana Young) is connected wirelessly to a real-time bowed-string physical model (written by Stefania Serafin). (From [150].)

Figure 2: Chris Chafe playing the celletto--a block of solid maple with a piezo-ceramic pick-up under each string (inlaid by Max Mathews). The pick-up signals are processed externally.

Note that matching a controller to its synthesis algorithms in the context of a particular instrument family, as obvious as that may sound at first, is still a relatively novel subject. This is because most commercially available synthesizers are designed to be driven by keyboards and the Musical Instrument Digital Interface (MIDI) standard.⁴ As a result, there is often an unavoidable delay, or latency between controller signals and the synthesizer response. MIDI itself introduces up to three milliseconds of delay for each musical note, and there is often much more delay than that associated with sound buffering. These delays are often unacceptable to serious performing musicians. For string controllers, it is typical to drive a synthesizer using the measured pitch of the string vibration. However, at least a period of vibration must pass before the synthesizer can respond, and one period is too long to wait. For example, a note near the bottom range of the guitar has a period larger than 10 milliseconds. This delay is comparable to that of being more than 10 feet away, and few players can put up with it except within a narrow range of playing styles. When the controller and synthesis algorithm are matched, such delays are easily eliminated. As a simple example, when a guitar string is plucked, the initial sound is independent of the pitch of the note (since that is determined by later acoustic reflections on the string). A matched synthesis algorithm can emit the initial signal immediately, well before the pitch is known. In short, a virtual acoustic synthesis algorithm can simulate the physical response of a desired instrument with no perceivable latency whatsoever. Few musicians have yet experienced this degree of virtual instrument playability.

This article will focus on synthesis algorithms for virtual acoustic instruments, neglecting the important companion topics of controllers and controller-algorithm interfaces [197]. Moreover, we will restrict attention here to synthesis of traditional musical instruments, such as strings and winds, leaving aside the many new variations which become possible in this domain, such as ``bowed pipes,'' ``reed-driven strings,'' and impossibly large instruments, to name a few. We will also emphasize methods which are, in the opinion of the author, most cost-effective for delivering maximum sound quality and playability.