VERY BASIC PHYSICS OF THE FLUTE
The sound is created by “cutting” the air against the edge of one end of an open pipe (both ends are open.) Even though the flute *looks* like it is open on only one end (the bottom), the mouth hole also acts as an open end, creating vibrations with antinodes on both ends of the tube.
Flute players can change the pitch by changing the length of the tube with the fingers see above (how one plays the fundamentals of the first octave) or by increasing the air speed in order to force the sound waves to the next note in the harmonic overtone series (see below).
Each fundamental on the flute has the ability to produce both even and odd harmonics of the harmonic overtone series. Fundamental notes exist on all chromatic notes between B3 and Eb5 (as seen below). By increasing the air speed, a flute player is able to produce different partials of a note without changing their fingering. Technically, one could play every chromatic note on the instrument this way, but many harmonics are out of tune, difficult to produce accurately at all, but especially in fast passagework, have variable volume level, and are often "weak" or "ghostlike". This can make for incredibly beautiful color, but where the harmonics run into one of the issues above, an alternate fingering is used. Please see the charts below for all possible harmonics on the flute. Please note, that the lowest fundamentals are capable of achieving harmonics that are much further up in the harmonic overtone series, while the higher fundamentals are only capable of achieving the first few overtones.
As you can see, notes can be played with varying fundamental fingerings. This is how we can create timbril trills, or play the same note while giving the illusion that the harmony is changing.
Learn more about flute physics and see lots of diagrams at these places: