A musical motto consisting of three notes, F–A-flat–F, was significant to Brahms. In 1853 his friend Joseph Joachim had taken as his motto "Free, but lonely", in German, Frei aber einsam, and from the notes represented by the first letters of these words, F–A–E, Schumann, Brahms and Dietrich had jointly composed a violin sonata dedicated to Joachim. At the time of the Third Symphony, Brahms was a fifty-year-old bachelor who declared himself to be Frei aber froh, "Free but Happy". His F–A–F motto, and some altered variations of it, can be heard throughout the symphony.
At the beginning of the symphony the motto is the melody of the first three measures, and it is the bass line underlying the main theme in the next three. The motto persists, either boldly or disguised, as the melody or accompaniment throughout the movement. For the third movement, poco allegretto instead of using a rapid scherzo, standard in 19th century symphony, Brahms created a unique kind of third movement that is moderate in tempo (poco allegretto) and intensely lyrical in character.[2] The finale is a lyrical, passionate movement, rich in melody that is intensely exploited, altered, and developed. The movement ends with reference to the motto heard in the first movement - one which quotes a motif heard in Schumann's Symphony No. 3, Rhenish in the first movement just before the second theme enters in the recapitulation - then fades away to a quiet ending. (Wikipedia)