I'm thinking particularly of thermionic triode valves (tubes) here, but I suppose the reasons are probably similar whether it's a bipolar, jfet, mosfet etc... If your not sure about valves, a triode is super simple. It's just a hot cathode that emits electrons thermionically, an anode that pulls the subsequent electron cloud towards itself and grid near the cathode with a negative voltage on it that's used to control the current flow by electrostatic repulsion. Why, when a current flows through these devices, and particularly as they go into cliping, does that current suddenly fracture into harmonics? Since the fracturing occurs at integers of the fundamental, I'm guessing that it has something to do with energy (somehow) being injected / removed at the centre of the wavelength of the oscillation. I understand, from playing the electric guitar, that if I tap a string halfway along it's length (inject energy at this point) I cause the harmonic pattern to redistribute itself so as to produce a waveform with more and / or higher harmonic components. And that if I put diodes on a big coil, like a transformer's winding, the reverse current can cause ringing in the coil. In this instance, energy stored in the capacitance of the diode is being injected back into the coil and, I assume, it's because that energy re-enters the coil just as the waveform on it reaches halfway that it produces a harmonic on it; or that the period of the discharge happens to be double the frequency of the original waveform, although that would be one unlucky stroke of coincidence. But I'm wondering what it is that causes the electrons to do the same as a processing element begins to clip off the current flow. The harmonic pattern seems quite closely related to the way in which the clipping off occurs, which suggests that the generation of the harmonics is closely related to this process as well. Also, if my electrons now have twice the oscillating frequency of the fundamental, they should be oscillating at twice the velocity right? For some reason I'm getting pictures of the 'water hammer' effect you get when you shut a valve off quickly. The interruption in the flow causes a pressure wave to shudder back through the pipes. But I don't think those sudders are related to any fundamental, just the design of the pipe system. Whereas the 'shuddering' as a current flow is clipped is specifically related to the fundamental frequency and even changes depending on the frequency of that fundamental. I expect this effect also occurs, at minute levels, as the electrons pass through the crystal boundaries in a real world conductor. Any ideas?