# Non-linearity of a guitar pickup

I basically understand induction and why a pickup generates a signal.

What I don't understand, and this is the nature of my question, is the following:

When a string moves back and forth in front of the pickup, then the pickup will be unable to tell if the string moves left or right. Apart from the fact that one side will be closer to the edge of the pickup (which should be negligible), the system is symmetric and the two directions are indistinguishable.

However, then the pickup would not produce the fundamental. The lowest frequency would be twice the fundamental and due to the non-linearity, the signal would contain even harmonics, i.e. it will be distorted. Yet the response curve cannot be a simple square function, because the sensitivity decreases as the string moves further away from the pickup

Still we do hear the fundamental. This would leave one explanation: in addition to moving back and forth, the string must also move up and down. This will also produce distortion, because a vibrating string a meter away will not produce any signal at all which tells us there must be another, possibly smaller non-linearity involved.

• How does the string actually move?
• What would be the response curve of a pickup?

Both desriptive explanation and formulas are welcome as an answer.