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Placement changes the frequency response dramatically. Closer to the fretboard means deeper resonance, closer to the bridge means higher. What this means for guitar players is that you will have a more direct punchier sound near the bridge and a more mellow sound near the neck. How this applies to what players do with them depends entirely on the genre.
More pickups means more options, but most of my guitars only have 2 pickups and I never use the middle one in the guitar that has 3.
the different overtone standing waves on a given string will have nodes and antinodes in different places up and down the string. The pickup placement will reinforce some overtones and reduce others in the output signal
Is there a reliable way to. Measure that or is just felt out?
these overtones/harmonics positions also change every time you fret a string, so the vast majority of guitar playing cannot be optimized in this way. For example, if you do this for open (unfrettted) strings then the pickups will not match the wave patterns when you use frets 1-11.
By all means try moving the pickups around to see what you think sounds best, but personally I would not worry about perfectly matching the strings' wave patterns. Maybe it's worthwhile to obsess over this if you're very concerned about how open chords sound (chords that use some un-fretted strings).
The tricky thing about this is I'm not actually building a guitar, I'm just salvaging the guts of one to make an electric hurdy gurdy. Far as I can tell it's never been done, all the electric gurdys I've found use piazo pickups tucked into an acoustic body.
My current plan is to extend the neck to the wheel and put a hollow so I can freely slide the pickups back and fourth. Then when I find where I like them I'll just make a cap that locks then in.
you could empirically measure it by plucking a string and moving a pickup across the strings (maybe mounted on a jig above, or in a dummy body with a mechanism to move one set of pickups along a hollowed out channel; then capture the output and do a spectrum analysis showing spectral content vs pickup position.
it can be modeled as an increasing integer number of half-wavelength vibrational modes that would exist between the fret and bridge on a string, with the magnitude of each at a given position summing into your modeled output.
there are certainly effects from neighboring strings and other subtle resonance effects - I’m not a luthier so not really sure on that.
Not all guitars have 3 pickups.
The placement of the pickup makes a big difference in the harmonic overtones that will be picked up.
The harmonic overtones greatly influence the tone.
On top of what others have said, I don’t think there’s an objective “place where you strum” like on my bass, I use a pick and play resting on the bridge, so all my picking is just in front of the bridge. It gives a lot more bite that I like in my sound.
On my telecaster, I do the same, for that twinkly twang. On my 7 string, I play closer to what would be considered “the place” but still leave my pickup selection at the bridge, again, to help get me out of the muddy range.
I imagine that the convention just became placing 2-3 evenly spaced between the neck and bridge, because with a switch and blend pot, a single model could accommodate any kind of player.
That does make sense, in all the videos I've seen since, guitar players can be all over the area and even up the neck. My assumption had been that the open space between the 2nd and 3rd pickup, or second and hum bucker on some models, was to give a designated area so your paying doesn't directly affect the pickup but it looks like in practice that's neither here nor there.
People with bad technique may have problems with a pickup being near where they play. This is a player problem, of course because depending on the response you want, you need to play on various parts of the string.
There's no real connection with pickup placement. It's purely the desired frequency response. Just like the playing position.
On a bass, players sometimes use a pickup to anchor their thumb, so having a convenient spot can be handy. Some even attach a bridge across the top to have a shelf for any spot.