What is Anharmonicity constant, fundamental, overtone, hot band?

Example 6.14 (Hydrogen chloride)

For $\ce{H^{35}Cl}$, $\tilde\omega_e = 2990.95\,\mathrm{cm}^{-1}$ and $\tilde\omega_ex_e = 52.82\,\mathrm{cm}^{-1}$: the fundamental is at $\tilde\omega_e - 2\tilde\omega_ex_e = 2885.3\,\mathrm{cm}^{-1}$ and the first overtone at $2\tilde\omega_e - 6\tilde\omega_ex_e = 5665.0\,\mathrm{cm}^{-1}$, slightly less than twice the fundamental. The Morse model predicts $D_e = 42\,342\,\mathrm{cm}^{-1}$ and $D_0 = 40\,860\,\mathrm{cm}^{-1}$; the true $D_0$, from the enthalpies of formation of H, Cl and HCl at $0\,\mathrm{K}$, is $35\,760\,\mathrm{cm}^{-1}$ ($4.43\,\mathrm{eV}$). The real potential flattens out faster than a Morse curve fitted at the bottom: Birge–Sponer extrapolations from the lowest levels overestimate dissociation energies.