If you know the resonant frequency and height of the resonant peak, you know about 90 percent of a pickup's transfer characteristics; these two parameters are the key to the "secret" of a pickup's sound (some other effects cannot be described using this model, but their influence is less important).
What all this means is that overtones in the range around the resonant frequency are amplified, overtones above the resonant frequency are progressively reduced, and the fundamental vibration and the overtones far below the resonant frequency are reproduced without alteration.
How Resonance Affects Sound
The resonant frequency of most available pickups in combination with normal guitar cables lies between 2,000 and 5,000 Hz. This is the range where the human ear has its highest sensitivity. A quick subjective correlation of frequency to sound is that at 2,000 Hz the sound is warm and mellow, at 3,000 Hz brilliant or present, at 4,000 Hz piercing, and at 5,000 Hz or more brittle and thin. The sound also depends on the height of the peak, of course. A high peak produces a powerful, characteristic sound; a low peak produces a weaker sound, especially with solid body guitars that have no acoustic body resonance. The height of the peak of most available pickups ranges between 1 and 4 (0 to 12 dB), it is dependent on the magnetic material in the coil, on the external resistive load , and on the metal case (without casing it is higher; many guitarists prefer this).
The resonant frequency depends on both the inductance L (with most available pickups, between 1 and 10 Henries) and the capacitance C. C is the sum of the winding capacitance of the coil (usually about 80 - 200 pF) and the cable capacitance (about 300 - 1,000 pF). Since different guitar cables have different amounts of capacitance, it is clear that using different guitar cables with an unbuffered pickup will change the resonant frequency and hence the overall sound.
