But the basic idea behind it was simple. He believed that a new generation of jazz improvisers deserved new harmonic techniques, and that traditional Western tonality was running its course. The Lydian chromatic concept — based on the Lydian mode, or scale, rather than the familiar do-re-mi major scale — was a way for musicians to improvise in any key, on any chord, without sacrificing the music’s blues roots.

Mr. Russell proposed that chords and scales were interrelated. He sought ways for an improvising musician to play more notes that fit harmonically with whatever he was playing; to put it another way, he was trying to develop a system in which there are no “wrong” notes.

Miles Davis most famously put Mr. Russell’s ideas into practice. His “Milestones,” written and recorded in 1958, swung back and forth between two scales, rejecting the rapid chord changes that had become prevalent in modern jazz. His landmark album “Kind of Blue,” recorded a year later, is widely regarded as the first great document of modal jazz.

Subsequent recordings by, among many others, the saxophonists John Coltrane (a participant in the “Kind of Blue” sessions) and Eric Dolphy (who also recorded with Mr. Russell), helped spread the gospel of modal jazz. Mr. Russell still stayed mostly behind the scenes, and, in later years, was primarily a teacher, but his fellow musicians acknowledged and appreciated his influence.

George Russell was born in Cincinnati on June 23, 1923, and grew up in a foster home. His adoptive father was a chef on the Baltimore & Ohio Railroad, and his adoptive mother was a nurse. He played drums with the Boy Scouts’ drum-and-bugle corps and attended Wilberforce University in Ohio on a scholarship. At Wilberforce he played with the Collegians, the university’s imposing jazz and dance band. In 1941, while hospitalized for tuberculosis, he learned the science of harmony from a fellow patient. At that time he composed “New World” for the saxophonist and bandleader Benny Carter.

He later moved to New York to play drums with Carter’s band, but he gave up the instrument as soon as Max Roach was called in to replace him. “Max had it all on drums,” he said. “I decided that writing was my field.”

In 1947 he composed the modal introduction to “Cubano Be” and other sections of the multipart “Cubano Be, Cubano Bop,” an early example of Afro-Cuban jazz recorded by Gillespie. He later wrote “A Bird in Igor’s Yard,” an early experiment in classical-jazz crossover, for the clarinetist Buddy DeFranco.

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He was part of the circle that convened around the arranger Gil Evans’s Manhattan apartment in the late 1940s, a group that included Miles Davis; returning to music after an illness, he wrote “Odjenar” and “Ezz-Thetic” for a Lee Konitz album recorded in 1951 that also included Davis.

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In 1956 he began his own career as a recording artist and a bandleader with the album “The Jazz Workshop.” His other albums from that period included “New York, N.Y.” (1959) and “Ezz-Thetics” (1961).

In 1958 he taught at the Lenox School of Jazz in Massachusetts, run by the pianist and composer John Lewis, who called Mr. Russell’s Lydian chromatic concept “the first profound theoretical contribution to come from jazz.”

In 1964 Mr. Russell, who as a black man was dismayed by race relations in the United States, moved to Scandinavia. He returned in 1969 and joined the faculty of the New England Conservatory, where he taught until 2004.

He also began touring with his own groups, notably the Living Time Orchestra, a large international ensemble he led from the mid-1980s on, which experimented with all kinds of music, including funk, electronics and jazz-rock. A 21-piece version of that band recorded “The African Game,” an album for Blue Note in 1983.

Among the many awards Mr. Russell received were a MacArthur Foundation grant in 1989 and a National Endowment for the Arts Jazz Masters fellowship in 1990.

In addition to his wife, he is survived by his son, Jock Millgardh, of Los Angeles, and three grandchildren.

On the first few albums released under his name, Mr. Russell composed the music and led the ensemble but did not perform, and although he later played piano in the groups he led, he did not have a high opinion of himself as a pianist. “I don’t play the piano,” he once said. “I play the Lydian concept.”