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Scope not lined up with bore

Ripper, no sorry I should have been more specific. If the scope is installed incorrectly (scope cant), its height plays a role.

For holding the gun unlevel (gun cant), the scope height is irrelevant provided you are using either mildots or the turrets to establish your point of aim. The error is determined solely by the cant angle and how much the projectile drops.
 
Often as not I have found that when assembling a gun there is a tiny bit of play in the scope mount, the mount on the gun not the rings, and the problem you describe can be taken care of by simple moving the mount to the right or left at the front as needed before tightening it down. If this is not enough you can shim the rifle mount with a piece from a soda can to make things right.
 
OK I got you now Nervoustrig. I just went in there and checked two of my guns in the mirror after putting a piece of orange masking tape on the barrel and everything lines up good. So I guess I’ve just been lucky. I can’t help it, I’m just old school and and do what works for me and until I actually have problems just like the poster did then I will use A different approach. But when I do the eyeball method, I just don’t slap the scope on there and then swivel it around and say that’s good enough. I take my time and look at it over and over then I make sure that when I tighten up my mounts, I go back and forth from side to side because if you tighten one side Too much it can swivel the scope. At least that’s what has happened to me before. 
 
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You say parallax is a problem...is this a fixed parallax scope? Otherwise if it's adjustable, set it to the lowest range (say, 10 yards) and step back half that distance (5 yards) from the mirror. Your reflection should be clear in the mirror and free of parallax error. With the scope loose in the rings, rotate it until the vertical bar of the reticle simultaneously bisects both the muzzle and the scope's objective bell. Then lock it down.

I prefer to use the scope's highest magnification for a nice big sight picture. That makes it easier for me to judge that the reticle it cutting them both right down the middle. Freehand won't suffice. Improvise a rest to steady it so you can really concentrate on getting it centered.

And yes as you said it is a good idea first to mechanically center the scope so the reticle is centered in the tube. If you aren't familiar with that, don't worry, it's easy by just counting full rotations of the turrets. Then go back to the approximate midway point. (There are also two other ways of doing it...read here if interested https://www.gatewaytoairguns.org/GTA/index.php?topic=116903)
 
OK, you guys way more knowledgeable with guns and scopes but I am more a mathematics/trigonometry guru ;)

If the dowetail or picatinny or nato rail mount - is machined off the center (let say angled error and not parallel to the barrel either horizontally or vertically or both) that means any ring you attach to that mounting feature will follow that offcenter=angle, unless your rings have some machining errors as well and unintentionally you just zero it...

We talking 0.1 degree angle offsets = meaning not parallel...that will drop your "MOA" or "MILL" somewhere else...and in this case you zero the scope @ 50 and at 20 it will hit Left at 70 it will hit Right....and like this.

I like the idea of centering the scope reticle with a mirror to the barrel hole, but that will be accurate only for the given distance (to the mirror + back to the barrel), all this if the machining have a flaw...if you go with that game then better do it longest possible distance.

Otherwise you need to shim the rings, shoot it, shim it, shoot it until you get tired or you get there to acceptable POA=POI.

For example:

We have the FX Impact 1" (or maybe 1.5" I never measure it) scope rail, that is not hard attached to the main body, you can tighten the scope rings to that rail and "swivel" the rail to get the two parallels running together. Onse parallel then you do zeroing the scope in Horizontal and Vertical. Right?
 
OK, you guys way more knowledgeable with guns and scopes but I am more a mathematics/trigonometry guru ;)

If the dowetail or picatinny or nato rail mount - is machined off the center (let say angled error and not parallel to the barrel either horizontally or vertically or both) that means any ring you attach to that mounting feature will follow that offcenter=angle, unless your rings have some machining errors as well and unintentionally you just zero it... parallel then you do zeroing the scope in Horizontal and Vertical. Right?...

The turret adjustments can be used to change the angle of the erector tube, that is inside the scope body, both horizontally and vertically. Unless the dovetail is severely misaligned, the turrets typically have plenty of adjustment to bring the erector tube into alignment with the barrel bore-line. Use that and rotate the scope tube in the mounts so that the vertical reticle intersects the bore, and you are good to go.

Ultimately , you end up with the erector tube perfectly parallel in the horizontal plane and angled down about 20moa in the vertical plane. There are even mounts/adapters that purposely angle the whole scope downward so as not to use up too much of he vertical turret adjustment range.
 
I mounted a big x50 scope and tuned the scope rail to zero, don't touch the turrets. Find some "no wind" tunnel and clamp the gun in a vise, shot it 20-50-70 and adjust the rail until all distances POI hit the same H&V. Takes some time but worth it.

Now I can remove my big scope for storing, also swapping red dots and holo sights depend what game I want to play next couple days. Only thing that can mess the mind is me.
 
Nothing new here guys, probably rail not centered perfectly with bore or scope mount could be out of specs , like I said before try different mounts and see what happen, or if you can turn barrel in receiver, try that.

Easy way to fix it ,just zero your gun (windage) at the longest distance you shooting and you done, or if you want your scope to be perfect in line with the bore and optically centered you will need windage adjustable mounts or turn barrel if you can.

As @bigHUN mentioned , rail or mounts can be out of specs tiny bit to be 2"-3" off at 100 yards or barrel could be bent and honestly I don't remember when was the last time rail and bore was perfectly centered on any of my guns.

B