Forte came up with his system to address a real need in analyzing non-diatonic music. There were all kinds of terminology in play often using variants of diatonic terminology. As I said, the Forte names are nice and abstract and the rules for merging pitches into set classes are objective and not subjective. There are those, myself included, who feel that his method is a little too objective in that some feel that musical ramifications are ignored in his formulas.
The classic example is set class 3-11 ( I think) where Forte's theory merges the pitch set for the major and minor triads into the same set class, thus saying that these two pitch collections are exactly the same, which, of course, is not really true. My way of dealing with this issue is by incorporating the concept of a subclass within Forte's class, one subclass for the prime form and one for the inversion. Thus, one can, when desired, refer to entities with differing musical purposes using my extension to Forte's naming scheme.
