[font=trebuchet ms]The normal connection for humbucker pickups is with the coils in series. One of the coils is RWRP (Reverse-Wound, Reverse-Polarity) relative to the other one. The coils are wound with the wire going in the opposite direction, and the magnets are placed upside-down in the coil bobbin. Any disturbance in the field of the pickup magnets caused by vibrating steel strings will induce currents in the coils that are in-phase with each other. Disturbance caused by an external magnetic field, like the transformer of an amplifier, will induce currents that are out-of-phase. These out-of-phase noise signals cancel each other out. Any connection scheme that uses both coils of a humbucker must keep the two coils properly in phase with each other, or there will be almost zero output.
A coil tap switch shorts-out one of the coils, leaving only one coil functional, for single-coil operation. This also defeats the humbucking feature of the pickup, so you get the same noise vulnerability as a normal single-coil pickup.
Connecting the coils in parallel produces a lower output that is close to the single-coil sound, while retaining the quiet humbucking function.
Out-of-phase connection refers to reversing the output of one pickup relative to another. This causes partial cancellation, making the same sort of hollow, flanging kind of sound that a Strat produces with the pickup selector in the 2nd or 4th position. The middle pickup of a Strat is RWRP relative to the neck and bridge pickups. That's why there is less hum with this pickup connected to either of the others, and also why there is noticeable hollowness in the sound.[/font]
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