A recently proposed parametric model re-conceptualizes capacity curves as composed by linear and non-linear parts. The normalized non-linear capacity curve can be modelled by a cumulative lognormal function. While the linear part is defined by the initial stiffness, the non-linear part keeps the information about the physical degradation of the structure for increasing drifts. Besides, the non-linear part of capacity curves allows defining new curves related to energy loss and to tangent and secant stiffness degradation. It has been shown that an adequate combination of the energy loss and secant stiffness degradation functions leads to a good pointer of physical damage and, therefore, it can be used as a new damage index. This new damage index can be calibrated in such a way that it is equivalent to the well-known Park and Ang damage index, which, in turn, can be obtained from incremental dynamic analyses. In this paper the theoretical formulation of the parametric model and the one of the new damage index are reviewed first. Then the relation between the degradation of the building and the increase of its fundamental period of response is investigated, showing that the increase of the period can be also a good damage forecaster.