I've just bought a split-coil single that I asked to be reverse wound, so that it would cancel the hum when run on its own. I wanted to check that it had been done by putting the two coils together, which should result in them sticking together I believe. I tried this, but they are neither attracting nor repelling. I tested the poles with a mangetised screwdriver and I'm getting a result where one of the coils is equally magnetised on both ends of the pole pieces, while the other has a stronger pull (than the other coil) on the top of the poles, but nothing on the bottom. Is this normal?
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In designs such as the DiMarzio HS series and Seymour Duncan YJM Fury, the rod magnets are not as tall as the bobbin form(s). Thus, the exposed end of each polepiece will attract ferrous metal whereas the underside end will not to the same extent.
Your test only really confirms opposite magnetic polarity. The coil winding direction also needs to be reversed to achieve noise-cancellation.
Formerly TheGuitarWeasel ... Oil City Pickups ... Oil City Blog 7 String.org profile and message
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The nearest that I can get to replicating your different magnetic field strength at each end phenomenon is with a semi-functional DiMarzio HS-2 replacement pickup for Stratocaster. This design includes a grounded metal sheet around three surfaces of the upper coil. The only possible uses of this are screening against RF interference and, arguably, deflecting the magnetic field from around the rod magnet polepieces towards the strings.
The metal sheet reduces the magnetic attraction sensed at the bottom of the DiMarzio pickup.
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Formerly TheGuitarWeasel ... Oil City Pickups ... Oil City Blog 7 String.org profile and message
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You could use connector blocks rather than make a solder joint, so no permanent damage will occur in case it is faulty & you need to send it back.
If @OilCityPickups can't make a diagnosis without the proper tools, you (or I) don't have much chance
Photographs or cross-sectional drawings of the internal structure of the pickup would help greatly.
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With respect, on its own, a d.c. resistance meter reading means very little.
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If you have a twin pickup guitar with the reasonable gap between the pickups you can rig up some blocks of wood/Lego/whatever with some tape and suspend the pickup face down about 5mm or so above the strings, where you would naturally fit a middle pickup.
Wire it or tape it to a guitar lead and see what happens. I do this all the time when I want to know whether a pickup is functional before I fit it. Obviously it'll sound like a middle pickup rather than whatever position you intend to fit it in, but it'll let you know whether it works and a good idea of how powerful it is when you compare it to others on the same amp settings.
I wouldn't have assumed a pickup could go straight to the lead like that but now you mention it, it's so obvious that it would.
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If you measured the DC resistance of a PAF and then a Filtertron you might well think the Filtertron was broken.