I actually live in Weston Creek haha (Holder to be specific). Let me do some investigating as to whether my hypothesis actually has any sense at all first and then I'll get in touch.
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I'm in Duffy. If you PM an address I am happy to drop the caps around on the afternoon school run. I have 50 of each value, so won't miss some.
Are you taking into account the pickups' own capacitance? That can vary a bit depending on the randomness and tightness of the winds.
I haven't because the idea of this method is to utilise a capacitor in parallel with the pickup that is significantly larger (10x or more) so the pickup capacitance is negligible and can be ignored when doing the calculations on the circuit.
I actually had a spare cap (47nF) which I also used and I got a third different inductance value. I am at a bit of a loss to explain what could be the issue. If it was just one pickup then I'd say maybe I did something when winding but all three are consistently showing a relationship to each other which suggests to me something else is going on.
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Have you tried the method of hooking a known resistance in series with the pickup, driving the circuit from the sine wave generator and adjusting the frequency until the voltage across the resistor is the same as that across the pickup? At that point, the impedance is the same as the resistor value, so you can solve for the inductance. Might be tedious unless you have 2 voltmeters though. You could always borrow my DMM if you need a second meter.
It might be interesting to see if this method gives values close to the parallel cap method. You could also test with different resistor values. I suspect that every test will give a slightly different result, so maybe just take the mean of all of them?
DC
My LCR meter gave a capacitance value of around 12nF for my kit humbuckers (though I don't know how accurate that will be). Have you measured the pickup capacitance to check, or have you just assumed that it will be small?
I set up that circuit using the two channels of the oscilloscope to measure p to p voltage. Got different results again haha.
12nF seems quite high? I was under the impression most humbuckers usually measured in the 100's of pF range? Unfortunately I don't have a LCR meter and the oscilloscope method for measuring capacitance doesn't work on the pickup for some reason. I get an unusual wave form on the display.
I think you have discovered the uncertainty principle of pickups: there is a fundamental limit to the precision with which you can predict (or in this case measure) the paired properties of capacitance and inductance.
Can you just measure the capacitance with a DMM? That's what I do. It seems quite accurate based on measuring components of known value and tolerance.
How different were the inductance results using the serial resistor method? Is there a pattern to the variations? It could just be that each method is an approximation with a certain amount of systematic error, but this error differs for each method. Taking the mean of all tests might get you close to a workable answer.
Another approach might be to calibrate your tests by using an inductor of known inductance.
Good luck!
Useful little tool I stumbled across. https://blog.philadelphialuthiertool...acing-Tool.pdf