Several gradual semantics for abstract and bipolar argumentation have been proposed in the literature, ascribing to each argument a value taken from a scale, i.e. an ordered set. These values somewhat match the arguments’ dialectical status and provide an indication of their dialectical strength, in the context of the given argumentation framework. These research efforts have been complemented by formulations of several properties that these gradual semantics may satisfy. More recently a synthesis of many literature properties into more general groupings based on parametric definitions has been proposed. In this paper we show how this generalised parametric formulation enables the identification of new properties not previously considered in the literature and discuss their usefulness to capture alternative requirements coming from different application contexts.