  The formalizations of periods of time inside a linear model of Time are
usually based on the notion of intervals, that may contain or may not their
endpoints. This is not enought when the periods are written in terms of coarse
granularities with respect to the event taken into account. For instance, how
to express the inter-war period in terms of a {\em years} interval? This paper
presents a new type of intervals, neither open, nor closed or open-closed and
the extension of operations on intervals of this new type, in order to reduce
the gap between the discourse related to temporal relationship and its
translation into a discretized model of Time.
