Flute Headjoint Cork Position and Damping of Higher Modes

Abstract

The effect of embouchure hole size and cork position on tuning of the flute normal modes (input admittance maxima) is well known (Benade and French, 1964). The observation that the “stuffiness” of the higher played modes rises sharply as the cork is pulled is familar to flutists. The fact that perceived “stuffiness” correlates well with the physical damping parameter tanhαL suggests examination of the real part of the admittance function. For a tube of radius α and length L jointed to a head cavity of length r at an embouchure hole of radius b and length t, the imaginary part of the admittance has maxima at frequencies that are near fn = nc/2[L+r+(a/b)2t]. However the damping (contributed mainly by the pipe) has a maximum near fm = (2m−1)(c/4L). Going up the series, the fn's precess toward some fm. We find the damping (and stuffiness) rises rapidly, the resonances being completely obliterated in the immediate neighborhood of fm. The resonances reappear beyond fm but are not usually playable for other reasons. The highest notes attainable on any flute vary with the cork position in agreement with predictions based on measured and/or calculated admittance values at the embouchure hole. Also, a suitably chosen cork position will slightly raise the admittance of the first few flute resonances above simple pipe values, improving the response of the instrument.