Tedd:

I assume you mean 14-15 feet, not inches for the span.

The situation you are describing sounds like one in which the purlins are supported by the rafters rather than vice versa. In this case the total load carried by the rafters will be the same as in the case with no purlins, Thus, the purlins don't reduce the work that has to be done by the rafters. Rather, they simply give more points at which the roof deck can be attached.

In barn roofs, there is often a purlin plate which supports the rafters at mid-span. In this case the distance spanned by the rafters is halved and thus permits them to be smaller and on a wider spacing.

It's not possible to answer your girder question without knowing the actual loads, but in timber-framing 12 feet is a common span and often supported by normal-sized plates.