Balanced words have been studied a lot in the last decades. In particular, Christoffel words that are a special case of finite balanced words. In this talk, I introduce the Balance matrix that studies the balancedness of these words and I define some tools to extend this property by defining a second order of balancedness. I recall some properties about the continued fraction development and the Stern-Brocot tree to prove a recursive formula based on the shape of the path from the root of the Stern-Brocot. Finally, I show that among all infinite paths in the Stern-Brocot tree, the one that converges to φ, the golden ratio, minimizes the growth of the second order balance.