Why do pickups sound the way they do?
Recently my good friend George asked for some advice on what kind of sound to expect from different pickups. This is my attempt to answer that question based upon the physical construction of the three most common kinds of pickups.
Let's start with strat-style pickups. These have a single coil and a narrow aperture (width). They sense a very narrow strip of the string, causing them to more accurately reproduce higher frequencies. These pickups have a very sharp, articulate sound with strong pick transients.
A humbucker pickup is wider and has two coils. Ideally the second coil doesn't respond to the strings; it's only there to cancel ambient electromagnetic fields (i.e. to "buck" the "hum"). In practice there's a small amount of field leakage that creates a small amount of cancellation of due to string motion at point spaced by the width of the side-by-side coils. This causes response to vary in a complex manner depending upon where the string is both fretted and picked. The best way to describe the sound, I think, is that it has a slightly "hollow" characteristic much like comb filtering.
In addition to the comb filtering, the electrical inductance of the second coil is in series with the signal; this causes a certain amount of opposition to transients and higher-frequency harmonics. In other words, humbuckers don't sound as sharp or articulate as strat pickups.
Finally, the field leakage that causes the second coil to introduce a bit of comb filtering also causes a bit of compression at lower frequencies because the string tends to have the same velocity over both coils at lower frequencies.
A P-90 pickup has a wide aperture like a humbucker, but has a single coil like a strat pickup. I think the best way of describing the P-90 is that it's articulate like a strat pickup without being as sharp-sounding. At the same time, it lacks the slight hollowness and compression of the humbucker.
Beyond these general differences there are many variations. Some variations, like the number of turns and size of the wire used to wind the coils, have reasonably predictable outcomes: more turns and smaller wire tend to produce hotter pickups with less sparkle and more of a midrange bite.
Other variations, like the type of magnet material and the exact details of the magnetic structure have less well-known outcomes; these are largely the domain of experienced pickup designers who arrive at their results through extensive design and trial builds.
Keep in mind, too, that other factors affect the sound of an electric guitar. Contrary to some people's expectations, an electric guitar is not reducible to a plank, strings and pickups. The choices of materials, shapes, construction and geometry all contribute to the sound of an electric guitar.
Furthermore, the guitar's sound is always shaped by the amplifier, speaker and cabinet and by any processing added to the sound. Increasing distortion, in particular, does interesting and mostly-unpredictable things to a guitar's sound by clipping the more prominent aspects of the guitar's signal and emphasizing the finer-grained details that would otherwise go unnoticed when playing through a low-gain amplifier.