No house should ever be on a hill or on anything. It should be of the hill. Belonging to it. Hill and house should live together each the happier for the other.
Britten's opera tends to see things in simpler terms. It portrays an Aschenbach who wants a richer form of sexual fulfillment, and who is hemmed in by the social conventions to which he subscribes. But Visconti's use of the Mahler Adagietto is perfect for what I take to be Aschenbach's sexual desire.