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.

Recently, we illustrated the use of the ${\gamma}$–g absolute B(E2) values in the Davydov–Filippov model (DFM), instead of the ${\gamma}$−g B(E2) ratios,for analysing the spectral features of the (${\gamma}$${\le}$20°) deformed nuclei. Here, we illustrate the application of the absolute ${\gamma}$−g B(E2) values to the triaxial (γ${\ge}$20°) nuclei to seek the new role of the ${\gamma}$ variable in these nuclei, and to derive the underlying physics. The decrease of the absolute ${\gamma}$−g B(E2) value for ${\gamma}$${\ge}$20°, instead of an increase observed for ${\gamma}$${\le}$20° deformed nuclei is explained. The increase of B(E2, 2$_γ$ − 0$^+$$_1$ ) in spite of the negative band mixing parameter, for deformed nuclei, reveals a new view of the band mixing angle, in contrast to its role for the triaxial nuclei. The three moments of inertia in DF model, for ${}^{158}$Dyand ${}^{120}$Xe display their degree of triaxiality.