[kazinator]

> However it would be a mistake to to call flute sound simple: as you see, every level has its own regular pattern that can’t be recreated with a simple mix of sinusoidal tones.

The resonance of the flute's air chamber is driven by the noise of forced air stream, which is why it contains high frequencies at all. Of course you can't recreate the flute sound just with some periodic sinusoidals, because the noise component has to be present. The noise is complex and is itself filtered by the flute's chamber, in a different way depending on which valves are closed. You can play a recognizeable scale on a flute without getting a tone out of it, just using air noise, the same way you can produce a musical tune using chhhh sounds out your mouth. Those notes, or something like them, are still there in the background when a tone is being produced. There is no flute tone without them.