The theory might be obscure but in practice it's as clear as day. Miles Davis's 1959 album, Kind of Blue - for many, the best jazz record ever made - is the most famous application of the method; John Coltrane's A Love Supreme of 1964 is another. The modal music of the 1960s that Davis and Coltrane inspired became what we now know as modern jazz. If it was modern, Russell's book was in there somewhere, even if, like Martin Luther's little primer, almost no one involved had read it.
Once the idea caught on, though, it was as if it was part of the air people breathed and Russell didn't receive much credit for his authorship. "It's on the liner notes of Kind of Blue that Miles was influenced by me," says Russell, "but the most he would say is that he learnt about modes from Bill Evans and that Bill learnt from George. Even Bill - who was a very close friend - never admitted to studying with me, but friends said he had read the book and was very into it."
If Russell feels ignored by history - and he has a right to, for he is one of the most important US composers of the century, whether you count the book or not - he has, at 74, reached a sort of affable equanimity. "That's kind of how it goes," he says when we meet in Boston, where he has been a professor at the New England Conservatory of Music since 1969. "Whereas at one time I might have felt left out because I didn't have a band like Ellington's that performed 364 days a year, I now know that was a blessing. The main thing is that I know that, when I want to perform, I can."
The big band with whom Russell plays the Barbican tonight, the Living Time Orchestra, has been going for 14 years. Consisting largely of British musicians like star saxophonist Andy Sheppard, it's an incredible group by any standards and Russell's music really is a glory to hear. Although melodically and harmonically complex, the band's sound is bold and explosive and, in full flight, almost unbelievably powerful. In essence it's the sound of mid-century urban America in all its convulsive energy, but beefed up by rock rhythms and high-tech keyboard voicings into a completely contemporary ensemble. Conducting from the front with a great sense of showmanship, Russell has even been known to rap a little. It is, in short, the very opposite of the now-dominant retro-aesthetic of Wynton Marsalis, about which Russell - for all his equanimity - completely loses his cool.
"This virtual jazz, cloned jazz, is such a dead idea. The concept that, after 1950, all jazz is bunk! I can understand the social reasons for it - rock had just about KO'd jazz, and jazz couldn't get up off the floor - even Miles was playing to only 400 people. And then along comes Wynton, with this idea that the real jazz all happened before 1950, and he doesn't help the situation at all!"
Marsalis's revisionist spin on jazz history is particularly irksome for Russell because he was part of the great movement of modernism which Marsalis appears to deny. As for his great theory - the Lydian concept - "There's no way you can't use it," he says. "You're in it whether you know it or not. I was reluctant about putting the book out again in this restrictive and fascist climate, and I took it off the market for eight or nine years for revisions, but something tells me the time is now right. I've finished revising the first volume and it's just awaiting typesetting."
If he senses a change in the wind, it comes from an unusual direction. "There's every evidence that black people don't monopolise rhythmic intelligence," he says. "Go and see Riverdance, for example. I don't know where it came from but, boy, you can't say those people don't have rhythm. It's so refreshing to see that, because it just blows a hole in everything. As Marsalis would preach: it shows that all God's children got rhythm regardless of race, creed or colour!"
George Russell: 7.30pm tonight, at the Barbican, London (0171-638 8891).