Thus, there's no way to get from c'' to d'' with a minor change in fingering- unless you use the trill keys, which are there for exactly that purpose. That's why you have to move so many fingers going from c'' to d'': you're going from the highest note of the fundamentals, with all fingerholes open, to the lowest of the second harmonics, with almost all fingers down. Starting with the next tone higher from c'', d'', the sound is produced not by playing the first harmonic, but rather the second, which is twice the frequency of the first, or an octave higher. This is the lowest sound you can get for any given fingering. Basically (leaving out a few keys for the moment) the modern flute plays the notes in the first octave of its range, from c' (middle C) to c'' (an octave higher), by successively opening fingerholes, effectively shortening the playing length of the tube, and sounding what's called the fundamental tone (also known as the first harmonic). In order to answer your questions completely, we must understand a little about how a flute works.
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