Generic term for musical piece

I searched for "hyponym song" and found an interesting page. While the page provides song six senses, only the first ("A short musical composition with words") seems to apply.

One section says:

Hypernyms ("song" is a kind of...): composition; musical composition; opus; piece; piece of music (a musical work that has been created)

I would go with any of these. It should be of little concern that piece can be used in other contexts, as it is a versatile word.

You can call Handel's Messiah a piece and you can call Justin Bieber's "U Smile" a piece. I would only call the former an opus.

As to the (possibly rhetorical) question on why no one has coined a hypernym of song. The hyponyms convey information about the genre, pedigree, length, or quality of the piece. Song does not. Track does not. One wouldn't call Handel's Messiah a ditty or Justin Bieber's "U Smile" a magnum opus, except for comic effect.

I'd need context, but go with "piece" or "work" for most uses. If you're looking for a term that includes arias, symphonies, songs, mouth music, smooth jazz, and dubstep—I doubt there is one. We do have the term "oeuvre", but when used (rarely) it tends to refer to a person's total body of work. (See what I did there, with "work"?)