Modified fractions, granularity and scale structure

Pragmatic enrichments arising from the use of modified fractions have been little studied, but offer interesting insights into the subtleties of scale structure and granularity. In this chapter I present some new experimental data on the interpretation of these expressions. I argue that these data suggest that modified fractions, like modified integers, give rise to pragmatic enrichments which are conditioned by scale granularity, but that we need to refine the notion of granularity somewhat to extend it to this domain. There is also evidence for enrichments that are not easily captured in classical quantity implicature terms, but which I suggest could be explained by appeal to typicality effects.