only real way to eliminate one of the coils is to bypass it with a wire…..the cap does this for higher frequencies and shunts them to ground so instead of exciting the instrument they get suppressed which is why it sounds darker…..
the voicing change happens because you can “tune” the response of an inductor with a cap….. the tuning formula is Fr = 1/2PI x square root of the product of L (inductance) and (capacitance) where
Fr= resonant freq
PI= 6.28
The holy grail parameter (for me) has always been inductance of a Thunderbird pickup and have never been able to secure that very elusive number, although through work, I could set up a measurement, I haven’t gotten around to it hoping I can find a published number the way Ohmic numbers are but have not been that lucky. It is fairly safe to say that for a linearly wound coil, the inductance is directly proportional to the resistance but because so many different winding methods are used it’s not a safe assumption. That leaves an empirical approach……from a Bill Lawrence paper I read, pickup inductances range from 2 to 10 Henries (some higher) so assuming half way inductance (5 Henries) and the .01 value of that cap (from Irv’s photo) and using the above math gives me a response of 712 Hz….
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So, in short

when you flick that pot you shunt some high frequencies to ground AND add a filter response centered at 712 Hz that will inevitably alter the original voicing….
Really hoping this makes sense…
Sorry for the verbosity….