Born in Eckartsberga, Province of Saxony, he was a pupil of Ferdinand David. He became a member of the Leipzig Gewandhaus Orchestra, and in 1853 moved to the court orchestra of Saxe-Weimar-Eisenach in Weimar. From 1860 he taught at the Charitable Society of Violin Playing. At the suggestion of the Bavarian Court Kapellmeister Hans von Bülow - whom he had met in Basel in 1866 and organised joint chamber music - Abel went on to become concertmaster of the court orchestra in Munich in 1867. He took up teaching at the Musikschule in Munich managed by Hans von Bülow, where he became Professor in 1880 and retired in 1894.
- Theodore Baker and Alfred Remy, ed. (1919). "Abel, Ludwig". Baker's Biographical Dictionary of Musicians (3rd ed.). p. 2.
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