In comparison to the string tension force (50 – 200 N) the magnetic forces are very small; the lateral string displacement caused by them is less than 0.1 mm. Nevertheless, the effect of the magnetic field must not be totally ignored, because its stiffness changes the frequency of the string. The nearer the string comes to the magnet, the more it is pulled. [...]
4.11.2 Field-Induced Deviations of the Tone Frequency
When a magnetic pickup approaches a string, three effects can be anticipated: The tone frequency decreases, chorus-like beat frequencies evolve and the amplitude changes. The frequencies, especially the fundamental, will decrease due to the negative field stiffness, which can be audible for large values. The detuning between the fretboard-normal and fretboard-parallel vibrations induces beat frequencies; the altered frequency relationship between the partial tones in the subsequent non-linear systems causes additional partial tones, which can further increase the chorus impression. True damping, i.e. removal of vibrating energy, occurs only to a negligible extent. [...]