Derek Bermel recalled the moment things went awry in 2006 during rehearsals for his composition "The Migration Series." Trumpeter Wynton Marsalis had commissioned the piece, which paired the Jazz at Lincoln Center Orchestra and the American Composers Orchestra. All seemed well until the musicians reached a section marked by contrapuntal rhythms.

"I knew something was wrong," Mr. Bermel, a composer, conductor and clarinetist, said in an interview. "I felt the jazz band and the symphony orchestra pulling apart. The orchestra was going with the conductor, and the jazz band was going with the rhythm section—piano, bass and drums."

Mr. Bermel solved the problem by reassigning parts in his score. "Right then, I began to think about how a composer builds hybridity into a piece of music," he said. "How can awareness of the separate cultures of jazz and classical music fit into one musical architecture?"

Those are among the challenges addressed by the second class of the three-year-old Jazz Composers Orchestra Institute, which connects composers working primarily in jazz with symphony orchestras to seek a deepened context for such collaboration. The JCOI will present the first of three public readings of new symphonic works by these composers on Tuesday and Wednesday at Kleinhans Music Hall, in Buffalo, N.Y., with the Buffalo Philharmonic (there will be readings with the ACO at Columbia University's Miller Theater June 3 and 4, and with the La Jolla Symphony and Chorus, at UC San Diego's Mandeville Auditorium, Sept. 19 and 20). Thus concludes a process begun in August, when 37 composers attended a weeklong series of workshops and seminars at UCLA's Herb Alpert School of Music (17 of them now get the chance to work directly with orchestras).

Jazz and classical worlds have long intersected. Pianist James P. Johnson and saxophonist Ornette Coleman composed for symphony orchestras. George Gershwin and Leonard Bernstein incorporated jazz elements into orchestral works. Gunther Schuller proposed a "Third Stream"—somewhere between classical music and jazz—more than a half-century ago.

If that vision hasn't exactly materialized, quite a few jazz musicians have worked lately in classical contexts. For Maria Schneider's latest CD, "Winter Morning Walks," with opera singer Dawn Upshaw, the composer-arranger conducted the St. Paul and Australian chamber orchestras. Saxophonist Wayne Shorter has recently composed for and performed with both the Los Angeles Philharmonic and Orpheus Chamber Orchestra. Earlier this month, pianist Marcus Roberts performed an original piano concerto with the Atlanta Symphony Orchestra. Wadada Leo Smith's "Ten Freedom Summers," which paired the trumpeter's jazz quartet with a chamber orchestra, was a 2013 Pulitzer Prize finalist for music.

The JCOI, created in 2010, grew from conversations between George Lewis (then head of Columbia University's Center for Jazz Studies) and Michael Geller, the ACO's executive director. Mr. Lewis's celebrated work as a trombonist and composer demonstrates his ability to think beyond genre. "The word 'jazz' is not going to hold me back from doing what I want to do with a set of instruments," he said. "Still, there is a professional and socially constituted jazz field, and people identified with that field don't usually have access to an orchestra." If the JCOI fills a practical need, Mr. Geller thinks it extends both ways. "This program means an influx of music that is completely contemporary and offers a different perspective," he said.

Beyond opportunity, the program immerses musicians in the symphonic world. The workshop week—"a boot camp for musical modernists," Mr. Lewis called it— included a survey of symphonic innovation since about 1970, which Mr. Lewis thinks is too often overlooked. (He said that Gérard Grisey's "Partiels," composed in 1975, elicited "37 mouths open in astonishment at the same time.") There was practical instruction of many sorts. Harpist Anne LeBaron demonstrated her instrument's possibilities. An orchestra librarian shared the cost of an orchestra rehearsal (roughly $300 per minute).

Inevitably, issues of jazz aesthetics arose. Courtney Bryan, a 30-year-old pianist who studied jazz in her native New Orleans and classical music at Oberlin Conservatory in Ohio, asked about "strategies to notate the feeling of improvisation, without asking musicians to improvise." Mr. Bermel, who, as the ACO's creative adviser, worked closely with Mr. Lewis on the workshops, stressed one essential truth. "In a symphony orchestra, rhythm and momentum are driven by the strings," he said. "Most people don't realize that."

At his apartment in Brooklyn, N.Y., bassist Gregg August pulled out the score to his piece "Una Rumba Sinfonica," which will be played in Buffalo. "This middle section came out of Derek's statement about the strings," he said as he pointed out measures in which deconstructed polyrhythms drawn from Afro-Cuban music are scored for violins, violas and cellos. Mr. August, principal bassist with the Brooklyn Philharmonic, is best known for his work in jazz and Latin groups. His JCOI proposal described his belief that "Cuban rumba can inspire an entirely new way of writing for orchestra."

In preparation for orchestral readings, each jazz musician works with a mentor composer. Flautist Nicole Mitchell, a composer in the 2010-11 program, is now among those mentors. "My own orchestra reading was traumatic," she said. "I felt separated from my music up there on the stand while I sat in the audience. Jazz is really an oral tradition. Even though most of us write our music out, a lot of communication happens in real time, and musicians are directly involved with the composer."

As Ms. Schneider said of her recent project, "We're used to leaving room for someone to bring the music fully to life. Suddenly, if it's not on the page, it doesn't exist. It's a completely different sensibility." There are other differences, too. "Orchestra musicians look at a conductor," Mr. August said. "They're used to seeing the time, instead of relying on feeling it, like we do in jazz."

The institute's community is diverse. The previous class included pianist Phillip Golub, then in high school, and bassist Rufus Reid, then 66 and with a long and stellar jazz discography to his credit. Mr. Reid gained both the technical expertise, he said, and "the audacity to compose for orchestra." He wasn't interested in some grand Third Stream ambition. "I just had new ideas that required an orchestra," he said.

Mr. Lewis didn't think Mr. Reid's piece, "Mass Transit," swung in any jazz sense. "But it sounded like his bass playing," Mr. Lewis said, "with his particular sense of wonder and surprise and drama. Some things go beyond genre, as long as you know what you're doing and who you're doing it with."
