Long story short, the classic "ding-dong" doorbell chime is the first two notes of the bells played Westminster Palace, which in turn are based on Handel's opera The Messiah. Read more about it, it's neat.
My grandparents own a "ding dong" clock, which would count every quarter hour and then count the entire hour just as you heard... then it would fucking mark the hour with a number of tolls... the fucking insanity. If that clock still exists next time I am there, it's existence will be short.