I have been reading up on Galant schemata (stock melodic phrases) recently and have run into a question regarding their universality.
All of the various schemas (Prinner, Pastorale, Fenaroli, etc) that make up a classical sentence seem to accompany either tonic, subdominant, or dominant harmony. But, then, what schema's (if any) should be referred to when a ii, iii, or vi chord are involved?
I understand that perhaps these chords do fall under these three umbrellas (for example, the vi chord may be considered a prolongation of the tonic), though this seems to be controversial: Schenkerian analysts hold, for example, that the mediant scale degree is an expansion of the tonic because they have two common tones. Riemannian theory, on the other hand, considers the mediant the "dominant parallel".
Summing up, can we accompany the supertonic, mediant, and submediant harmonies with the various schemata of classical music by assuming their status as either tonic, subdominant, or dominant? Or, on the contrary, are these harmonies to be excluded when working on melodies based on the schemata?