Coupled‐Oscillator Systems

Abstract

Professor Miller Puckette, Chair Coupled Oscillator Systems (COS) are presented as a method for sound synthesis and musical instrumentation. Seven systems ranging in size from 3 to 9 oscillators are described with different arrangements all containing a topology of velocity based coupling terms. First, each system is described mathematically. Then, each system is analyzed with recurrence plots and recurrence quantification analysis. The analysis characterizes the non-linear dynamics of the output signals and shows why certain ways of structuring COS may be preferable to others. The goal of the COS designs presented is to increase the non-stationarity of the signal, while also increasing the coherence of the phase transistors over an (quasi-) attractor landscape. Varieties of dynamical phenomena are located and quantified, such as drifts, phase transitions and higher xiii order periodicities. The durations of residence in attractors also reflected higher order temporal proportions. Of key interest, as found by analysis, was the presence of chaotic itinerancy (CI).Orderly CI in neural dynamics corresponds to production of intentional sequences of action and thought. Here cases of synthesis dynamics are located that reflect the quantitative aspects of orderly itinerancy and as a result the production of abstract musical sequences with perceived intentional organization. A theoretical chapter considers novel concepts, such as, extended and embedded intentionality in conjunction with auditory cues to discuss the implications of this tool as an instrument for musical improvisation. Finally, if the phenomena produced by a COS sound musical and are consistent with the phenomenon of CI observed in the brain, can we consider the brain and its dynamics to be a kind of musical phenomenon itself? xiv