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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.
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John W. Coltman (2006) studied this question.
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