This article designs a method of improving traditional, qualitative semantic maps based on grammaticalisation paths, by including both quantitative data (frequency) and information concerning a gram's environment (the relation to the other maps). The incorporation of qualitative evidence transforms vectored maps into waves, while the introduction of the contextual factor combines waves organised along the same grammaticalisation template into a stream. The structure of a wave delivers, in turn, the statistical prototypicality of a gram (i.e. the prototypicality that is conditioned by the gram's own wave), whereas the structure of the stream yields product prototypicality (i.e. the prototypicality that is a combination of the gram's wave and the other waves of the stream). It is additionally hypothesised that the product prototypicality may be an overt indicator of the psychological perception of the grams by speakers.