Full disclosure, I'm not crazy about p basses, although most band mates have preferred the sound to anything else I used. But what makes them so overwhelmingly the world's favorite? Thanks in advance!
It's plug and play. Set the eq and go. Also, it may not have the perfect bedroom tone, but the kids always make it sit in the mix well
The neck pickup gives a heavier/punchier tone than J pickups but we notice that because we're bassists. The tone from a standard P pickup is really versatile. The neck is more broad than a jazz neck. That's my favorite part. So much that I have a couple Jazz with P necks. Neck shape is a subjective thing. The P body is more squared at the back where a Jazz looks like you take a P and smoosh it forward? I honestly care a lot about the neck shape and not as much about the body shape. But Precision is the benchmark because of its heritage.
If it has a P pickup in the sweet spot and has the general look of a Fender Precision, I'll casually call it a "P bass," or a "P clone." I reserve the term Precision Bass for Fender and Squier models. (I prefer ones with Jazz necks, personally.) To me, it's the midrange character you get from that pickup in that location that is most important to why it works so well in so many mixes. That also happens to be my favorite tone anyway, even practicing by myself, so I like P basses quite a bit.
After many decades of J style and humbucker equiped basses I bought a P Bass and started to take it to gigs. Everyone loves that sound of it, musicians and sound guys alike. I had a think about this and I believe that that pickup in that position gives it a nice round bottom and enough bite on the top without being overwhelming, the mid forward sound then allows it to sit in the ensemble sound nicely, never too muddy, never to sharp, just exactly right. That's my take on it anyway. I still love and use J basses, you can't beat the slap sound on those and the StingRay is also in use but if the gig requires simple finger style/pick playing then the P is right on the money.
Does the bass need a fender pickup in the sweet spot? I had a Yamaha bb1200 once. It was non active and had the same style pickup in generally the same spot, but it didn't get any love from anyone but me. I sold it because the neck was too much like a fender.
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I think it stems from being the first widely used bass guitar and being on so many early records of the era. The next generation wanted 'that sound' and used P-Basses. It just kept going from there. Like others have said, they are also the ultimate plug-n-play bass. Less fiddling with knobs and gear.
What makes a p-bass a p-bass, you ask? This is a Platonic forms type question. Is there an ideal P, one that serves that as the mental archetype of the P-bass? Idealtypen, to borrow the German word? Could one play Max Webster covers on such a Max Weber concept bass? Would the ideal P have some ineffable quality? And if so, what would we call it? If the ideal chair, in the Platonic sense, has a transcendent quality of chair-ness, what quality would the ideal P have? *ahem* Okay, my nonsense aside, I think Yogi Bear hit it : the right pickup in the right spot. GT
this discussion has been done literally countless times, the reason this one does not need to be done countless times is because the answer is generally agreed upon. split coil pickup placed in the correct (fender) position. some folks might say it needs to have fender on the headstock, but i think most don't care. If your playing a carvin P model, nobody is going to claim it's not a P style instrument.
The Fender P bass is probably the most recorded bass in history. We have become accustomed to its sound. It fits right where it is needed in the sonic spectrum of popular music.