Harold Arlen, 81, who composed more than 500 songs including such favorites as "Over the Rainbow," and "That Old Black Magic," died of natural causes yesterday at his Manhattan apartment.

"Over the Rainbow," which Judy Garland immortalized in her role of Dorothy in the movie version of "The Wizard of Oz," was one of Arlen's most popular tunes.

Another was "Stormy Weather," often associated with the careers of singers Ethel Waters and Lena Horne.

Mr. Arlen's music also enhanced such Broadway shows as "Bloomer Girl," "St. Louis Woman," "Jamaica" and "House of Flowers." His film credits include music for the early version of "A Star Is Born" and "Cabin in the Sky."

In 1973, he was awarded the Handel Medallion, New York City's highest cultural award, by Mayor John Lindsay. Three years later, he was among the first Americans to receive a National Music Award, given for contributions to American music. And in June 1984, the Kool Jazz Festival honored Mr. Arlen at a Carnegie Hall concert of his music.

Alec Wilder, author of the authoritative volume "American Popular Songs," said once that Mr. Arlen, "had not only an outstanding melodic gift, but harmonic sensibilities of the most sophisticated sort."

Born Chaim Arluk in Buffalo, the son of a cantor, Mr. Arlen was forced by his mother to take piano lessons that he didn't much like until he first heard jazz. In his teens he became a pianist-vocalist-arranger for collegiate groups in upper New York state.

In the early 1920s Mr. Arlen worked with dance bands as a pianist, singer and arranger. One of his bands was his own group, "The Snappy Trio," which later became "The Southbound Shufflers."

Within a few years he was writing the music for "Earl Carroll Vanities," and the "Cotton Club Parade."

In 1938, Mr. Arlen's songwriting career took off when a promoter heard him improvising at a piano and put him in touch with lyricist Ted Kochler. The improvised tune became "Get Happy."

He moved to Hollywood in the late 1930s. where he wrote for a number of movies, including "The Wizard of Oz."

Mr. Arlen and cowriter E.Y. (Yip) Harburg won the Academy Award for Best Song in 1939 for their "Over the Rainbow," which had become Judy Garland's theme song.

That was followed by other popular songs including, "I've Got the World on a String," "It's Only a Paper Moon" and "Come Rain or Come Shine." He continued writing until his wife's death in 1978.

Mr. Arlen once told a Washington Post reporter that his happiest moment came on a trip to Europe.

He said, "I didn't go to Europe for many years and one day I found myself a lone tourist among a score of Europeans, on a Seine riverboat. A little trio was playing 'Stormy Weather.' "