P Bass - A String - harmonics and intonation

[GeoffBass]

Hi
I have a tuning problem with a P Bass ('63) which is driving me crazy. Other strings are fine, but the A String harmonics (produced over the 12 fret and 5th fret) are way sharp compared to the open string note ... so far sharp that I cannot use these harmonics to help me tune the bass.
This problem is not related to the frets ... but to the characteristic of the A string itself and I notice the same problem with flats (TI) and round wounds (Rotosound, Fender).
The bass does have a fair amount of truss rod slap on certain notes when the strings are played hard, but its hard to see this would causing this problem. Only other thing I can think of is it might be down to the resonance of the timber?
I've been using a Peterson softstrobe app on my iPad and realise that its a big ask for an old P bass to play in tune all over the neck ... totally understand this.
But this A string thing is weird and I wonder if others have noticed it ... been able to live with it ... or whatever.
Also, pretty sure it not how the string is springing over the nut (witness point) ... as I have had different nut in the bass trying that angle ... problem seems in the string and how it vibrates (and produces harmonics).

Any ideas folks?

[GeoffBass]

Me again ... sorry for error in my post ... the fundamental note (A) is way sharp, relative to the harmonics found over the 12th and 5th frets.
If I use harmonics to tune the A string to D and E strings, then my open A string is way sharp and beats against an A note stopped at the 5th fret on the E string.
Hope this is clear.

[punkjazzben]

How's the break angle at the nut? If its not acute enough, that could cause the string to, in layman's terms, get confused as to where it is supposed to stop.

I know you've checked it, but maybe photos would be good?

A-strings on Fender Precisions are a PITA! A lot of the time it just causes a 'rattle', but sometimes it'll effect intonation. The solution is to ensure a clean break angle by getting enough wraps on the tuner (and wrap towards the bottom) and then making you sure you give the string a solid push down behind the nut and at the bridge to ensure a good witness point.

[GeoffBass]

thks ... I've been hung up on this witness point idea too ... tried a second string retainer to hold the A and D down tighter (does stop rattles) but with or without it still get the A string problem. Pretty sure I have bent the string down over the nut (and saddle) well enough but have not used pliers (grin) ... I put pressure on it to the point of thinking I might damage the string. How far do you go with this!