  In the study of disordered models like spin glasses the key object of
interest is the rugged energy hypersurface defined in configuration space. The
statistical mechanics calculation of the Gibbs-Boltzmann Partition Function
gives the information necessary to understand the equilibrium behavior of the
system as a function of the temperature but is not enough if we are interested
in more general aspects of the hypersurface: it does not give us, for instance,
the different degrees of ruggedness at different scales. In the context of the
Replica Symmetry Breaking (RSB) approach we discuss here a rather simple
extension that can provide a much more detailed picture. The attractiveness of
the method relies in that it is conceptually transparent and the additional
calculations are rather straightforward. We think that this approach reveals an
ultrametric organisation with many levels in models like p-spin glasses when we
include saddle points. In this first paper we present the detailed calculations
for the spherical p-spin glass model where we discover that the corresponding
decreasing Parisi function $q(x)$ codes this hidden ultrametric organisation.
