On one thing most musicians are generally agreed: Bach was probably the greatest of all. Explaining his elusive genius, though, is not so easy. Asked why, in Dylan Thomas's words, 'Bach is best', even seasoned professionals find themselves struggling. 'It's impossible,' says Dietrich Fischer-Dieskau. 'His music is the language of the soul, so we can never fully understand him.'

Soprano Nancy Argenta is prepared to have a go, though. 'The key to Bach is the spiritual dimension. He was further along the line of godliness than most of us. For me, Bach is a seer, a wise man, a beacon along the path.' For conductor Helmuth Rilling — who has recorded more music by Bach than most — his genius had a more earthly foundation. 'He was the great consolidator, summing up the best of what had gone before, refining the best ideas of his own time.' The true extent of Bach's genius, Rilling believes, is only now becoming apparent. It's not enough, he says, simply to look at Bach's own work alone. 'He's the teacher par excellence. His music has influenced every later generation of composers and musicians — a heritage that continues right up to our own time. My friend Krzysztof Penderecki told me that without Bach he would never have written his own St Luke Passion.'

Canadian pianist Angela Hewitt marvels at the way Bach's music still sounds so fresh and vital. But it's the richness of his invention that elevates his work above all others. 'It's music that makes you think. It compels you. The more you listen, the more you hear; the more attentive you are, the more you realize there is to discover in it.' The secret of Bach's unassailable position in the pantheon of great composers is partly due, she says, to the didactic nature of much of his instrumental music. 'Many players get their first taste of Bach through his keyboard music. It's an experience that stays with them throughout their lives. And kids respond really well to it both because of the dance element, and also because of the music's seriousness. It's not off-putting. All children want to be taken seriously and Bach does just that.'

Sir John Eliot Gardiner has never forgotten his early acquaintance with Bach. 'I actually grew up under his very eyes. The original of the famous Haussmann portrait of the composer hung in my parents' house during the war for safekeeping. It spooked me, but I've since grown to love it. If you look at it from the nose downwards there's a much more sympathetic, compassionate human being than the nose, eyes and wig of the serious Thomaskantor suggest.

'There's a similar dichotomy in the music. For me it's like the intersection of two planes. The horizontal plane is the melodic and contrapuntal writing, the vertical plane is the dance rhythm based on a basso continuo of incredible elasticity and, buoyancy. And it's the intersection of these two that's so gripping and entrancing to the listener at so many levels. It can appeal on a visceral and purely sensual level, or at a more highly intellectual level in terms of the brilliance of the working out of his contrapuntal lines, and then there's the spiritual level.'

Gardiner is more willing than most to discuss Bach's music in clear-cut technical terms. But even though he's currently engaged in performing a complete cycle of the church cantatas, we run into problems trying to pin down the so-called 'spiritual quality' in Bach's music. 'Thank goodness it is indefinable,' he says. 'If we could define what it is that moved or uplifted us in Bach then we'd have killed it off. The wonderful thing is that the music of Bach can appeal to the eye and intellect when you look at it on the page. But its fundamental appeal is to the ear and to the emotions and to the spirit when it's performed. And that's the huge joy of performance, that you can see it coming alive before your eyes. The challenge for the interpreter is to be technically on top of the huge demands that he makes of both instrumentalists and singers.'

There's strong agreement among performers that one of the most appealing qualities of Bach's music is the extraordinary technical challenges it sets them. The composer's great skill is that this seems to arise naturally from the fundamental substance of the music rather than being grafted on as mere virtuoso display. 'You get such huge rewards from playing his music,' says Angela Hewitt. 'The more you put into it the more it pays back, and with much greater interest than from other composers.' But having just performed the entire Second Book of the 48 from memory at a concert recently, Angela Hewitt wryly observes that the fugues, for instance, don't sound obviously impressive. 'Listening to the music, people simply don't realize how difficult it is to play. We all appreciate Bach on different levels. The amazing thing is that such intimate music works so well in a concert hall and has the power to draw everyone in, and that such subtle music has such popular appeal.'

Bach the healer

Nancy Argenta wonders whether it's the sense of order and balance in Bach's music which helps explain its appeal to such a mixed congregation of listeners. 'Bach can be very reassuring. When you're feeling frazzled you need Bach not Beethoven to relax you. He has a calmness that makes people feel that all's well with the world and that they'll be all right.' But that same carefully ordered and regulated quality has sometimes led to charges of pedantry and longwindedness. John Eliot Gardiner will have none of it. Even when Bach is austere he never finds him dull. The music 'has a sheen and a fascination and it may not always come from the instrumentation, it may not even come from the gratifying way he writes the vocal lines – sometimes they're not very gratifying at all – but there is an unquestionable intrinsic interest in the music itself which is both intellectual and sensual. Even in some of the most austere of his pieces I find there's a sensuality.'

Angela Hewitt – who admits to having yawned through some bottom-numbingly-long performances of the St Matthew Passion – feels that many of the problems people have with Bach are the result of interpretations that have been ill-considered or simply boring. 'Bach should never bore us,' she says. 'From time to time he may have been a little less inspired, but then his own standards were so high.'

For Dietrich Fischer-Dieskau, the problem with many Bach performances, both live and recorded, is their lack of spontaneity. 'It's an easy trap to fall into. The music obviously requires careful preparation, but there's a danger of over-rehearsing (a problem that Bach must seldom have faced). I remember a performance of the St Matthew Passion with Mengelberg in which I sang the Evangelist. "We are not rehearsing this work; we are doing it as in Bach's time," he said. Somehow it all came together, and how exciting that was. I felt the composer's presence vividly.'

Bach the obsessive

We know very little about Bach the man, but it's always tempting to extrapolate from the music and draw our own conclusions. Nancy Argenta found her recent experience of singing Bach's German adaptation of Pergolesi's Stabat mater surprisingly revealing. 'It's hard to improve on the simplicity of Pergolesi's original design, but Bach just couldn't keep his fingers off it. He couldn't resist tinkering, even down to the smallest detail. He seems to have had an obsessive streak; he was obviously a perfectionist, striving for some impossible goal.'

But did he have a sense of his own greatness? Dietrich Fischer-Dieskau thinks he did. 'As Schiller said, the genius knows what he is.' John Eliot Gardiner thinks not. 'I think he saw himself as an artisan – a very good artisan – but not a "great" composer. I don't think that was a meaningful concept to him. I think he had a sense of his own worth as a keyboard player and as a servant of the church. We do, of course, have The Art of Fugue and the B minor Mass which might be interpreted as having an eye on posterity. But I prefer to see them as just a personal testimony: this is what I've achieved, this is the best of me.'

Gardiner is suspicious of people who try to tie up composers' biographies too closely with their music. But in Bach's case he's prepared to chance his arm. 'The fact that he was so theologically absorbed, even obsessed, doesn't necessarily mean that he was a joyless or humourless person. I can't help feeling that as a human being he must have been immensely lively and vivacious and had a jolly good sense of humour.' Would Gardiner have liked him? 'I'd have been terrified, because of his prodigious musicality and indomitable, implacable will to get things right. But I'd have adored to have heard him play and conduct his music. How wonderful that would have been.'

Bach as seen by others

'In Bach all the vital cells of music are united as the world is in God; there's never been any polyphony greater than this!' Gustav Mahler

'He, who possessed the most profound knowledge of all the contrapuntal arts (and even artifices) understood how to make art subservient to beauty.' CPE Bach

'Not Brook [Bach is German for 'brook'] but Sea should be his name.' Ludwig van Beethoven

'Johann Sebastian Bach has done everything completely, he was a man through and through.' Franz Schubert

'Bach is a colossus...beneath whom all musicians pass and will continue to pass. Mozart is the most beautiful, Rossini the most brilliant, but Bach is the most comprehensive: he has said all there is to say.' Charles Gounod

'With my prying nose I dipped into all composers, and found that the houses they erected were stable in the exact proportion that Bach was used in the foundation.' James Huneker critic and essayist

'Bach almost persuades me to be a Christian.' Roger Fry

'Sometimes you have to miss him out of your work schedule for a day and you always feel worse for it. If you are playing Bach it makes you appreciate every other kind of music.' Nigel Kennedy

'As with many great composers, one sees parallels in the construction of music and the construction of architecture. It's particularly the mathematical formulae in Bach that interest me; point and counterpoint, [with] variations on a theme and all these mathematical games and explorations going on; the structures, the cyclical nature of pieces where the grand theme is reiterated at the end. As architects [too] we're trying to achieve point and counterpoint within a harmonic whole.' Michael Wilford architect

'JS Bach was allowed to write music of a kind which in its real values only the expert is capable of understanding...At the climax of contrapuntal art, in Bach, something quite new simultaneously begins – the art of development through motivic variation.' Arnold Schoenberg

'Bach is a terminal point. Nothing comes from him; everything merely leads up to him.' Albert Schweitzer

'If [Bach] wants to move you, to make you cry, he does this musically (not theatrically) – he employs devices which explain what expressivity is rather than telling you how sad he is – like Mahler!...Bach's music is about music – he asks questions of his material. Look at those often chromatic bass-lines, so much less conventional than in other Baroque composers (apart from Purcell) and...the monumental structures, the volcanic rhythm of something like the great Passacaglia in C minor for organ. The crunching dissonances propel the music forward in a huge wave of sound. What of the St Matthew Passion? Is there a single work more powerful, more painfully moving in the whole of Western classical music? As Michael Tippett remarked to me once, we are all pygmies in comparison to someone like Bach.' Steve Martland

'The most stupendous miracle in all music.' Richard Wagner

'I think that if I were required to spend the rest of my life on a desert island, and to listen to or play the music of any one composer during all that time, that composer would almost certainly be Bach. I really can't think of any other music which is so all-encompassing, which moves me so deeply and so consistently, and which, to use a rather imprecise word, is valuable beyond all of its skill and brilliance for something more meaningful than that – its humanity.' Glenn Gould

'No one can do what he did. He showed how to use the fugue, to compose, to use development, to introduce people to modern music and symphonic works. All that he does is nearly perfect...Many composers are known for one or two pieces, but the proportion with him is enormous; more than 80 per cent. [This greatness is] the quality, the beauty of the harmonies; the two things combined. When you listen you're in another world...I would say he would be the best on the planet.' Jacques Loussier

'For the past 80 years I have started each day in the same manner. It is not a mechanical routine, but something essential to my daily life. I go to the piano, and I play two preludes and fugues of Bach. I cannot think of doing otherwise. It is a sort of benediction on the house. But that is not its only meaning for me. It is a rediscovery of the world of which I have the joy of being a part. It fills me with awareness of the wonder of life, with a feeling of the incredible marvel of being a human being. The music is never the same for me, never. Each day it is something new, fantastic and unbelievable. That is Bach, like nature, a miracle.' Pablo Casals

'When Disney asks, "What does the Toccata and Fugue represent?" Stokowski answers, "It is a motif or decorative pattern which gradually develops more and more. Finally it becomes perfectly free. It's a growth likes tree growing from a seed."...The real nature of this conversation was made clear to me by David Raskin, one of filmdom's finest composers and a professor of music at the University of Southen California. Stoki was talking to men who knew nothing about music. Walt was scared to death by the very name of Bach Stoki was trying to convince Disney and his staff that if it were compelling and colourful enough it would be acceptable even to those who would ordinarily reject it. He was right...and did a tremendous service to music.' Abram Chasins biographer to Leopold Stokowski, who conducted the Fantasia soundtrack

'[Bach's music] represents the idea – as very few people can – of great structure with great heart. To build them both together, is that not the top achievement? Art comes out of the combination of the two of those in perfect balance. Their coming together is the greatest thing in art.' Tom Phillips artist

'If you really feel for what is beautiful, if it truly gladdens you, then your mind becomes enlarged rather than narrowed. I always get upset when some praise only Beethoven, others only Palestrina and still others only Mozart or Bach. All four of them, I say, or none at all.' Felix Mendelssohn

'I expressed it to myself as if the eternal harmony were communing with itself, as might have happened in God's bosom shortly before the creation of the world.' Johann Wolfgang von Goethe