Musical Sound Synthesis by Means of Two-Variable Functions: Experimental Criteria and Results

The main purpose of our research has been to study and to experiment with a synthesis technique by which we can dynamically control time-varying spectra using a small number of parameters. We have studied and experimented with the technique introduced in (Mitsuhashi 1982), and we have implemented the technique on a digital signal processor (a Digital Music Systems DMX-1000) for real-time synthesis and on a Fairlight CMI Series IIX (controlled via a DEC VAX-1I1/750) for interactive experimentation and composition. The technique is based on the sampling of a two-variable function along a particular orbit; the orbit is calculated by expressions that represent time-dependent relations of the two variables. We can control the dynamic development of spectra by varying time-dependent and/or timeindependent parameters within the orbit expressions. The waveforms we obtain, as will be seen later, can be either periodic or aperiodic. As this technique gives us many new possibilities of synthesis control, we think that it will be useful to carry out systematic experimentation in order to identify suitable criteria for varying functions and orbital parameters.