A host of alternative energy formulae for the ground bands of even $Z$ even $N$ nuclei are available in the literature. The usual approach is to compare the relative numerical accuracy of the predictions of the level energies by these formulae, for varying deformations of the nuclear core and for high spins. The soft rotor formula and variable moment of inertia model, the $ab$ and $pq$ formulae, the rotation vibration interaction and power index formulae are illustrated. Here, a new perspective is presented, with emphasis on the limitation of the region of their physical validity and on deriving useful meaning of their parameters.