My response is in keeping with St. Pius X's teaching on Sacred Music. Any LITURGICAL singing is a function of the clerical state, and therefore women cannot exercise it. They can participate in singing other things, provided there's no risk of inciting concupiscence. But they cannot sing the liturgical portions ... and yet this is done anyway in most Trad chapels.
One can make a case for the fact that the singing in a Missa Cantata is not strictly liturgical, since the priest and servers make all the responses anyway, that it's just more window-dressing. But in a Missa Solemnis, the choir makes the responses in lieu of the servers, and therefore it's liturgical function.
Now, o dull-witted one, the major point is that it's not true that women cannot participate in any chapel functions. The principal here, as Matthew also agreed, is that men should not be in a position to be subordinated to men. In an all-female congregation, for instance, say at a girls' school, there would be nothing wrong with women taking up the collection.