Composing For Improvisation with Chaotic Oscillators

This paper describes a novel method for composing andimprovisation with real-time chaotic oscillators. Recentlydiscovered algebraically simple nonlinear third-order differential equations are solved and acoustical descriptors relating to their frequency spectrums are determined accordingto the MPEG-7 specification. A second nonlinearity is thenadded to these equations: a real-time audio signal. Descriptive properties of the complex behaviour of these equationsare then determined as a function of difference tones derived from a Just Intonation scale and the amplitude ofthe audio signal. By using only the real-time audio signalfrom live performer/s as an input the causal relationshipbetween acoustic performance gestures and computer output, including any visual or performer-instruction output,is deterministic even if the chaotic behaviours are not.