Acoustics of classical and modern flutes - impedance spectra,
sound spectra, sounds and fingerings
Joe Wolfe, John Smith, John Tann and Neville H. Fletcher
Finger holes have important acoustic influence both when closed (when they contribute small extra volumes to the bore) and when open (when they provide an inertive shunt to the outside air). The internal standing wave in the flute bore always extends some distance past the first open hole (which is why "cross-fingerings" work to produce semitones) and, in the case of notes in the third octave, along the whole bore (which is why high-octave fingerings are complex) .
Benade  has examined the behaviour of a row of open finger holes and concluded that they act as a high-pass filter, the cut-off frequency being determined by the hole size and spacing in such a way that small holes give a low cut-off frequency, this frequency typically being in the range 1500-2000 Hz. Above the cut-off frequency, waves propagate rather freely along the instrument bore and are not reflected, hence eliminating high-frequency resonances and reducing the strength of higher harmonics in the tone. It is largely for this reason that classical flutes sound 'mellow', with a cut-off of around 1500 Hz on most fingerings, while the modern flute is much 'brighter' in tone quality, having a cut-off somewhat above 2000 Hz. This cut-off frequency also limits the pitch of the highest note playable on the instrument, about A6 on a classical flute and about F7 on a modern flute.
While the tone holes on a modern flute are all nearly the same size, the finger holes on a classical flute are much smaller and have different diameters, partly to bring their positions conveniently under the fingers, and partly to adjust the intonation on cross-fingered and high-octave notes. This means that the tone quality is not completely uniform from one note to another across the compass of the instrument, a feature regarded as a deficiency in modern music, but sometimes exploited to advantage in music of earlier centuries.