Mr. Hoyt is an assistant professor of music history at the University of South Carolina and serves as a program annotator and lecturer for the Mostly Mozart Festival in New York. He outlined his findings at a meeting of the American Musicological Society in early November.

The Mozart theory “cleans up the picture,” said Bruce Alan Brown, a professor of musicology at the University of Southern California. “It tells us something not just about the state of his finances,” he added, “but the manner in which he got along with the high aristocracy,” the main patrons of Viennese music at the time.

Mr. Hoyt acknowledged that he had to make assumptions to arrive at the 1,000 thaler figure and the date of May 2, 1789, among them that the rate of interest was 4 percent instead of the more usual 5 percent, and that the conversion rate was one mentioned by Mozart in a letter to his wife. No other set of variables produces such a round number in Prussian currency or such a date. Mozart was not likely to have borrowed from Lichnowsky before the hastily arranged trip because the prince was paying for the journey.

Lichnowsky, obligated to spend time in Berlin because of his holdings and military position in Prussia, invited Mozart along. They left Vienna on April 8 and made stops in Dresden, Leipzig, Potsdam and Berlin before Lichnowsky split off to return to Leipzig. Mozart made his way back to Vienna on June 4. It was his last extended trip abroad after a lifetime of journeying.

The trip was not much of a success musically. Mozart wrote little music in connection with it. Nor does the tour appear to have been a financial success, and Mr. Hoyt’s research, he said, helps nail down that it was indeed something of a bust.