Is there a name for non-pawn pieces? I'm trying to describe chess to a person, and one of my sentences was:

"Two rows, one with pawns and another with [non-pawns]"

What would the collection of King, Queen, Bishops, Knights and Towers be called?
As you probably know, sometimes the word "pieces" itself is used for that (you can say for example: white has two pieces and three pawns left). But that isn't very practical to use.

The only solution I can think of is using light pieces, heavy pieces and a king.

Not a one word, but at least it can be used in your sentence.