  We examine the $N_p N_n$ scheme based on a recently proposed simple empirical
formula which is highly valid for the excitation energy of the first excited
natural parity even multipole states in even-even nuclei. We demonstrate
explicitly that the $N_p N_n$ scheme for the excitation energy emerges from the
separate exponential dependence of the excitation energy on the valence nucleon
numbers $N_p$ and $N_n$ together with the fact that only a limited set of
numbers is allowed for the $N_p$ and $N_n$ of the existing nuclei.
