Given the open string is tuned to concert pitch, for each half-step note above that pitch there is some string length that produces that note. Put the frets in the right spots and you have a bass that can be properly intonated.
Now, there are various opinions on exactly what frequency those notes are supposed to be, eg. "Just Temperament" versus "Equal Temperament", but if you pick one, it's possible to have a neck with the frets in the right places.
That's all true in theory. In practice, there are a lot of factors that affect the exact pitch that comes from a fretted string.
- how hard you push down on the string can increase the tension a bit since you're basically pulling it down over the fret
- how straight your fretting finger is; if not perpendicular to the fretboard it can bend the string up or down a little
- the nature of a vibrating string is to start off a little bit sharp and then settle down into pitch
- different types and brands of strings have different harmonics which can suggest to the ear a different pitch than the fundamental of the vibrating string itself. This is especially true of old roundwound strings. They can get so wolfy it's really hard to tune them. It's also especially true of lower notes, like the low B. The fundamental is so low people can't really hear it, so what they perceive is actually a note suggested by the string's overtones.
So just set the 12th fret intonation properly and tune the bass with a decent tuner and the job will get done for all real-world intents and purposes.
In my opinion, in a band situation the most productive thing we can do to sound "in tune" is to all use the same tuner. If my tuner is a little out of sync with the guitarist's tuner, then the band is going to sound a little sour.
Exactly. I was going to clarify my earlier post with essentially this same information. And it's not physics really more closer to geometry in the science department. Having a guitar or bass intonated exactly at pitch across the spectrum would not necessarily be a desired effect. For instance - tune a piano with every key at the correct pitch for that note instead of starting at middle C and tuning every octave relative to that - then play said piano. I bet you will never want to hear that godawful noise again. But, it is possible on *some* guitars and basses to have every note on every fret be in tune, other factors that affect this are whether the fret spacing is mathematically correct, are the frets all of equal height, is the nut slotted perfectly, how straight is the neck (theoretically you would have to have a perfectly straight neck however most players prefer at least a little relief), are the strings tension equal up and down the neck (strings will lose their "rigidity" in some places making the tension somewhat different at different spots on the neck).
So this is off-topic, but (for those that don't know and assuming most of you already do know this so ignore me) when setting up a bass, this is what I do. 1st, I set the action to approximately where I think I want it (most people don't touch the action until after they adjust the truss rod - I do an approximation of action first). 2nd, I adjust the truss rod. Personally, I like a very little amount of relief - almost perfectly straight but not quite - there are measurements you can make and such, and I do usually end up using feeler guages, but I don't rely on them, just use them for ballpark. I also use my eyes and my ears and my hands to make the bass feel right for me. Then I let the bass rest for at least a day to let the neck settle. 3rd I re-adjust the action - this time to exactly where I want it. Last comes setting the intonation. Most people's idea of setting the intonation is having the bass be in-tune with the open string and at the twelfth fret - there is nothing wrong with that, but it's not very thorough. I start with that. Then I check the first, second and third fret - that will tell you if the nut is slotted correctly (or on an adjustable nut whether the height is correct) - make adjustments to the nut if necessary, re-tune and re-check at the twelfth fret. Then re-check frets 1, 2 and 3 again. If all is good there, I go to the fifth, ninth and fifteenth fret, making little adjustments if necessary as I go - the more relief you have in your neck, the more these notes will be slightly off, especially above the twelfth fret - on a 2 octave bass I also check the 24th fret. Many times the ninth and fifteenth will be sooo close to being in tune (a half cent or so) that no further adjustment is necessary. Sometimes, in order to be closer at some of the other points, you may need to come slightly off exact pitch at the twelfth fret. If your neck is relatively straight and the instruments geometry is very good, sometimes you can actually get the bass to be in tune on every note - the goal is to make it as close as possible along the entire fingerboard - it takes time and patience, but the bottom line, unless you can hire a personal tech that knows exactly how YOU like your bass set up, really only YOU can make it perfect for you. And perfect for you may not be perfect for me. I play fingerstyle and prefer pretty low action, pick players typically want higher action (to avoid fret slap) - it's all preference. And remember, changing the guage of strings you use will affect neck relief and intonation, so if you change guages, you will need to redo your setup, also, temperature and humidity changes can make a difference - it's a good idea to check your setup from time to time anyway.
OK, sorry to the OP - this was off topic. But on topic, when it comes to the bridge, that's a decision you have to make for yourself. BA bridges are not the only alternates out there (they are what I use on my Js, but that's because they are cheap and easy to install). Babicz, Hipshot, Schaller, etc all make high quality hi-mass bridges, so those are others you could look into/try, but if you are happy with the stock bridge, there is no reason to change it. For me, it's a good upgrade on my Js, well worth it. Didn't work out so well on the P I had. All of my other basses have stock bridges (Warwick, Ibanez, Ken Smith) and I have no desire to change them.
Another quick off-topic note -- my Geddy Lee Jazz came stock with a BAII (BTW - I know Fender was putting BAII bridges stock on several basses for a while - the highway 1 series comes to mind). I love Geddy, but I'm not trying to imitate his sound, I happen to love the way that bass feels, but I didn't like the way it sounded and although the neck was fast feeling, a little perspiration on my left hand and it would start to feel a little sticky. I lightly sanded the back of the neck to remove a layer of varnish, I replaced the tuners with Hipshot tuners and an X-Tender key, and I replaced the pickups with EMGs (they were free to me - I may or may not have chosen something different if I had to pay for them), I also changed the tone stack so it's V/B/bass-treble stack, and I managed to rout the cavity just slightly deeper so the battery goes under the pots - nice that I didn't have to route for a battery box. I also removed the tuxedo looking white pickguard and filled the holes so the bass is all black - that's my most "customized" bass and my goto instrument for hard rock gigs.