Composing For Improvisation with Chaotic Oscillators

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