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hum-buckers - how they function

The P-Bass pickup is really a genius invention. Humbuckers don't sound like single coil pickups due to the extra impedance of the second coil. A P Bass pickup is more like a single coil pickup split in two, so the impedance stays the same. The 2 coils are wound out of phase for hum rejection, so there SHOULD be some phase problems on the center 2 strings where they overlap, but the magnetic polarity is reversed on one half, so the output signal is put back IN phase, while the noise is out of phase and cancelled. So very clever.
 
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So a wider pickup should lose more of the higher frequencies. Is that right?

That's half of the story. The other half is that it's a wavelength filter. The same wavelength on different strings are at different frequencies. So, the filter combination of a pickup width and your G string (assuming normal tuning) rolls off higher in frequency than the E string and the same pickup.

On a two pickup bass, the spacing between the two pickups (this also happens with one pickup, but it's most apparent on a two pickup bass) makes a comb filter - that filter has a lot of dips in the frequency response, starting in the low mids (the scoop you hear playing a jazz bass) and continuing upwards from there in frequency. Again, the dips are different when you tune the string differently - each string has its own filter. That's why the same note on two different strings sounds different. A bass tuned in D standard will sound different than the same bass tuned in E standard, even playing the same notes because of this.
 
the best way to reduce the filtering is to make one pickup reasonably louder than the other one by putting it closer to strings

a volume control does not quite do what you think it should, UNLESS the pickups each go through their own buffer before reaching the volume control
 
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the best way to reduce the filtering is to make one pickup reasonably louder than the other one by putting it closer to strings

a volume control does not quite do what you think it should, UNLESS the pickups each go through their own buffer before reaching the volume control

IMHO, rolling off one of the pickups (with a volume control) works just fine with a passive bass like a Fender Jazz or Rickenbacker 4001.
 
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Just as an aside on this - when I replaced the 3-pos. switch in my Mustang P/J with an A.C balance pot, the sound definitely changed, and for the better IMHO. Sorry - I can't describe it - just richer. Of course the balance pot is going to have some effect - it is changing the overall impedance of the circuit by adding some extra resistance.

As another aside - my genius engineer feels that ALL guitars and basses should have a 10-50K resistor in series with each pickup to minimize the effect they have on each other, especially in VVT setups. Since the resistor is in series, and a low value for this type of circuit feeding the high impedance of the amp, there is little volume loss. For those that are not techies - a 50K pot does cut your volume because part of the signal is sent to ground.
 
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Is the comb filter based on nodes?
and would it be possible to limit the amount of filtering with a strategic spacing?

Yes, and kinda. If you pick up a 51 style P bass and play the 5th harmonic (not the musical 5th, but the harmonic of an open string that has a wavelength of 15th of the open string length, you can hear it acoustically, but through the pickup (which is located on a node for that note), you'll get pretty much nothing out - that's one of the dips in that comb filter.

With more than one pickup, you can play a bit with the spacings of the pickups to try to minimize the worst part of the comb filtering, but it's kinda like a balloon - make it better here, it pops out more there. You pretty much have to decide what you think "better" means before going in to do that exercise (I've actually done that), because there is no magic place where everything gets better at once. OK, if you move the pickup under the bridge, then there is no comb filtering. But there is also no output.
 
As another aside - my genius engineer feels that ALL guitars and basses should have a 10-50K resistor in series with each pickup to minimize the effect they have on each other, especially in VVT setups. Since the resistor is in series, and a low value for this type of circuit feeding the high impedance of the amp, there is little volume loss.

This Engineer will tell you that he pretty much hates VVT setups, because...nothing really works like it should. Adding a 10K-50K series resistor does help some things, but...it definitely takes away some of the high range of your tone pot (which is where I live all the time) - that series resistance damps the resonance between your pickup's inductance and the cable capacitance that gives you articulation/snarl when everything is up full. Without snarl, I cease to be happy.
 
No Snarl - No good! I have often wondered about the mid cut on Jazz basses, and how the spacing and placement affect it. I am sure Leo tested this a lot. Of course, this exemplifies why the P-Bass works so well - no comb filtering. Full range response.

And - yes - I think that the VBT cut the very top end a little, but you would only notice this at full volume comparisons.
 
Just as a thought experiment, if you were to take those 2 opposing coils and locate them say 50' apart from each other, (hypothetical but of course very impractical), each would be receptive to different sources of random EMI. The same coils would no longer be "hum bucking" or hum canceling. The result would be noisy as hell. My point is the ability of opposing symmetrical coils is also dependent on their placement relative to one another.
 
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No Snarl - No good! Of course, this exemplifies why the P-Bass works so well - no comb filtering. Full range response.

Well.... The P bass definitely has comb filtering. It has a big old hump in the same general area where the J has its first (most audible) dip. An octave higher, the P has a big dip. They both comb filter; they’re just different comb filters. One zigs, the other one zags.
 
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Just as a thought experiment, if you were to take those 2 opposing coils and locate them say 50' apart from each other, (hypothetical but of course very impractical), each would be receptive to different sources of random EMI. The same coils would no longer be "hum bucking" or hum canceling. The result would be noisy as hell. My point is the ability of opposing symmetrical coils is also dependent on their placement relative to one another.

Absolutely true - if you get close to a hum source (say a power transformer) the field is non uniform, and you’ll get hum. In that case, the distance between the pickups on a J (even with both pickups on) will hum more than a bass with a closely spaced humbucker.
 
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What you're calling hum-canceling is traditionally known as a split-coil design, like the photo of p-style pickups above.
They're actually a good compromise between single-coil sound & having hum-canceling pickups.

Hum-Bucker & Hum-Canceling are synonymous.
P bass pickups (4 string bass for this illustration) are technically split coil humbuckers where half the strings are picked up by one portion of the pickup set while the the other two strings are picked up by the other portion of the pickup set. On a Jazz bass two coils (split coil) can be housed in a single typical Jazz bass bass and cover known as noiseless or humbucking. On guitars and some bass pickups utilize two full size coils side by side in one wider housing. Also fatter tone is typically due-to coils being wired in-series like a P bass pickup or wiring two Jazz bass pickups in series. You get higher output and loose some highs. Having said this some P bass pickups are wound to get more highs along with higher output.
 
There is a way to retain an insane amount of highs while still getting the hum bucked. This is done by wiring the pickups in parallel, but buffering them so that they cannot influence each other. This is one of the reasons that active jazz bass pickups sound so bright - the other being a really low number of windings that shifts the resonant freq of the pickup up.