I say if Leo invented the single coil pickup to have hum then you can't do better than to pay a lot of money to get a vintage hummer!
Leo did not invent the single coil. One of the first guitar pickups was invented and patented by George Beauchamp in 1934. That was the Rickenbacker horseshoe pickup.
There were also humbuckers back before Seth Lover invited the familiar Gibson humbucker in 1959.
Now as far as Leo, he did design several humbuckers, the most notable being the Precision Bass pickup. If he thought single coils were good enough, he would have left one in the P bass. He also hired Lover, who designed the Wide Range humbucker used in the Tele deluxe.
Leo loved to design pickups, so his next design was the Musicman pickup. He must have through that was an improvement.
After that he invented, and patented, the Magnetic Field Design pickups used in his G&L basses.
Just kidding. But first you say there is no difference and then you say "the only difference is..." Well which is it? I'll tell you which it is: THERE IS A DIFFERENCE! As the reasonable people here have said SOME (but certainly not all) humcancelling pickups come close. Some are QUITE different!
I said you can make a humbucker that sounds like a single coil. You would be hard pressed to tell the difference. I make some myself.
I also said you can get several different jazz bass
single coils, and they will sound very different. Even from Fender and in the same model bass. Over the years they keep changing them. One might be bright and edgy, while another might be darker and thicker. Even though they are real single coils.
Now when I did my Neo Jazzbuckers, I wasn't trying to sound like a single coil. I actually wanted them to sound like the full size humbuckers. I figured we already have a slew of Jazz bass pickups, so let me offer a different tone. But they sounded a lot like single coils anyway.
Lately I went back to winding them a little lower to keep them nice and bright.
As usual, note that "different" means different, NOT "better" or "worse".
And it depends on how your hum cancelling pickups are made:
A quick review: Usual "soapbar" types have two single coil pickups side by side. Work great except that pickup senses the strings at two places at once so you get a somewhat denser sound with less pristine clarity. It's simple geometry and it CANNOT be made to sound like a single coil.
This is true, however, the very narrow humbuckers like the Duncan Rails and my aforementioned Jazzbuckers do have a very single coil like tone because of the narrow aperture.
Another type is the Side by side pickup like a P-bass. Does a P-bass pickup sound like a jazz pickup? NO they don't. Why? well in this case you sense the strings at only one place but you have two pickups with smaller coils sensing only two strings at a time. Even if you put them in series to add up the inductance it's still not quite the same as a single coil. And in a P-bass the pickups on one set of strings is slightly offset from the pickup on the other two strings. A single coil picks up the same harmonics in every string.
Yes, and no. You left out the coil geometry. P basses have a very squat coil, and a Jazz bass has a tall narrow coil.
Even forgetting that a P bass is a split humbucker, you still have a difference in tone. A good example to use is a Strat vs. a Jazzmaster. Strats have a tall narrow coil, similar to a Jazz bass, while the Jazzmaster has a squat side coil, similar to a P bass. The Strat is bright and chimey while the Jazzmaster has a more mellow, rounder tone, smiler to a P bass.
Which leads to the totally side by side jazz pickup. (like Nordy) Better and closer to single coils (closest in my opinion) but still not exactly right because in this case of pure geometry. The reason P-bass pickups are offset is because you need the ROOM to wind the wire you need on each coil. Side by side humcancellers suffer from that lack of needed winding space. You aren't going to find many "overwound" side by sides!
The issue with the split coils is you have two smaller coils. The inductance is very different in each. But you can get them very close as with the Dimarzio Area J and Nordstrand nj4sv.
And finally there is "stacked coil" "noiseless" pickup Well that IS a single coil pickup with a dummy coil added to cancel hum. Well, since they actually ARE single coil pickups they should sound just like one, right? Wrong. The problem is the dummy coil has lots of inductance even without the magnets and cores and therefore very much changes the sound of the pickup. My experience with these (my MIM Fender V has them) is they do NOT sound close to single coils at all.
There is another issue with stacks. There is a lot of low frequency phase cancelation between the top and bottom coils. This produces a weak thin signal. To compensate for this, they are often over wound. On top of that, to prevent them from becoming too tall, they are wound with thinner gauge wire. This changes the tone.
I tried a few stack designs. The first one was for a Tele style guitar I built. My intention was to have it on the hot side, and not like a vintage tele pickup, so I would it to about 14k. To my surprise, it sounded just like a tele lead pickup, just a little lower output.
I also did a prototype Jazz bass stack, and wasn't crazy about that. It was very bright.
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EMG J pickups are stacks.
So far as I know the ONLY single coils that sound like single coils without hum are those systems with a phantom coil that is ELECTRONICALLY mixed in the signal so it cancels hum but does not get into the signal path. But this is an active system and not common.
You left out sidewinders. They sense the strings in a single location like a single coil.
Bottom line: Hum cancelling pickups do NOT sound like single coil pickups, but some aren't too bad. You just have to give them a listen and use your subjective judgement as to what is decent sounding in YOUR taste.
No, they do sound like single coils, but you are implying that they is only one single coil tone. Does a DarkStar sound like a Jazz bass? No, but it's a single coil. Same is true of the old Guild 302 bass. Those were single coils as well. How about Bartolini 9CBJS S3s? Also different sounding single coils. Another example are Lace Sensors.
So here's some examples I have. I won't list what they are (don't cheat and look at the URL after they open!). None of them are single coils, but they all get what you would expect from a Jazz type bass. I think they are all usable tones, and why would you want to sound exactly like someone else's Jazz bass? There is not only one single coil tone.
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