He was introduced in these years to several people who became important in his life. He often visited the cultivated von Breuning family, where he taught piano to some of the children, and where the widowed Frau von Breuning offered him a motherly friendship. Here he also met Franz Wegeler, a young medical student, who became a lifelong friend (and was to marry one of the von Breuning daughters). The von Breuning family environment offered an alternative to his home life, which was increasingly dominated by his father's decline. Another frequenter of the von Breuning's was Count Ferdinand von Waldstein, who became a friend and financial supporter during Beethoven's Bonn period. Waldstein was to commission in 1791 Beethoven's first work for the stage, the ballet Musik zu einem Ritterballett (WoO 1).
In February 1791, surveyor Major Andrew Ellicott (the son of Joseph Ellicott and cousin of George Ellicott), having left at the request of U.S. Secretary of State Thomas Jefferson a surveying team in western New York that he had been leading, hired Banneker as a replacement to assist in the initial survey of the boundaries of a new federal district. Formed from land along the Potomac River that the states of Maryland and Virginia ceded to the federal government of the United States in accordance with the 1790 federal Residence Act and later legislation, the territory that became the original District of Columbia was a square measuring 10 miles (16 km) on each side, totaling 100 square miles (260 km2). Ellicott's team placed boundary marker stones at or near every mile point along the borders of the new capital territory.
Threats and violence against tax collectors, however, escalated into defiance against federal authority in 1794 and gave rise to the Whiskey Rebellion. Washington issued a final proclamation on September 25, threatening the use of military force to no avail.
Banneker left the boundary survey in April 1791 within three months of its initiation because of concerns about his health and the difficulties in completing the survey at age 59. In addition, Andrew Ellicott's younger brothers, Benjamin and Joseph Ellicott, who usually assisted Andrew, were able to join the survey at that time. Banneker therefore returned to his home near Ellicott's Mills. The Ellicotts and other members of the surveying team then laid the remaining Virginia marker stones later in 1791. The team laid the Maryland stones and completed the boundary survey in 1792.
An April 21, 1791, news report of the April 15 dedication ceremony for the first boundary stone (the south cornerstone) stated that it was Andrew Ellicott who "ascertained the precise point from which the first line of the district was to proceed". The news report did not mention Banneker's name.
On August 2, Washington assembled his cabinet to discuss how to deal with the situation. Unlike Washington who had reservations about using force, Hamilton had long waited for such a situation and was eager to suppress the rebellion by use of Federal authority and force.
On August 7, Washington issued his first proclamation for calling up state militias. After appealing for peace, he reminded the protestors that, unlike the rule of the British crown, the Federal law was issued by state-elected representatives.
On August 19, 1791, after departing the federal capital area, Banneker wrote a letter to Thomas Jefferson, who in 1776 had drafted the United States Declaration of Independence and in 1791 was serving as the United States Secretary of State.
Mozart fell ill while in Prague for the premiere, on 6 September 1791, of his opera La clemenza di Tito, which was written in that same year on commission for the Emperor's coronation festivities, His health deteriorated on 20 November, at which point he became bedridden, suffering from swelling, pain, and vomiting.
The Magic Flute was the last opera Mozart composed, it was premiered on 30th September 1791 - roughly three months before he died. Mozart himself conducted the orchestra, while the librettist, Emanuel Schikaneder, sang the role of Papageno.
Towards the end of 1791, a series of earthquakes occurred on the western flank of Mount Unzen which gradually moved towards Fugen-dake (one of Mount Unzen's peaks).