Humbuckers

One problem with single coil pickups is that — along with the musical signal — they also pick up mains hum. Mains hum consists of a fundamental signal at a nominal 50 or 60 Hz, depending on local alternating current frequency, and usually some harmonic content. The changing magnetic flux caused by the mains current links with the windings of the pickup, inducing a voltage by transformer action.
To overcome this effect, the humbucking pickup was developed, concurrently and independently by Seth Lover of Gibson and Ray Butts, working for Gretsch. Who developed it first is a matter of some debate, but Seth Lover was awarded the first patent (U.S. Patent 2,896,491). Ultimately, both men developed essentially the same concept.
A humbucking pickup, shown in the image on the right, is comprised of two coils. Each coil is wound reverse to one another. However, the six magnetic poles, are opposite in polarity in each winding. Since Ambient hum from power-supply transformers, radio frequencies, or electrical devices reaches the coils as common-mode noise, and induces an electrical current of equal magnitude in each coil. The sine wave signals in each pickup, created by the electro-magnetic interference, are equal, and are 180 degrees out of phase to one another. This is due to the reverse winding of the pickup coils. And leads to the two signals canceling each other, once they meet on the signal path. However the signal from the guitar string is magnified, doubled, due to the phase reversal caused by the out of phase magnets. The magnets being out of phase in conjunction with the coil windings being out of phase, put the guitar string signal from each pickup in phase with one another. When the two in phase guitar string sine wave signals meet, the amplitude of the wave doubles, and doubles the signal strength.
One side-effect of this technique is that, when wired in series, as is most common, the overall inductance of the pickup is increased, which lowers its resonance frequency and attenuates the higher frequencies, giving a fatter and less trebly tone than either of the two component single-coil pickups would give alone. A second side-effect of the technique is that, because the two coils are wired in series, the resulting signal that is output by the pickup is larger in amplitude, thus more able to overdrive the early stages of the amplifier. This is the essence of the "humbucker tone."
An alternative wiring places the coils in buck parallel. The equal common-mode mains hum interference cancels, while the string variation signal sums. This method has a more neutral effect on resonant frequency: mutual capacitance is doubled (which if inductance were constant would result in a lowering of resonant frequency), and inductance is halved (which would raise the resonant frequency without the capacitance change). The net is NO change in resonant frequency. This pickup wiring is rare, as guitarists have come to expect that humbucking 'has a sound', and is not neutral. On fine jazz guitars, the parallel wiring will produce significantly cleaner sound however, as the lowered source impedance will drive capacitive cable with lower high frequency attenuation.
A side-by-side humbucking pickup senses a wider section of the string (has a wider aperture) than a single-coil pickup. This affects tone.[1]by picking up a larger portion of the vibrating string more lower harmonics are present in signal produced by the pickup resulting in a "fatter" tone. Stacked humbuckers have the narower aperture of a single coil and sound closer to one.