Well, hello folks. I know I only come here occasionally, but to follow up on the 4002 comments earlier, many years ago the RIC website actually had a drawing of a 4002 pickup on it for a short while. Indeed, they are split coil humbuckers, with one coil for GD and the other for AE.
One overlooked aspect of tone on a bass is pickup
placement. A 4001/3 simply will not ever sound like a 4002, even if you use 4002 pickups and circuits, because of the different overtone structure of the sampling point of the string. A 4002 sounds like a J-bass with attitude because of the pickup placement. See this article:
http://www.till.com/articles/PickupResponse/index.html
Moreover, with the individual coils more "circular," there is a different resistance to inductance characteristic as compared to an oblong coil as on toasters, high gains, and HB-1's & -2's. So yes, the clarity associated with a P-bass is there, not because of magnets or windings, but because of the coil shape affecting the resistance and inductance characteristics. But because of the body construction, it is clarity with character and drive, not just vanilla ice cream.
Finally, my 4002
was wired like the factory schematic as set forth on the RIC website, and I was able to consult it to learn the finer points. After many years, I finally wanted to get the rest of the low end out of it, so I did get a RIC push-pull and put in a bypass to the .01 to the mid pickup. As Cassius pointed out, I gained improved versatility of the pickup in spades. So much so I'm considering doing another one to the bridge pickup to switch between the stock .01, which cuts at @ 150 or 160 Hz, and the 4001/3 .0047, which cuts at @ 330 Hz.
A lot of bass amplifiers in the late '70's and early '80's had different cabinet proportions and porting (if any) than now, combined with then-new stiffer cones to handle more wattage. All these factors changed the "Q" or amp/speaker resonance, and usually created a "hump" in the amp's signature at @ 150 Hz. So it makes sense why RIC chose the .01 at that time instead of the .0047 for the 4002. But now with twenty more years of speaker and amp technology, those values really don't make sense anymore, especially since 150 or 160 Hz is now the crossover frequency for a lot of bi-amp rigs. With the crossover and the .01 onboard cap, this creates an audible "hole" that I could hear out front.
Another item I could hear, which I expounded on at length on a thread over at RIC, is the fact that you can never have two completely identical pickups or capacitors due to manufacturing tolerances. So with both pickups on, and the coils being different and the capacitors interacting so that the hinge frequency was just slightly different from front to rear, I could always hear phasing when playing onstage with both pickups on. Now that I've bypassed the mid pickup .01 cap, I don't hear that phasing anymore with both pickups on. Pop the cap back in the circuit with a pull, and it comes back.
And since my body chemistry eats nickel, for years I have used GHS Progressives 45-60-80-105 that I purchase as singles instead of a complete set to approximate the gauges and feel of an original RIC set. They are the only strings that combine consistency, long life, tone, and especially the E string doesn't go "thunk" after just one set. I haven't adjusted my bridge in, well, years if not decades.
Now, if RIC would only reissue the 4002, but with the circuit mods as I've done, slant frets, the original smaller headstock, lose the XLR....