The degree of Al saturation of an igneous rock may be given by its aluminium saturation index (ASI), defined as the molar ratio Al2O3/(CaO+K2O+Na2O). One suggested origin for mildly peraluminous granites (ASI 1-1.1) is fractional crystallization of subaluminous magmas (ASI <1); hornblende, having ASI <0.5, could be a major driving force in such a fractionation process. The effectiveness of the process depends not only on the precipitation of hornblende out of the reacting system, but also on the composition, nature and abundance of the other precipitating phases. Precipitation of feldspar (ASI=1), for instance, would retard or even prevent Al enrichment in the melt of the ASI of melt <1, but would enhance such evolution if the ASI of the melt is >1. For hornblende to effectively cause a melt to evolve into a peraluminous composition, it must be able to coexist with peraluminous magmas; e.g. at = or <5 kbar hornblende can coexist with strongly peraluminous melts (ASI approx 1.5). Potentials and problems of using coarse-grained granitic rocks to prove courses of magmatic evolution are illustrated by a suite of samples from the Grayling Lake pluton, SW Montana. Such rocks generally contain a large cumulate component and should not be used as a primary test for the occurrence or efficacy of a fractionation process that might lead to peraluminous melts. The process is unlikely to give rise to peraluminous plutons of batholithic dimensions. A differential equation is presented which allows the direct use of mineral chemistry and modal abundance to predict the path of incremental evolution of a given magma.-R.A.H.