He introduced this concept in 1985 and at first met resistance from musicians who were not willing to learn the vocabulary and respond to the signals; he was often in a position of asking artists to reorient themselves to his imagination and make something new out of familiar materials. But he demanded to be taken seriously, and he was. After 10 years he had made enough recordings to release “Testament,” a well-received 10-disc set of his work. After 20, he had become an internationally admired creative force, presenting conductions at concert halls worldwide and maintaining regular workshops and performances at the East Village spaces Nublu, Lucky Cheng’s and the Stone.

Mr. Morris, who also played cornet, began his career as a jazz musician in Los Angeles. After settling in New York in the early 1980s, he took his place among both the downtown improvising musicians of the Kitchen and the Knitting Factory and the purveyors of multidisciplinary, mixed-media art flourishing in the city.

Though the bulk of his conductions were with those trained in jazz or new music, many different kinds of performers could take part, as long as they had learned his method. (Five days of rehearsal was his preference.) Conduction No. 1, “Current Trends in Racism in Modern America,” was performed in 1985, at the Kitchen, with a 10-piece ensemble including the saxophonists John Zorn and Frank Lowe, the turntablist Christian Marclay and the composer Yasunao Tone. Others were for full classical orchestras; electronic instruments and music boxes; dancers, actors and visual artists; and gatherings of 19 poets (No. 27) or 15 trumpets (No. 134).

Mr. Morris occasionally used written music or texts, by himself or others — he did this with the saxophonist David Murray’s big band and octet in the early 1990s, and in more recent years with the group Burnt Sugar, an ensemble influenced by his methods, for which he conducted a version of Stravinsky’s “Rite of Spring” — but most often he used no written material at all.

In decades of workshops around the world, and for a stretch, from 1998 to 2001, at Bilgi University in Istanbul, he taught his signals and gestures. Some of these were common to all conductors; some were adapted from the California jazz bandleaders Horace Tapscott and Charles Moffett, whom he had known early in his career (he also cited Sun Ra, Lukas Foss and “Four Improvisations by the Orchestra’' recorded by the New York Philharmonic under Leonard Bernstein’s direction as influences); many were his own.