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 enough 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 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.