For a helix with constant radius, the pitch is related to the slope of the constant tangent with respect to the axis:

pitch = PI * 2 * radius * slope

So as the radius of that helix decreases, with constant pitch, the slope increases.

The slope of a helicoid increases closer to the axis.

For a helicoid created from sweep of a variable pitch helix, and intercepted with a surface of revolution that has variable radii,
the SLOPE at some point on the surface helix, could possibly decrease, stay the same or increase, w.r.t. the variable pitch helix. (?)

- Brian