add class to parent ul of active menu

So, I have a 3 or 4 layer deep menu (ul li). For any given active menu item, I want to have the branch around it visible, but not other branches.

eg:

ul li
ul li – branch 1
li
li ul
li – active page
li
ul li – branch 2
/ul

etc.

Is there a way to set some sort of parent class on all parent uls?
eg:
ul li (parent)
ul li – branch 1 (parent)
li
li ul (parent)
li – active page
li
ul li – branch 2 (not a parent, do not show)
/ul

Or really, and plugin or anything that will add a richer set of classes to menu items so that I can get at them effectively with either jquery or CSS?