“There has never been in the history of music a child prodigy to equal Mendelssohn,” pianist and author Charles Rosen once wrote. “As a teenager, he was a much better composer than either Beethoven or Mozart at the same age.” And yet, as Rosen continues, “Mendelssohn’s precocity was a curse as well as a gift. Because of it, he never matched the extravagance of his greater contemporaries.”

That may be true. Though what does extravagance have to do with genius? Anyway, as those of us who love Felix Mendelssohn’s music know, there’s a lot more to admire in his substantial oeuvre than those great masterpieces of his teenage years, the Octet and the Overture to A Midsummer Night’s Dream, the Violin Concerto and maybe some of the Songs Without Words. Like the five symphonies, for instance, which achieve a startling unity and variety within single works and in relation to each other through Mendelssohn elegantly working out the implications of existing models.

The First wears its debt to Mozart on its sleeve but is impeccably crafted and exhilarating to listen to. The Second, the extraordinary symphony-cantata known as the Hymn of Praise, seeks to reconcile the Baroque...