Hurford, a modest, understated character, is in fact one of the world's leading interpreters of this wonderful music, and has recorded the whole 20 hours or so of it all, twice - once in the 1970s for LP (recently re- released on 17 CDs by Decca), and more recently in a new digital edition (on EMI). This is, however, the first time he has attempted a live project such as this - playing 15 concerts of different music over three weeks. A mammoth enterprise, surely? Hurford agrees: "I did have some second thoughts, a few months ago. But then I realised, as a Bach player (and I'm 67, now), one does not go on for ever. It's very demanding in terms of reflexes and co-ordination. But if I can succeed in attracting a whole new audience to the concerts - if it results in more people wanting to hear Bach - then it's worth it. I don't think I'll do it all again so close together, though - it's too incredibly demanding."
But why should anyone attempt such a thing, anyway? Indeed, what makes someone devote their life, virtually, to one instrument and one composer? Perhaps the clue lies in something Wilfrid Mellers once wrote of the Leipzig Cantor in his fascinating study Bach and the Dance of God: "His appeal is almost primeval, for in his music one is seldom totally divorced from a motor rhythm [which] is regular, reiterated, non-developing, as unremittent as the turning earth, as continuous as the surging sea... Over this earth- beat independent polyphonies sing and wing, often transcending, even contradicting, the beat, so that the lines induce ecstasy, as does religious chant."
Long before the term "new age" was invented, people were attracted to these qualities in music, especially when realised with the structural and intellectual rigour of Bach. But these transcendent works have to be realised, by mere mortals, and interpreting them is not as straightforward an activity as it might at first seem. "What fascinates me," continues Hurford, "apart from the hallmark rhythmic figuration, is the harmonic inventiveness, that creates such spiritual shifts. The challenge is one of expressing this on an instrument which is arguably the most difficult to make music on - the organ. With other instruments, the notes are always limited in length - the problem is to make a smooth, legato line; with the organ, it's the exact opposite. Was it Brendel who said, `For me the essence of music is silence'? On the surface you don't have silence with the organ; if you wedged a key down and went away for the evening, the tone would still be sounding when you came back the next morning. This has to be turned round, so that you can have both legato and articulated notes, like with woodwind. You have to find it in a different way. I feel my instrument does get rather a bad press, sometimes; probably because players will use the most obvious features - loudness, playing lots of notes very fast - losing sight of what Bach found so attractive about the organ - using it as a beautiful way of creating musical line."
Given the immense variety of the uvre, ranging as it does over the whole of Bach's life, and containing everything from tiny Chorales to immense Preludes and Fugues, how did he approach planning the series? "My favourite listener is the man in the street," he says, "someone who is interested, knows of Bach and, while he's at the Festival, would like to come to an organ recital. It's the same as with the recordings - each one is a concert in itself."
Llike the great critic Ernest Newman, Hurford believes that "the Chorale Preludes are the key to the very heart of Bach".
"In planning this series, I started with the Chorale Preludes - the `Eighteen', the Orgelbuchlein, and so on - and spread them through; the next thing was to choose good starting and finishing pieces - not necessarily loud for the latter, but one should always end with a big piece. The one mistake I feel I've made, so far, was ending the second programme with the Canonic Variations on `Von Himmel Hoch' - not enough zip."
And putting yourself in the place of the listener is important. "You have to learn to put your ears at the back of the church and think `What are they hearing?' Essentially the intensity of sound can be enormous - you have to be careful. I remember at a recital in Australia once, the organist played the Prelude and Fugue in D minor right through on full organ; it's one of the few times I've really recoiled on behalf of my instrument - people gradually got up and walked out! I'm lucky - I've got my wife as my `ears at the back'."
Silence, as he's already mentioned, is a big issue with Hurford. "My Who's Who entry lists my hobbies as `walking, wine and silence'. One of the great attractions of Edinburgh is access to silence - the silence of the Pentland Hills, for example. Yesterday was my first rest day, and we went for a walk up there - it was so peaceful, we both fell asleep, and got severely sunburnt! And here at Greyfriars, with its kirkyard - you wouldn't know you were in the middle of a city." An ideal setting for playing, and listening to, this sublime music, on the magnificent Peter Collins organ of 1990.
What is it, then, about Bach's music, and his organ music in particular, that makes it so supremely great? "It's his simultaneous mastery of technique and ability to convey what is deepest in his spirit in the music that he writes; to communicate the deepest emotions to people who feel the same." Sitting in Greyfriars Kirk, listening to this timeless music, with the afternoon sun streaming through the stained glass windows behind the great organ case like Shelley's dome of glass staining the white light of eternity, one knows that this is a very special experience. Through the medium of Peter Hurford and the mind of Bach, we have a chance to partake of, in Spinoza's words, "The highest endeavour of the mind, and the highest virtue". Seize the opportunity while you can - it may not come again too soon.
Recitals daily at 5.45pm, Greyfriars Kirk (booking: 0131-473 2000) to Saturday