And yet even Ravi Shankar was powerless to counter the negative aspects of popularism. "That was almost 30 years ago, right?" he asks with a characteristically quizzical smile. "There was Vietnam, the hippies, the 'drug culture' - everything happened at the same time."
Shankar had in fact started his career here much earlier, in 1956 - "and I was already playing to full houses. I had my audiences trained: they were appreciative, and I was well-known as a 'classical musician from India'. But when George Harrison became my pupil, I became a cult figure, a superstar."
Stardom, however, offered scant rewards. "It was a very difficult period for me. Luckily, I wasn't too young - I was in my late forties - so I could take on that sort of popularity. But I was extremely unhappy about the superficiality of it all, especially the wrong information that Dr Timothy Leary, Allen Ginsberg and others were propagating - that everyone in India takes drugs. It was a hodgepodge of Kama Sutra, tantra, yoga, hash and LSD, while the true spiritual quality of our music was almost completely lost."
But isn't there also an infectiously rhythmic aspect to Indian music that the Sixties would have found instantly engaging? "Oh, sure," smiles Shankar, "we have a lot of splashy speed and dance; it can be as exciting as jazz, if not more so. But that flippant attitude - all the 'yeah-yeahs' and whistling - was completely out of place in our music. I'd say to the fans, 'You never behave like that when you go to hear Bach or Beethoven; just because George is my student, it doesn't justify this kind of listening.' "
So disillusionment set in. "And I found that I was gradually becoming unpopular with the kids." The spectre of Jimi Hendrix burning his guitar on stage caused particular discomfort: "To me, that was a sacrilege! We have such respect for the instrument; it's like a godly thing, and we express all our highest sentiments through it."
Yet Shankar now has a similar sacrilege to combat far closer to home. "We're witnessing violent commercialisation of the arts in India at the moment. And there's one really pernicious influence: MTV. I hate it; it has infiltrated our country, and is doing incalculable damage. In fact, we are trying to start a counter-movement. MTV might be OK for the rich and upper-class kids in the large cities - they're in any case fond of hard rock and pop, and can take it - but it has penetrated beyond them to the poor rural people. They hear these things and their minds are re- shaped. And not only musically, but visually - through images of excessive sex and violence."
Shankar is keen to establish superior options. "Here there's Channel 4 and BBC2, which means that good music gets enough of an airing to balance things out: that's exactly the sort of thing we're trying to fight for in India. But our other channels are products of India's new-found free enterprise economy. You can't blame the public - it's the fault of those who are exploiting them. In Britain, it's just one of a whole barrage of influences that have been active for so long that people can take it. But with us... it's ruinous!"
Years ago Shankar's own commercial success provoked much jealousy back home. "I had trouble from bad men in my own country. They accused me of becoming a hippy, of taking a sacrilegious stand towards our old, pure music. They also said that I was 'commercialising' it, which I wasn't. It was the other way around: I was trying to put our music in the right place" - in other words, in a wider cultural context.
But were the Sixties really so destructive? Didn't they also see a significant extension of our creative sensibilities? "Definitely. I should have mentioned that. You know, there were young people who felt that, creatively speaking, they had somehow hit a brick wall: they could no longer write music in the style of the old masters, they wanted something new, a modern kind of inspiration. So they started to broaden their minds, listening not only to their own music, but to Chinese, African, Balinese and Javanese music, or whatever. Jazz musicians, pop musicians, even those working in the classical field - all of them made the voyage. And they were really listening, especially to Indian music, which offered them both melodic richness and a whole rhythmic structure. Take Philip Glass. We met in Paris when I was working on music for a film, and spent about eight days together. He learnt from me, obviously - but then he went even further himself, travelling to India many times and trying to understand as much as possible."
So much for the West's attraction to the East. But are there Indian devotees of Western classical music? "Not very many, I'm sorry to say. There's a very, very small group of fans in cities like Bombay, Delhi, Calcutta and Madras, but they are happy listening to CDs. We also have a little Western classical air-time on All-India Radio - that's in addition to light classical, pop and rock, although there's very little jazz."
Shankar himself is, however, a keen classical music enthusiast. "I have always been a great devotee of baroque music," he says with enthusiasm. "I find a lot of melody in it - more simplicity, more spirituality - maybe because of its connection with church music. Mozart was always a great love and Beethoven, of course. Then there are the more lyrical Russians, Tchaikovsky and Rimsky-Korsakov. But I have problems with Schoenberg and the 12-tone system.
He has also listened to many of the composers most influenced by Indian music, such as Messiaen, Hovhaness and Peggy Glanville-Hicks. "I saw a whole wave of them, but I think that the present generation goes a little deeper into the subject than they did. It's the same with yoga, where the earlier English commentators tended towards relative superficiality. Now there are many who understand."
Shankar has waged a lifelong battle against foreign incomprehension. "I experienced it right from childhood. Musicians who came to our home in Paris would quote us the 'three Es': 'It's all so exciting, exotic and esoteric,' they'd say, 'but where does the music actually start?' They were listening with regimented ears and couldn't really stomach a piece that played for more than half an hour, let alone one that hovered around a single note."
Of course, things are different now. But has our absorption of Indian music been reciprocated in India? "Certainly in our film music, which forms a major part of our pop culture: ordinary people love this kind of stuff, and much of it incorporates Western-style instrumentation. As to serious music, no - there's very little influence."
But what about his moves towards so-called "East-West Fusion"? The very question raises a wry smile. "First of all, the word 'fusion' bugs me a little, because fusion suggests a mixture of styles, whereas I have always been primarily interested in the sound of the instruments.
"You know, our Indian instruments have a lot of disadvantages: they are not good in unison; and although the 'buzzing' sound is beautiful when played solo, it becomes very disturbing when you hear two or three sitars together. I wanted to project ideas to a bigger audience, to convey the essence and technique of Indian music to people who don't normally come to our classical recitals. That's how it started. Then I got commissions from the London Symphony and New York Philharmonic Orchestras, but I never attempted 'mixing' the musics, or using harmony and counterpoint in the Western sense. And to be honest, I didn't really have sufficient knowledge to do so, although I did receive some very basic Western music education at school. I also trained myself not to do certain things, such as use unnecessary harmonies, which would kill the spirit of raga. But I was always fascinated how 50 violins could sound like a single instrument."
Shankar gained a good deal of experience recording Indian instruments when he was with All-India Radio. "And I soon realised that using them in orchestration imposes its own set of limitations. So I became interested in using violin, viola, cello, double-bass and then, gradually, I started employing different wind instruments - the Western flute, for example, because the bamboo flute, which is so beautiful as a solo instrument, can only really 'project' when amplified. I heard jazz, which fascinated me; then I discovered the attractive sonorities of Japanese instruments. But ultimately it was the range, tonal quality and especially the dynamics of Western instruments that made the biggest impact on me: you could hear everything, from the softest to the loudest note - with no microphone."
Colleagues and critics couldn't understand this double-identity of a traditionalist with a will to explore. "And yet I've always kept my traditional performances quite separate - although, perhaps, that's what disturbed people most. But, as a composer, even in my childhood, I wanted to do so many new things and was never frightened of experimentation. Good things have come out of all this; some new things, too - film music, for example, which initially went over everyone's head but that's now accepted as the norm, even copied. But I've never tried to copy anyone myself. That's why I'm still here! If I were only exploiting, or playing to the gallery, I would have been finished long ago."
And while Shankar acknowledges the "speed, virtuosity and technical finish" of younger players, he bemoans a certain lack of soul in their performances. "Whether in classical music - Indian or Western - or even in jazz, I find that nowadays there's less to touch the heart, less depth and spirituality... But that's the price we pay for a life dominated by science and practical matters, with too little space left for the soul."
n Ravi Shankar: 15 July 7.30pm Barbican, London EC2 (booking 0171 638 8891)