What is the medical term meaning heart muscle's ability to generate its own electrical impulses?

This is not a muscle (eg biceps brachi etc) but a muscle type. Chardiac muscle is a specialised muscle type that can contract as well as carry a current. There are also special cells in the heart, that make up the purkinje fibres, which contain very little contractile matter and are mostly for the conductance of the AP but are still considered muscle cells.