Page  324 ï~~COMPOSITION BY EX NON-LINEAR DYNAi Agostino Di Sc C.S.C. University c Via S. Francesco, 11 - 351 Abstract: This paper briefly reports on the auti dynamic systems; Whereas most mathematical support pitch- and duration- oriented compos far more concerned with formal articulation a applied: some examples are provided reg organization; further examples are discussed it is in direct relation to the design of sound struct of granular sound synthesis and elaboration. Introduction. In a series of compositions I have bee systems. The evolution of these system is unpredict shows alternatively both ordered structures and chaoti

Page  325 ï~~sometimes in our work rescaled to be a 1). T attracted, (2) limit-cycles attracted, (3) chaotic. 4f on. Beyond a certain threshold (a 3.569946) ch (also of odd-number cycles) eventually emerge. This kind of system is explored 'in depth wi ax i4 1(ax2 1-1 where a-parameter is kept constant (a 4, chaotic ics" the derivative function of the ou a-parametrer of a gaussian distribution of events wi words the probability density function is f(x) 2;r(y1 + -y The progressive removal of sounds from the central in successive "frames" is almost linear for a whil aleatoric, with differently sized changes; the hidden is difficult to perceive, of course, but it is felt defii -- - I * Iw. w.. 1.

Page  326 ï~~from discrete sonic images to audio rate intermodulatio of sound [McAdams & Bregman 1979]. No doubt, how( and strictly linked to much specific aesthetics. Our effor sonic by-products of previous use of this technique. Let's define a digital sound grain as a sequenc sequences of more than two 0-samples on the time-axis. as a long "vocabula ' of sound units, whose number c Our software system was designed to accomplish the I previously digitalized or synthesized signal; (2) perfo granulated sound according to various segmentation equation systems of the kind we have seen before; (5) i finite and integerly numbered "vocabula of grains an a new.sound file. (As for larger scale applications, sc programming environment with 8 bytes numerical precis The granulation the 2nd step claims for, is performed v samples by the signal s(t) [sin (2x a (t) where the length of a single gain hannens to be dener

Page  327 ï~~conception of "convenient" materials as the actual cc using a n.1. system for direct sound synthesis (as in "evei been tested: (1) a linear frequency sweeping sine fr logarithmic (or even an exponential) frequency sweet non-integer ratios (given some reference frequency) output signal (this third technique is largely indebted Deterministic chaos procedures seem to be e musical problem: an unusual experiencing of time w the traditional "logical continuity" wherever claimed (having approached music definitely as a "language") f 4 the repercussion of the established, whose sense is he a new conception of time as suggested by non-rever, 1988], in which time is not where the events are but is take time, it is time; these are some general categorP closely linked to musical creative experience. However I do not propose a mere translatio Henon's attractor! Once again purely formalized pro( they only aid us in sensed motion throughout and w ordered oscillation to turbolence, and. eventually. bac