The loss factor of viscoelastic materials as a function of frequency has at least one peak. The relation between the magnitude and width of the loss factor peak is investigated in this paper by means of the fractional derivative Zener model with special reference to polymeric materials used for sound and vibration damping. It is shown that the magnitude and width are interrelated through the dispersion of dynamic modulus and the rate of frequency variation of loss factor. Moreover, it is proved that the relation between the magnitude and width of the loss factor peak is not unequivocal; either proportionality or inverse proportionality may exist between them. The important consequence of prediction on the proportionality is that, in contrast to the common belief concerning polymers, it is physically possible to increase the loss factor while simultaneously broadening the peak. The validity of model predictions is discussed and it is proved that the predictions are of a general nature, because they obey fundamental physical principles. Experimental data supporting the theoretical predictions are presented.