Leonard Bernstein was born on August 25, 1918. One of the major figures of 20th-century American music, Bernstein was a composer, conductor, and educator whose celebrity extended far wider than was usual for classical musicians. In part, that was because he wasn't only a classical musician. In addition to his music for the concert hall, Bernstein wrote for Broadway and Hollywood, and became a television star with a long-running series of musical lectures.
Bernstein was already a skilled pianist when he began his college education at Harvard in 1935. During his time at Harvard, he met Aaron Copland, who became an important mentor. Bernstein never formally studied composition with Copland, but often turned to him for advice and comments about his music, and often referred to Copland as his "only real composition teacher."
After Harvard, Bernstein studied conducting with Fritz Reiner and Serge Koussevitzky, and developed quickly enough that he was appointed assistant conductor of the New York Philharmonic in 1943. He made his national debut on short notice on November 14 of that year when guest conductor Bruno Walter was taken ill; Bernstein took his place for a concert that was nationally broadcast and received glowing reviews. He quickly became a popular guest conductor with major American orchestras.
At the same time, he was becoming known as a composer. In 1944, he composed music for the Jerome Robbins ballet Fancy Free, about three sailors enjoying a day of liberty in New York; by the end of the year, he had teamed with lyricists Betty Comden and Adolph Green to expand that idea into the Broadway musical On the Town. Bernstein's first major concert work, the Symphony #1 ("Jeremiah") also premiered in 1944.
Being both composer and conductor, Bernstein made recordings of virtually all of his own concert music. If there's not a specific link to a Bernstein composition mentioned in this post, you'll find Bernstein's recording of it in the streaming set Bernstein Conducts Bernstein.
For the next twenty years, Bernstein was a towering figure on the American musical landscape. In the 1950s, he would have more Broadway success, with Wonderful Town and West Side Story; ventures into opera and operetta with Trouble in Tahiti and Candide; a violin concerto, the Serenade after Plato's Symposium; and his only original film score, to On the Waterfront.
In 1954, Bernstein made his first appearance on the television arts program Omnibus, an analysis of Beethoven's Fifth Symphony. His appearances there were so popular that they led to a series of Young People's Concerts, similar exercises in music appreciation for children. There were 43 Young People's Concerts between 1958 and 1972, each devoted to a specific composer or musical idea.
He also continued to break new ground as a conductor, leading the premiere performances of Olivier Messiaen's Turangalila-Symphonie and, roughly fifty years after it had been written, of Charles Ives' Second Symphony. In 1958, Bernstein was named music director of the New York Philharmonic, a post he held until 1969. That position limited the time he had for composing, and there were fewer major works in the 1960s. The decade did give us Bernstein's Symphony #3 ("Kaddish"), and the choral work Chichester Psalms.
During his time as director in New York, Bernstein held a Mahler festival in 1960. Interest in Mahler's music had declined since his death 50 years earlier, and Bernstein was a major contributor to the Mahler revival. Between 1960 and 1967, he became the first conductor to record a complete cycle of the Mahler symphonies.
Bernstein's major compositions after leaving the New York Philharmonic were not as well received as much of his earlier music had been. The 1971 Mass, written for the opening of the Kennedy Center, was a sprawling theater piece in which the Celebrant who is performing the Mass is confronted by a group of "street singers," singing in pop, rock, and blues styles, who challenge the relevance of the ritual to the modern world. They push the Celebrant to emotional and spiritual collapse—this is surely the only mass to ever include a mad scene—before his faith is restored by the simple song of a boy soprano. The Mass was met with generally negative reviews, but there have been several new recordings in the last decade, and the reputation of the piece seems to be improving.
And in 1976, Bernstein returned to Broadway with an unmitigated flop. The musical 1600 Pennsylvania Avenue looked at the first century of American history, with one pair of actors playing all of the presidents and first ladies, and another pair playing all of their servants. The musical closed in a week, and Bernstein was so frustrated by the reaction (and by the way his music had been trimmed during rehearsals) that he refused to allow a cast recording, and the Bernstein estate continues to refuse permission for the show to be recorded or even performed, though parts of it were eventually arranged into a choral work, A White House Cantata.
Bernstein spent much of his final decade revisiting earlier work. He conducted West Side Story for the first time, in a controversial recording that used opera singers instead of musical theater actors, and returned to the frequently-revised Candide to record what he called the "final revised version." The new opera A Quiet Place, originally written as a sequel to Trouble in Tahiti, was quickly revised to incorporate the earlier work as a flashback. Bernstein made his final appearance as a conductor in August of 1990 and died of a heart attack two months later.
Bernstein was often frustrated that his most serious work was not better received by critics and audiences. It is true that his musicals are more frequently performed than his orchestral work, and even in the concert hall, his most frequently performed pieces are derived from the theatre—the overture from Candide, the Symphonic Dances from West Side Story, the Three Dance Episodes from On the Town. But the Serenade seems to have taken a place among the standard repertory of violin concertos, and the Chichester Psalms is firmly established as an important choral work.
His legacy as a conductor may be even more important. As mentioned above, he was a key figure in the mid-century Mahler revival, and he also championed the music of Jean Sibelius, Carl Nielsen, and a large number of then-contemporary American composers. He was an important teacher of conducting whose students include Michael Tilson Thomas, Edo de Waart, Seiji Ozawa, and Marin Alsop, who has recorded much of his music in recent years.
In addition to the pieces linked above, much more of Bernstein's music, as conductor and composer, is available for streaming or download at Hoopla and Freegal.

