What about "Variations"

By 'composing' a variation on a song - would that be called proper composing?

I would call any song based on another song an ''arrangement''. But that's not a widespread oppinion, methinks.

Really?

Listen to Beethoven's "33 Variations on a Waltz by Diabelli" or Rachmaninov's "Rhapsody on a Theme by Paganini." You might change your mind about that.

I think it's what you do with it that counts... an arrangement where the notes are handed out to different instruments is a bit of a grey area, perhaps, but it's surely the amount of influence te second composer has....