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F#7 and G7 on the Boehm flute
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The Virtual Flute, when adjusted for maximum sensitivity in our laboratory, predicts that the notes F#7 and G7 are at the very limits of playability (see note names). The fingerings predicted are shown below.

F#7 B foot

Th     3   | 1   3 D# C# 
Th 1   3   | 1   3 D# C#
Th 1   3   | 1   3 D# C# gizmo

F#7 C foot

Th     3   | 1   3 D# C

G7 B foot

Th   2 3    |   2   tr1 C B

G7 C foot

Th   2 3 G# |   2

Our resident flutist, Jane Cavanagh, can play these notes for short durations, but they are of limited musical use.

There are simple acoustical reasons why the flute does not have helpful resonances in the upper half of its fourth octave. In this frequency range, the acoustic impedance of the volume of air between the cork and the embouchure hole dominates the effects of the main bore. (See Flute Acoustics.) If you look at any of the theoretical or measured impedance curves, you will see that the curves have little structure in the range 3 to 4 kHz. It is possible to shift this effect of the upstream air to higher frequencies by moving the cork closer to the embouchure hole. This does allow you to play higher notes, but it has highly undesirable consequences on the internal tuning of the instrument. The fingerings given above were predicted and played with the normal cork position, 17.5 mm beyond the centre of the blow hole.

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