A High Alpha Angle can support the chops.
A Low Alpha Angle will give you more chop room at the top of the cup.
Some mouthpiece manufacturers refer to alpha angle as "relief" or "undercut". This tells you nothing because it has no "physical quantity" that is defined mathematically. For instance, you know you can play on a GR Mouthpiece with an alpha angle of 15 degrees. What happens when you try one with a 17 degree alpha angle?
Let's say that you bottom out on it. Now we have defined parameters and if you wish to have a smaller volume cup, we know that 15 degrees works for you, and there is no guesswork when it comes to your next mouthpiece. If you just play another mouthpiece with an "undercut", how do you know if the next piece you try with a different "undercut" or "relief" will work? This is one reason why GR Technologies has defined the Parameters of the Mouthpiece.
Hint! Standard GR Mouthpieces have alpha angles that drop as the cups get larger in volume.
The alpha angle is lower on the MS cup than on the S cup. The reason for this is that players who are used to the larger volume cups, are also used to lower alpha angles. Also, this is an excellent system for finding out which alpha angle works for you.
Let's say your chops can not tolerate the higher alpha angle of the S cup. You feel great on the M cup but you want less volume for your lead playing. GR can custom build you a smaller volume piece yet keep the alpha angle of the M cup to give you the feel you are after!