Partials

The picture beneath shows the harmonics for C1 in the range of the flute:

The harmonics are build by the partials, if you leave the base tone. While playing the flute, the harmonics are essential for overblowing. The change of embouchure to play the higher octave, leads without changing the fingerings to the double frequency of the lower tone. This is the first harmonic or second partial at the same time.

For some notes of the second octave (d and dis) the opening of one key gives am easier response. The open key gives a so called overblow hole (like a octave key for other woodwinds).

Fork fingerings, which are very often found in the third octave, are not mainly for shortening the air column but to open a hole near the point, where inside the flute an additional pressure knot should be. The open hole is called soundhole and help to increase the frequency.

Thus the F3 might be played by three times overblowing F1 or by two times overblowing B1. The fingering for F3 combines the fingerings of both bases (F1 or B1). By lifting the middle finger of the left hand, the opened hole is at the position of the last hole of B1.