The elder brothers were the sons as well as pupils of the principal musician to the Duke of Brunswick, Ägidius Christoph Müller (1765–1841), and were all of them born in the city of Brunswick.

Karl (Carl) Friedrich Müller (1797–1873) was first violin in the quartet and was also concertmaster to the Duke.

The Müller brothers were ambitious for greater fame than could be obtained within their own limited environment, but their employer, the Duke of Brunswick, had stipulated that none of his musicians should participate in any musical performance outside that connected with his own corps.

Their first appearance outside Brunswick was in Hamburg, where they met with such success that they were invited to Berlin, where they were received with great enthusiasm.

They confined their programmes almost entirely to the works of Haydn, Mozart, and Beethoven, and were also a very important influence in cultivating music appreciation.