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Let's make a list of true low-impedance pickups

By "true low impedance", I mean that the coil itself is low wound with low inductance (that is, EMG P and J are out). This gives a wide frequency response (perfect for a filter-based preamp), but the output would need to be boosted to instrument level with a preamp or transformer.
The low-impedance pickups that I know:
  • Burns low-impedance pickups;
  • early 700Ω Alembic pickups;
  • original Gibson Les Paul Bass pickups;
  • Rickenbacker 4002 neck coil tap;
  • Ibanez Regulated Low-Z pickups;
  • EMG custom LoZ pickups;
  • Wal-style multicoil pickups;
  • Epiphone Jack Casady pickups;
  • Lace Alumitone and Aluma;
  • Cycfi Nu and XR.
There are also medium-impedance pickups that are close (but some of them may be no cigar):
  • Danelectro Lipsticks;
  • Alembic Activator and Series;
  • original 2kΩ Musicman Stingray;
  • very late Gibson 1.2kΩ mudbucker and the current Epiphone Sidewinder;
  • EMG 35DC.
 
By "true low impedance", I mean that the coil itself is low wound with low inductance (that is, EMG P and J are out). This gives a wide frequency response (perfect for a filter-based preamp), but the output would need to be boosted to instrument level with a preamp or transformer.
The low-impedance pickups that I know:
  • Burns low-impedance pickups;
  • early 700Ω Alembic pickups;
  • original Gibson Les Paul Bass pickups;
  • Rickenbacker 4002 neck coil tap;
  • Ibanez Regulated Low-Z pickups;
  • EMG custom LoZ pickups;
  • Wal-style multicoil pickups;
  • Epiphone Jack Casady pickups;
  • Lace Alumitone and Aluma;
  • Cycfi Nu and XR.
There are also medium-impedance pickups that are close (but some of them may be no cigar):
  • Danelectro Lipsticks;
  • Alembic Activator and Series;
  • original 2kΩ Musicman Stingray;
  • very late Gibson 1.2kΩ mudbucker and the current Epiphone Sidewinder;
  • EMG 35DC.
Are you sure about the wal pickups? What about lane poor?
 
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Are you sure about the wal pickups? What about lane poor?
Hey, I forgot Lane Poor. The Wal may be actually medium impedance? I'll change it in the next list.
Not sure what you mean by this when most of the pickups on your list don't need them.
The Alumitone transformer is included in the pickup shell. The transformer inductance makes it sound closer to traditional passive or EMG active pickups, and not flat response.
The Gibsons and Epiphones include transformers in the control circuit. The Rickenbacker coil tap outputs at mic level instead of instrument level. The Alembic and Cycfi needs (and often come with) their own preamps for a healthy output, while the EMG Lo-Z should use an internal preamp like a traditional EMG.
 
interesting subject I am going down the rabbit hole on. Super curious on the aluma tone J pickups.
Alumatones are (internally) very low impedance - it's just one turn of wire/aluminum, but on the output wires that you get (which is after the tiny transformer in the thing), they are definitely NOT low impedance.

As far as "flat response pickups", I haven't met any yet - everything I've measured or used ( I have measurements on about a hunderd kinds of bass pickups) has a resonant peak somewhere in the audible spectrum. but.....

If your desire is to have a "filter preamp" sound, there are plenty of pickups that will give you that frequency response, without even having a preamp in the bass - a lot of Bartolini pickups are low enough in impedance (a lot of other folks' hum cancellers fall into this category if wired in parallel) that you can capacitively load them, and by choosing various capacitor values, you can manipulate the peak to get the same sounds that you would get from a "filter" preamp. The difference is, in the passive version, you switch between various sounds, and with a "filter" preamp, you can sweep a range of sounds. My basses all incorporate this thinking - I know what resonant frequencies I like, so I have modes tuned to those frequencies, and can access a sound at the flick of a switch, rather than hunting with a knob. For live gigs, that's an advantage to me. If you don't now what you like, there is some work in getting to where that works as well for you.

By having low impedances pickups, the resonant peaks will be higher in amplitude than what you get with higher impedance pickups (you can tame them with a tone control to whatever you want if they are too high in amplitude). High impedance pickups have a lower limit as to the range of resonant frequencies you can get as well.

All it takes to use a low impedance/lower output bass with regular gear is a low noise boost pedal as the first pedal in your signal chain. That can easily get your bass's output into the regular range. that combo actually gets you more signal to noise ratio (less hiss) than you can get with a high impedance bass and regular electronics as well. It's not for everyone, but it can work very well.
 
I'm guessing if you are using a filter based preamp the more important thing than inpedence is to just have a pickup with a high resonant peak, I think 4k is the mkI Lustihand's max cutoff, 3k for East/ACG and 5.3k for Underhill, so roughly around those numbers.

Some pickups should have it, the EMG J is roughly 4khz humbuckers wired in parallel should be around that high as well. Of course of it's an active circuit your resonant peak should be higher than normal anyway because there shouldn't be any cable capacitance weighing it down. Going by Seymour Duncans unloaded resonant peak numbers, they are mostly in the 3.5+ range, even massive output ones like the quarter pounder, and I can't imagine most other passive bass pickups being much lower.

Which if I am understanding all of this correctly leads to the question of whether you really need special pickups to make proper use of filter based preamps anyway, since it seems like most passive pickups going straight to the pre unloaded, shouldn't have resonant peaks way lower than the highest cutoff frequency anyway.
 
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I'm guessing if you are using a filter based preamp the more important thing than inpedence is to just have a pickup with a high resonant peak, I think 4k is the mkI Lustihand's max cutoff, 3k for East/ACG and 5.3k for Underhill, so roughly around those numbers.
It needs a high frequency but smooth (low amplitude) resonance peak. A high-impedance Jazz Bass pickup (such as a passive or EMG J) has a high enough resonance peak, but they tend to be very sharp. If you load it down to be smooth, it also shifts down in frequency.
My reasoning of low impedance is two-fold:
  • if the resonant peak is so high that the entire audio band is essentially flat, then all the better (the Cycfi idea);
  • if the resonant peak can be loaded smooth but not too low in frequency, it's still good (the Bartolini idea).