Scanned Synthesis

This paper describes a new technique for the synthesis of musical sounds which we have named Scanned Synthesis. Scanned Synthesis is based on the psychoacoustics of how we hear and appreciate timbres and on our motor control (haptic) abilities to manipulate timbres during live performance. A unique feature of scanned synthesis is its emphasis on the performer's control of timbre. Scanned synthesis involves a slow dynamic system whose frequencies of vibration are below about 15 hz. The system is directly manipulated by motions of the performer. The vibrations of the system are a function of the initial conditions, the forces applied by the performer, and the dynamics of the system. Examples include slowly vibrating strings and two dimensional diffusion equations. To make audible frequencies, the "shape" of the dynamic system, along a closed path, is scanned periodically. The pitch is determined by the speed of the scanning function. Pitch control is completely separate from the dynamic system control. Thus timbre and pitch are independent. This system can be looked upon as a dynamic wave table controlled by the performer. 1. PSYCHOPHYSICAL BASIS The psychophysical basis for Scanned Synthesis comes from our knowledge about human auditory perception and human motor control abilities. In the 1960's Risset showed that the spectra of interesting timbres must change with time. We observe that musically interesting change rates are less than about 15 hz which is also the rate humans can move their bodies. We have named these rates Haptic rates. In the middle 1960's Jean-Claude Risset (1969a, 1969b) demonstrated that in order to make good simulations of traditional instruments the spectrum must change with time over the course of a note. For example, in a brass timbre, the proportion of high frequency energy in the spectrum must increase as the intensity of the sound increases at the beginning (attack part) of a note. 2. HAPTIC FREQUENCIES Over the last decades, many extensions of Risset's work led to a better understanding of the properties of spectral time variations that the ear hears and the brain likes. Spectral time variations can also be usefully characterized by their frequency spectrum. These frequencies are much lower (typically 0 to about 15hz) than audio frequencies (50hz to 10000hz). Either by a happy accident of nature or because of the way human beings are built, the frequency range of spectral changes the ear can understand is the same as the frequency range of movements of our body parts--arms, fingers, articulators, etc--that we can consciously control. Scanned synthesis provides methods for directly manipulating the spectrum of a sound by human movements. At present the terminology with which to describe spectral time variations is not well established. Some kinds of spectral time variations, particularly vibrato and tremolo, are called modulations. But other kinds, such as occur in brass timbres are unnamed. We here propose the name haptic frequencies to characterize these variations. 1) Manipulate 2) Scan Figure 1. Scanned Synthesis consists of 1) manipulating a dynamic system and 2) scanning out a wave-shape from along a path. 3. SCANNED SYNTHESIS The essence of scanned synthesis is to use a slowly vibrating object whose resonant frequencies are low enough so the performer can directly manipulate the object's vibrations by motions of his body and to scan (measure) the shape of the object along a periodic path by a periodic scanning function whose period is the fundamental frequency of the sound we wish to create. The scanning function translates the slowly changing spatial wave shape of the object into a sound wave with audio frequencies which the ear can hear. Scanned synthesis can be looked upon as a descendent of wave table synthesis. In wave table synthesis, points in a function of one independent variable are computed and stored in successive memory locations in a computer. This chunk of memory (the wave table) is scanned or read by a periodic scanning function to produce the samples of the audio sound wave. The period of the scanning function is the period of the synthesized sound. The scanning process is computationally simple and efficient. The computation of the wave table need only be done once, and thus can be computationally intensive. Controllers Performer audio D/A