Harvey Schmidt, who earned his shining spot in theatre history as composer of the longest-running musical ever, The Fantasticks, died February 28 at age 88.

The Texas-born songwriter met his longtime lyricist Tom Jones when they were both students at the University of Texas/Austin in the late 1940s, and over the course of a career that spanned nearly the next half-century, Mr. Schmidt never wrote with anyone else. It was also at UT that Jones came across Edmund Rostand’s short play, Les Romanesques, a parody of Romeo and Juliet, which he would develop into the musical Western Joy Comes to Dead Horse, and which eventually evolved into The Fantasticks.

The Fantasticks opened May 3, 1960, at the Sullivan Street Playhouse in Greenwich Village, and ran until January 13, 2002, a run of 17,162 performances—the longest continuous run of any show in American history, and the longest continuous run of any musical in the world. A 2006 revival ran for 4,390 performances at the Jerry Orbach Theatre in midtown Manhattan.

As a composer, Mr. Schmidt was the most idiosyncratic of the generation that gave us Stephen Sondheim, Kander & Ebb, Bock & Harnick and Strouse & Adams. That may have come from the fact that Mr. Schmidt never had formal musical training, and, indeed, never learned to read or write music. He invented his own style, and became more experimental as he grew older. Like Irving Berlin, Mr. Schmidt had a transcriber write down his melodies as he played them. But Mr. Schmidt also had a prodigious memory, playing piano for workshop productions of his in-progress musicals entirely off the top of his head.

Mr. Schmidt had the ability to write beautiful long-line lilting melodies like “My Cup Runneth Over,” “They Were You” and his best-known hit, the sweet waltz “Try To Remember,” which is often included in anthologies of the best songs written for the American musical theatre. He often traveled to get inspiration for his music, and it was on the trip to Mexico City in the 1950s when he found himself in a plaza as a thunderstorm was approaching. The melody to “Soon It’s Gonna Rain” came to him whole on the spot, and the song later found its way into The Fantasticks. The latter two songs were covered dozens of times by pop singers and cabaret singers around the world.

Under the title Joy Comes to Dead Horse, their show was originally conceived as a Western in the style of Oklahoma!, with an Anglo boy in love with a Latina girl named Maria. When West Side Story opened with a similar plot, the project seemed doomed for a time, but when director Word Baker came to Jones and Schmidt and offered them a spot on a no-budget summer theatre program he was programming at Barnard University in the summer of 1959, they stripped out the elaborate costumes, sets, and special effects—everything that might cost money—and presented a one-act, bare-bones version of their show as The Fantasticks.

Expanded to two acts, the resulting minimalist musical opened at the Sullivan Street Playhouse in Greenwich Village in spring of 1960 to mixed reviews. Mr. Schmidt asked producer Lore Noto to try keeping it open until the weekend so his family could come up from Texas to see it. The show stayed open for the next 42 years.

Harvey Schmidt was born September 12, 1929. Growing up in Texas during the Depression, Mr. Schmidt had little contact with legitimate theatre. His main experiences with show business consisted of passing medicine shows and carnivals, plus the local movie theatre, where he fell in love with the Hollywood musicals of Astaire and Rogers. Both experiences strongly affected his later work. His 1963 musical 110 in the Shade, based on The Rainmaker, was drawn directly from the sights and sounds of his childhood.

Born of Germans who settled in Texas at the turn of the 20th century, Mr. Schmidt was a sweet-natured man, forever in awe of his onetime upperclassman, lyricist Tom Jones. During his early years in New York he supported himself as graphic artist. Among his best-known works was the spiky logo for The Fantasticks, which he hand-painted onto the China silk curtain that hung on the stage at the Sullivan Street Playhouse. Each Christmas, Mr. Schmidt would record an album of his favorite songs from old movie musicals and send them to friends. The envelopes, which were hand-lettered in that same spiky handwriting, become treasured keepsakes for the recipients.

After The Fantasticks, Jones and Schmidt seemed to have a bright future as writers of experimental musicals. Snapped up by producer David Merrick, they finally got to write their musical Western, 110 in the Shade in 1963. (It was revived on Broadway in 2007, with Audra McDonald as Lizzie.) Jones and Schmidt were prolific writers. Legend says they wrote 110 songs for 110 in the Shade, though Mr. Schmidt said it only felt that way. In 1966 they wrote I Do! I Do!, a rare musical for two characters, for two of the biggest stars on Broadway, Robert Preston and Mary Martin. Celebration would prove to be the duo's final Broadway show, in 1969.

In the early 1970s they focused their energies on several experimental smaller musicals presented in a converted church they rented on West 48th Street, which they dubbed “Portfolio.” Among projects that emerged from the Portfolio period were The Bone Room, about a middle-aged museum worker who faces a midlife crisis; Portfolio Revue, which offered a retrospective of the team’s work; and Philemon, a musical about a street thief in ancient Antioch who is transformed by his first contact with early Christianity. Starring Dick Latessa, Philemon was the only Portfolio project to get a commercial run for Schmidt and Jones.

They spent most of the next two decades working on two big projects, Colette (a.k.a. The Garden of Earthly Delights and Colette Collage) and Grover’s Corners (a musicalization of Thornton Wilder’s Our Town), which never got the full-scale Broadway productions they envisioned.

Jones and Schmidt had a late-career burst of creativity, writing two new musicals and assembling a revue of their work over the course of five years: Mirette (1996), The Show Goes On (1997), and Roadside. The latter two were produced by the Off-Broadway York Theatre Company, which served as an artistic home for the team in their later years.

After that, Mr. Schmidt retired to Tomball, Texas.

During a 2012 visit to NYC, during which he was inducted into the Songwriters Hall of Fame, Mr. Schmidt visited The Fantasticks and told Playbill, “I was very touched…. It was like seeing it fresh. I was so moved by Tom [Jones’ book and lyrics] and hearing my music again. And there’s so much quality in this cast. I’m so glad I made it.”