Investigation of phase coupling phenomena in sustained portion of musical instruments sound

This work investigates aperiodicities that occur in the sustained portion of a sound of musical instrument played by a human player, due to synchronous versus asynchronous deviations of the partial phases. By using an additive sinusoidal analysis, phases of individual partials are precisely extracted and their correlation statistics and coupling effects are analyzed. It is shown that various musical instruments exhibit different phase coupling characteristics. The effect of phase coupling is compared to analysis by means of higher order statistics and it is shown that both methods are closely mathematically related. Following a detailed analysis of phase coupling for various musical instruments it is suggested that phase coupling is an important characteristic of a sustained portion of sound of individual musical instruments, and possibly even of instrumental families. Interesting differences in phase deviations where found for the flute, trumpet and cello. For the cello, the effect of vibrato is examined by comparing the analysis of a closed string sound played with a natural vibrato to analysis of an open string sound that contains no vibrato. Following, a possible model for phase deviations in the cello is presented and a simulation of phase fluctuations for this model is performed.