For multi-part compositions, the generic work type "Movement" would be useful. See Ian Anderson's Divinities: Twelve Dances with God; the individual tracks are movements of a whole, but not really better classifiable (as Arias, Motets, etc.).

For traditional music (Irish, Scottish, English, Canadian, American, especially), the generic "Tune" would be useful. I don't think it would be useful to break it down further (Reel, Jig, Hornpipe, Polka, Mazurka, Waltz, etc.), but Tune would definitely be a good addition.