Hi:
Hit the delete key or skip this message for any reason you like...I just came back to the top of this post because I now wonder who will find my comments of interest...at all...but you never know..
So, apologies to anyone who wonders what the (insert word of your choice) the point of this response is...
I'm new here & part-ignorant, but I also just asked someone the same or similar question - why the dirt cheap single-coil pickups I got on eBay for a why-am-I-starting-another-project? guitar project had one short magnet. I assumed it had something to do with a string that might be wound or not, but apparently I was wrong - I think it's the 3rd or 4th that some people make a choice about in some cases, my PU's have a stumpy 2nd or 5th magnet (they're not on the guitar - I hope I have enough sense to ask or look before mounting a PU backward...or would that be a lefty PU then?)
He's a guitarist AND electronics guy, I'm just the latter hoping to become both when I figure out which end of the guitar is which (OK, not that bad, but close).
He says the short magnet is one part of how they balanced the pickup's non-linear (frequency) response for all strings.
My two cents to add to this is that I believe it's not in the way one would expect a tone control and capacitor to interact with the electrical frequency response of the winding inductance, resistance and interwinding capacitance but in the magnetic properties of the pickup as a transducer - six magnetic strings that are not all the same width or mass, and not vibrating the same are all stuck inside one coil and contribute to a single combined output signal.
The complexity of variables in the electrical circuitry of an electric guitar is explained nicely by probably a number of people, but
buildyourguitar.com/resources/lemme/ is one I have read and found helpful/interesting...I had some trouble finding the English language version of this a 2nd time, but here it is.
Anyway, the number of electrical variables that model (mathematically explain) electric guitar function is abstract enough to deal with, and is out of the realm and interest of many readers.
The magnetic 'circuit' is a whole different beast...much of which is difficult to even be practically measured without affecting the response. The electrical properties are measureable but hard to understand for many people because it's 'invisible'. Magnetism is another level deeper into the 'invisible' realm because any measurements are made by proximity and not a contact or connection whose effect can be minimized
This stuff is outside my brain's ability to process...I finished all the math in an electrical engineering curriculum but didn't complete my degree. I think it falls into the category some people call 'black magic'. There is a certain amount of predictabilty and limitations to theory... fine-tuning by sophisticated approximation and repeated experimental changes are necessary (empirical results).
All part of why there are so many pickup designs, magnet options, Lollar's custom magnet degaussing, etc. It's not just how strong or long or wide heavy a magnet is...the concentration of and shape of the magnetic flux lines, the interaction of adjacent magnets (the end magnets don't have one on both sides, etc.).
I may even be wrong about some of this, but I am confident it's a pretty specialized field to analyze.
I thought they were supposed to have adjustment screws, so I guess the non-adjustable ones have to be installed at the right height (I decided I better not make my own guitar body for a first project).
I actually thought it would be cool to make my own pickups (saw an old 50's article on building one's own steel guitar with pickup), but $4.72 + shipping for 7 pickups cut me off from that idea...no matter how krappy they are, they are probably better than my own random results.
I'll try to stay on-topic and type less in the future.
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Uh, the future is here, I have something to add...
There's no law that says the magnets have to be uniform throughout the entire length or width...magnetizing can be far more complex than just magnetized/demagnetized, there can be a tailored profile (a number of variables). This is the stuff that gets kept out of patents and makes copying someone's design EXACTLY harder to do.