The pickup positioning have a likely effect on all notes because every note you play, open or not, will have its own set of harmonics
This is exactly my point. And as a string is played at different frets, the harmonics shift (I know you know that), which to me makes it seem impossible to pin down the optimum pickup placement with mathematical precision.
which will be affected by the position simply because pickups in harmonic nodes affect phase relations.
I don't doubt that. But IMO it's just as true of pickups that are not in harmonic nodes.
Unless it's strictly an open string and the pickup is in, say, the 24th fret position, a partial from the string's vibration won't be completely nullified - but even so, the harmonics will be diminished depending on the position of each pickup. And then we come to the fact pickups are connected in parallel, which imposes its own frequency spectrum change on the note, and some pickups in parallel may augment some partials of some notes and diminish cancel out the other.
I agree with all of this. My point is that nothing can be done to control any of it -- except using one coil per string. But even then, even if the pickup isn't at the 24th fret, at some time during play the pickup will likely be at the midpoint between a fretted string and the bridge, creating the same effect, for as long as the string is played at that fret.
And all bets are off with multiple pickups. Can there be an optimum pickup placement for multiple pickups to mitigate or maximize phase relationships when the strings are open? Probably.
Can there be an optimum pickup placement for multiple pickups to mitigate or maximize phase relationships whether the string is open or fretted at any point along the fretboard? I seriously doubt it.
The point being, using harmonic nodes is by no means the only way - but it's awfully convenient
No argument here.
and it's been used to great effect before.
This is the part I question, unless the "effect" is sales.
Believe it or not, I am open to arguments supporting the idea. I just haven't heard any yet that are compelling. Most of it (MM "sweet spot", Fender Jazz 70's bridge position, etc.) sounds like marketing.
Me, I mount pickups on over-string rails and slide them over till I get a tone I like, but I have time to *bleep* around with positions.
That was just pure dead brilliant! Many kudos to you sir!
What if the mid position loses out on some useful sounds the "by-the-bridge-pickup" position would provide?
Again, this can easily be avoided by trying before routing. Measure twice, cut once.
Again, I am willing to be persuaded. Especially if one were to conduct a test with a pickup-tryout rig like the one you showed.
But at this point, I still believe placing a 3rd pickup at the midpoint between two existing pickups provides greater tonal flexibility than placing it nearer to either pickup. If there is enough room between the neck pickup and the neck to put an additional pickup there, that would probably increase the tonal capability more than putting it between the pickups.
But for between existing pickups, unless one is going for a specific effect, if the goal is tonal flexibility, IMO the best option is the midpoint.

