Both the Langelier and Ryznar indicies are used to predict scaling (but are not considered useful to predict aggesivness or corrosiveness to plaster by many experts) . The Ryznar Stablility index is based on empirical evidence from obervations of scale thickness and water chemistry in municipal water systems. It is supposed to have some usefulness in predicting corrosiveness to steel The Langelier Saturation Index is a theoretical model of calcium carbonate satuation and pH is the main variable in this equations with temperature being the second most important. By this it means that biggest changes in the index will come from a change in pH or temperature. This goes along with what we commonly observe, high pH tends to create scaling conditions and low pH tends to create corrosive conditions.
The Hamilton Index was developed by Jock Hamilton of United Chemical based on empirical observation of swimming pools and usually is used with 'high pH' pools. Most pools on this system run at a pH of around 8.0. It is also interesting that many of the bromine based products that are made by United chemical function better at a higher pH.