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In a highly stimulating Science article, Max Mathews painted an exciting vision of ``the digital computer as a musical instrument'' [7]. ``Sound from numbers,'' it pointed out, was a completely general way to synthesize sound because the bandwidth and dynamic range of hearing are bounded: ``any perceivable sound can be so produced.'' In The Technology of Computer Music [8], Mathews wrote

``The two fundamental problems in sound synthesis are (1) the vast amount of data needed to specify a pressure function--hence the necessity of a very fast program--and (2) the need for a simple, powerful language in which to describe a complex sequence of sounds.''

Problem 1 has been solved to a large extent by the march of technology. Digital processor performance has increased at the rate of more than 40% per year for the past fifteen years, and the trend shows no sign of weakening. At present, multiple voices of many synthesis techniques can be sustained in real time on a personal computer.

Problem 2 remains unsolved, and cannot, in principle, ever be completely solved. Since it takes millions of samples to make a sound, nobody has the time to type in every sample of sound for a musical piece. Therefore, sound samples must be synthesized algorithmically, or derived from recordings of natural phenomena. In any case, a large number of samples must be specified or manipulated according a much smaller set of numbers. This implies a great sacrifice of generality.

The fundamental difficulty of digital synthesis is finding the smallest collection of synthesis techniques that span the gamut of musically desirable sounds with minimum redundancy. It is helpful when a technique is intuitively predictable. Predictability is good, for example, when analogies exist with well-known musical instruments, familiar sounds from daily experience, or established forms of communication (speech sounds).

The rest of this essay sketches one view of the development of digital synthesis techniques from the days of Max Mathews's experiments to the present. In the first half we present experiences with synthesizer hardware and assess the current state of the art. The second half begins with a taxonomy of synthesis techniques, from which we extrapolate future trends. We anticipate that synthesis in the future will be dominated by spectral and physical models. Spectral models are based largely on the perception of sound, while physical models are based on mathematical descriptions of acoustic musical instruments.

Sound synthesis and signal processing are inherently technical subjects. Although mathematical details will not be presented, this essay assumes familiarity with the engineering concepts behind computer music, particularly a conceptual understanding of a variety of sound synthesis techniques. For a general introduction to this field, see [16,14,15], and back issues of the Computer Music Journal.

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``Viewpoints on the History of Digital Synthesis'', by Julius O. Smith III, Proceedings of the International Computer Music Conference (ICMC-91, Montreal), pp. 1-10,
Computer Music Association, October 1991.
Revised with Curtis Roads for publication in Cahiers de l'IRCAM, September 1992, Institut de Recherche et Coordination Acoustique / Musique.
Copyright © 2005-12-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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