pickup resistance and output, humbucker vs single coil

Lots of questions here. I'm not sure I can cover everything, but hey, it is quarantine, so I'll give it a shot.

First, we have to be realistic about what DC Resistance reads and doesn't read. Any conductor (such as a wire) has some resistance. In the case of copper wire, it is usually not easily measured. If you take a 3 foot piece of house wire and measure end to end it will read zero ohm resistance, but only because the resistance is so low most measuring equipment won't be able to detect it. With the same thought experiment, there are two ways to increase the resistance. One, decrease the diameter of the wire, two, increase the length. At some point you'll have wire so long and so thin that the resistance will be measurable. Enter magnet wire. The wire in any pickup is extremely thin and extremely long by most comparisons. 42 awg is the most common wire gauge, and nominally it is about .0027", about the size of human hair. I'm not sure what the length works out to in feet, but it is long. Many Fender pickups are in the range of 7600-8200 winds. So, the DCR of a pickup primarily measures those two things: length of the wire, and the gauge of the wire.

The reason it can be useful is because it can roughly correlate to output. More length is probably going to mean more turns, and the turns around the coil is what impacts inductance, which is much more important. But, there are still many other variables. The gauge of the wire, the tolerance of the wire (that is, different thicknesses among a nominal gauge), bobbin size/shape, winding pattern (a scattered winding will use more wire for fewer turns - not a lot, but enough to distort measurements) and also winding tension. The tension affects it because the wire will actually stretch slightly thinner, especially around the ends of a bobbin, when wound very tight. Remember also that outer windings will use moore wire than inner windings, sometimes by quite a bit. When you're dealing with apples to apples comparisons, the numbers generally tell you something useful. A strat pickup at 6.2k ohm is hotter than one at 5.8k ohm. Also, a strat pickup at 8.1k ohm is likely being wound with a much thinner wire to get the higher reading... typically (but not always) a thinner wire is used for the sole purpose of getting more windings onto the bobbin, so the correlation holds up.

Your question, as I understand it, is asking how to determine output parity between a single coil and humbucker. The short answer is... I don't know! Seth Lover looked to the number of turns. When he was designing the humbucker, the p-90s were wound with 10,000 winds on the bobbin, so Seth divided that in two and a standard humbucker (nominally) has 5000 winds per bobbin. Putting the two in series effectively stacks them. In a very simple way, that is the way to do it. For many purposes, it may be "close enough for rock'n'roll". And, very crudely speaking, the p-90s of the late 50s and the original PAFs do seem to have roughly the same amount of output.

It isn't always so simple, of course. Other factors affect total "output" like magnets, construction, placement, form factor, eddy current loading and so on just make it all murky. Yeah, you can keep the magnet type the same, but you really couldn't have exactly the same magnet... at least, I don't think you could because the form factor would inevitably change.

Also, pickup output is a hard thing to measure, and as far as I know, there is no standardized way to measure it. Pickups are passive devices and don't really have "output" in a technical sense any more than a capacitor or a resistor. The output as we understand it is a translation of the input, which to them is a plucked string which is wildly inconsistent, so the RIGHT way to do it would be to have a special tone generator placed in front of the pickup at a specific distance and then measurements taken on the other end, probably with an oscilloscope. Some companies might have internal systems to do this, but I haven't seen anything industry wide.

That is a great overview, funkyk.

A guitar pickup is the most basic form of AC voltage generator there is. There are only two components: a magnet and a coil. Everything else (flatwork, bobbin, base plate, wood spacers, etc.) is included to hold the magnet(s) and the coil in firm relation with each other, because if one moves relative to the other in operation, power is reduced.  DC resistance is how most pickups are compared, because most people have a DMM and can read it for themselves.  But in reality, impedance is a better measurement because the coil produces AC, not DC.  However, measuring impedance requires special equipment.

If you want to get into the meat and potatoes of pickups, Dave Hunter wrote a pretty good book on the topic. But even after years of study on the subject and including information gathered from pickup makers, his conclusion is "it depends," because there are many variables involved.

$25 for the Kindle version:

www.amazon.com/Guitar-Pickups-Handbook-Dave-Hunter-ebook/dp/B004918XFU

Only $973 for the paper version. WHAT?!