Cylindricity is to itself and is a combination of roundness, straightness and size distortion (straightness of a surface).
If one had perpendicularity of a long hole with a diametrical tolerance zone, it would control the angle of the hole and the straightness of the axis. If, as an example, the perpendicularity is a diametrical tolerance zone of 0.1 mm, one could zero off on the bottom of the hole (centre) and then check the top of the hole. Let's say it was 0.08 mm off perpendicularity. One should also check the middle distance down the hole and let's say this is 0.09 mm. The 0.09 is the result that should be reported and it was caused by the hole axis not being straight.
It does not control size distortion as long as the hole is within tolerances and roundness really doesn't come into this as long as everything meets rule #1 on size.
Cylindricity is not controlled by Perpendicularity in any way, at least not in ASME Y14.5M-1994.
When applied to a cylindrical feature of size, Perpendicularity controls the orientation of the cylinder's axis. The cylinder's axis is defined as the axis of its Actual Mating Envelope, and is by definition perfectly straight.
Controlling the orientation of the axis does not control any of the cylinder's form characteristics (circularity, cylindricity, surface line straightness, derived median line straightness). These would be governed by the size tolerance (via Rule #1) or by explicit form controls if present.
Put it this way - a banana could be perpendicular to the floor within 0.001".
Think of a piece of bar stock with the ends chopped off at 45°. It is still cylindrical, but has no features to be perpendicular to. I realize that this is a simplification, along the lines of the banana, but they serve to illustrate the OP.
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