BOSTON -- George Russell is a chocolate-eyed, iron-willed musician's musician. After 40 years of writingfor and recording with famed big bands and small ensembles, he's better known for a theory related to Pythagorean mathematics than for the music he's made with Dizzy Gillespie, Miles Davis and dozens of other innovative jazz artists.

"The Lydian chromatic concept doesn't impinge on ideas, it just presents certain objective laws," Russell explains in the soft accent he's retained since his Cincinnati boyhood, when riverboat jazz and his father's music professorship at Oberlin College suggested his life's course. "It's a concept and objective theory of equal-tempered music, and how it behaves. Covers everybody, you know." He shrugs with the elegant confidence encountered only in people who are absolutely certain of what they say.

At age 64, Russell is an instructor eager to charge students at Boston's New England Conservatory with his own passion, and enthusiastic about expressing himself through his concept at concert performances. On Friday he will conduct his 21-piece Living Time Orchestra, convened for a rare appearance at Baird Auditorium in the Museum of Natural History to launch a jazz bands series coproduced by the Smithsonian Resident Associates and District Curators. In November he'll tour the United States with a sextet in which he'll play piano, though he began his career as a drummer and arranger free-lancing charts to Benny Carter and Earl Hines. Drawn to New York by the be-bop revolution, Russell first discovered the principles that led to his Lydian chromatic concept in the mid-'40s while hospitalized with tuberculosis.

"At that time, all that musicians knew was that there were a certain number of chords. Going down the chord river, you played the tones of the chords, and if you were a little adventurous you added a couple of tones that you felt objectively would fit. But I reasoned there had to be another way to do it, that for every chord there had to be a scale with a unity to that chord. I came up with the Lydian scale" -- an ancient mode of fixed intervals between tones -- "being the scale of unity.

"That was the foundation, and then I tried to destroy that notion myself," says Russell, who firmly believes that music operates as a science, with observable laws. "That's the way I worked. When I found something by ear, I wasn't satisfied with that. I had to find a justification why."

Most of his peers were satisfied with what they heard of his music, rather than curious about the structures of organization he discovered. Upon regaining his health, Russell wrote "Cubano-Be, Cubano-Bop." When his works were debuted at Carnegie Hall in 1947 they were hailed for seamlessly fusing symphonic drama and orchestral colorations with trumpeter Dizzy Gillespie's improvisations and an Afro-Cuban percussion section. Russell followed his early examples of "third stream" music with an even more adventurous three-minute concerto, "A Bird in Igor's Yard." Bird, of course, was the be-bop saxophonist Charlie Parker, and Igor was Stravinsky. Clarinetist Buddy De Franco recorded the composition in 1949 but it wasn't released until many years later.

Meanwhile, Russell had fallen in with jazz's most ambitious modernists. "One earmark of my generation was that we all reached for the impossible," he asserts, recalling jam sessions led by Thelonious Monk and Gerry Mulligan, rap sessions with arrangers Gil Evans and Miles Davis, and fiery if self-destructive talents of Parker, Fats Navarro, Sonny Berman and many more. "I don't see much of that now. I think my students at the conservatory are very conservative, essentially."

Early in the '50s, laboring over a volume he entitled "The Lydian Concept of Tonal Organization," Russell wondered how such basic information could have been overlooked by conventional musical analysis until the mid-20th century. Today he ascribes the omission to "the very nature of western thought, which has always been linear, horizontal, solving problems along a time scale."

"Pythagoras was educated during the 5th century in Babylon," Russell says, lecturing a graduate seminar at New England Conservatory. He stands with his weight on one leg, making small hand gestures, much as he does when conducting. "He brought back to Greece the mathematical formulations upon which the Lydian concept is based, but to the evolving western psyche the Lydian scale was going nowhere. The West needed an aggressive scale for martial music and found it in the major scale, which is an active force of growth, never at rest. The Lydian scale is the passive scale of creation. It isn't going anywhere -- but up, to higher levels of organization.

"The East, where vertical thinking is traditional, has ignored the horizontal force for so long it's become stagnant. Only now, in order to survive, has it begun to compete in the horizontal realm. Ideally, in my opinion, there should be a balance of the horizontal and vertical powers in a sane, civilized culture.

"I myself strive for a total music," Russell insists, perhaps in self-defense of charges that his music is overly intellectual. "And jazz is a total music. Jazz is physical, emotional and intellectual at the same time, the best of it. That's why it appeals to the world."

The appeal of Russell's jazz is evident on hearing it. Though few details of the Lydian concept can be deduced by a lay person listening to his albums, Russell's study of evolution, his concern about "technocentricity" and his fervent interest in humankind's survival are clearly presented through his programmatic liner notes and thrilling orchestrations for "The African Game," recorded for Blue Note in 1983.

The 45-minute suite, comprising nine "events" from "Organic Life on Earth Begins" through "The Future?" is performed by a troupe of disciplined young professionals who are sensitive to the dynamic shadings and textural blends available when standard jazz band brass, reeds, winds and drums are mixed with electric guitars, keyboards, even pencil sharpeners. Russell has long been willing to embrace unusual or advanced instrumental technology, though always in his own way.

On "So What," Russell's most recently released Blue Note album, he revamps the modal song by trumpeter Miles Davis that contributed to the widespread acceptance of his Lydian concept among musicians in the late '50s. But rather than the sparse and subtle surroundings in which Davis set his sketchy melody, Russell waves in a pulsing rock beat, glimmering synthesized sounds and the theme voiced by a thickly massed front line.

"Jazz has always been a music of innovation and energy," he says, "upon which various other musics could draw. Rock innovators always look to jazz, depending on it for impulses when rock becomes drained and mechanical and stale. But if jazz doesn't keep pace with rock -- and it hasn't, it's doggedly trying to remain traditional -- then it's lost its power as an influence." He's not about to let that happen, nor will he be locked into one style. "The African Game" and pieces from "So What" will both be featured at his Baird Auditorium concert.

However, everything he does expresses his Lydian concept, according to Russell. "I'm still working on the second book, which is called 'The Science of Tonal Gravity,' " a book that's taken 40 years to write. "It's the ultimate Lydian concept, with examples from John Coltrane and Wagner juxtaposed, Bach and Ornette Coleman." He had to write it.

"The only reason I have pursued this exhausting, incredible task of actually taking on traditional music theory, which I found woefully lacking, and trying to construct a more objective theory, was because it came from above, my ability to see what this concept meant, and what it was saying beyond music. I believe methods without philosophy are madness, and philosophies without methods are babble. I have a method and a philosophy, not a system. The Lydian concept of tonal organization is a way of seeing first music, and then life."

Howard Mandel is a New York writer.