Not sure if that began life as a riddle or what but the truth is pitch and diameter are not clearly related in that manner. If you are looking to raise rpms, you lower pitch and vice versa.
Diameter is all about increasing blade surface area. The larger the blade surface area the larger load the blades can carry. Yes, a larger diameter wheel will affect rpms but not in any linear relationship with pitch neccessarily. Numbers of blades, cup etc are also variables.
Most designers will try to keep the pitch and diameter not to exceed square, meaning the pitch in inches doesn't exceed the diameter in inches. In reality and especially now with higher speed engines, more HP on tap many props are over square just because the hull has a limiting propeller diameter and you want to go faster. You will notice that the newer designed DE's are being made to carry larger diameter props than hulls designed more than ten years ago. If you take a look at the pictures of the propeller in the 38' Flowers with 1000 hp thread you will notice an extremely larger diameter prop than 36/38 boats of the past.