In Quantum-Theoretical Re-Interpretation (1925), Heisenberg gives the following:
In order to characterize this radiation [of an electron] we first need the frequencies which appear as functions of two variables. In quantum theory these functions are of the form $$ \nu(n,\alpha) = \frac{1}{h}\left[W(n)-W(n-\alpha)\right], $$ and in classical theory of the form $$ \nu(n,\alpha) = \alpha\nu(n) = \alpha \frac{1}{h} \frac{dW}{dn}. $$
Here, $\nu$ is frequency, $n$ in the first equation is the quantum number of the first state, $\alpha$ is an integer such that the second state's quantum number is $n-\alpha$, and $W$ is the energy. Where does the classical equation come from, and how is $n$ to be interpreted? (It might be more specific to ask, how do we derive the classical equation from the correspondence principle?)