We report the results of a comprehensive study of lattice dynamics by means of far-infrared phonon spectroscopy in quaternary semimagnetic narrow-gap single crystals. A new version of the isodisplacement model is developed which takes into account the peculiarities of the dielectric function of narrow-gap semiconductors. This new approach is used to describe the phonon spectra transformation with composition for quaternary materials and is found to be in excellent agreement with the experimental data. The evidence for better quality and more stabilized crystalline structure of in comparison with ternary is presented and ascribed to the effect of magnetic doping.