At the risk of sounding redundant here and/or adding fuel to the discussion, a locomotive sounding square is when the exhaust occurs at an even tempo. Assuming that everything is good with the valve gear from the eccentric crank right up to the combination lever and valve rod, the locomotive can be brought square by proper positioning of the valve cages in the valve cylinder relative to the valve spool. The width of each ring set on the valve spool between the steam and exhaust edges of the ring set takes into account the width of the ports in the cages plus the amount of lap and lead, plus or minus the amount of exhaust lap or clearance between the exhaust edges in the cage ports and the exhaust edges on the spool ring set. The NKP originally had ¼” exhaust clearance on the 2-8-4’s but changed in later years to line and line exhaust edge alignment.
The locomotive can be made square by proper positioning of the valve cage exhaust edges front to back to correspond to the exhaust edges front to back on the valve spool. Of course the position of valve spool in the cylinder must be known. One way would be to measure the position of the valve in the cylinder by noting its location at both front and back dead center which are good points to measure as the valve gear imparts no motion to the valve at these points. Valve motion at these points is imparted only by the combination lever. As a nice check point, open up the peep holes front and back after the cages are set, and check if the lead is the same front and back.
A mushy, or different sound intensity of a squared exhaust could occur when there is blowby between the rings and cages, or port exhaust edges not parallel to the rings.