Everyone knows the sounds of the Westminster Quarters. (I experienced the 2 p.m. ringing of Big Tom, the bell at Lincoln Cathedral, which is where I first learned of the music's origin.) The number of chime sets correspond to the quarter hours that have passed. The permutations are always played in order, with the count of the hour struck at the top. But, there's an interesting story to this omnipresent melody, with an English connection, of course.
The Westminster Quarters are also called the Cambridge Chimes. The chimes originated at the church of St. Mary the Great in Cambridge, which has a long association to bells. The Society of Cambridge Youths was founded in 1724 to formalize the responsibility to ring St. Mary's bells.
The chimes were adopted in the mid-19th century by the clock tower at the Palace of Westminster, which houses the very famous bell, Big Ben, that sings out these tunes. The adoption of the Cambridge Chimes for Big Ben spread the use of the tune and thus the name from Cambridge Chimes to Westminster Quarters.
A little bit of Cambridge is experienced every time a clock or church bell rings out on the quarter of the hour.