Jet offset, harmonic content, and warble in the flute

The effects of jet offset in the flute, directing the jet above or below the edge, were explored by two distinct means-experiments with a Boehm flute sounded by an artificial blower, and time domain simulation. Very large changes in harmonic content and dynamics were observed, changing greatly with blowing pressure. Warble, a modulation of the tone at frequencies of the order of 20 Hz, was observed both in the experiment and in the simulation. The phenomenon is explained as a beat between the frequency of a second harmonic generated by nonlinearity in the jet current and a neighboring partial sustained by jet feedback near the second mode resonance. A second type of warble, in which amplitude modulation occurs in all partials but with different phases, is yet to be explained.