Could I put it through a planer? To shave a teeny tiny bit offWell, you start off by making every piece EXACTLY the same size. Exactly, not a 1/32" of a difference because dimensional errors compound themselves.
You'll need some sort of square, your school probably has a framing square . Then before drilling, clamp all the pieces together on a dead flat surface. A sheet of plywood or melamine is good for that. Then check that your construction is square by measuring the diagonals, they need to be EXACTLY the same..
Then if you plan on placing something on top of the structure I would recommend a ply or melamine again.
I mean, ya aint makin' a piano here
Does the make any sense?