The Lawn Institute brings us a clear list on proper grass height. "No matter the kind of grass you have, there is a simple; rule of thumb to follow when mowing your lawn.  Never remove more than one-third (1/3) of the leaf surface each time you mow. Leaf surface, or cutting height, refers to the length of grass above the soil.

Cutting below the optimum height impedes root development, which is key to having a dense, healthy lawn. Use the following chart to determine the best growing height for your kind of grass and when to mow it again"

The list can be read, simply by looking at the numbers. Type of Grass, the second number is the Best Mowing Height the third is Mow when it reaches.

Bluegrass - 2in. - 3 in.
Perennial ryegrass - 2in. - 3 in.
Tall fescue - 2in. - 3 in.
Fine Fescue - 2in. - 3 in.
St. Augustine - 2in. - 3 in.
Buffalograss - 2in. - 3 in.
Bermuda - 1.5. - 2.25 in.
Zoysia -  1.5. - 2.25 in.
Centipede - 1.5. - 2.25 in.