Dennis is Captain Haddock to Martin Hayes' Tintin, cavorting around the world having adventures, meeting faintly ridiculous people and dealing with episodic nonsense in notably different ways. Cahill huffs and puffs; Hayes deals with everything on a more conciliatory, cerebral level. The business of touring can be fun, and sometimes it can't. "Purgatory" is the phrase musicians use to describe those moments of down time when confidence ebbs away and they wonder what it's all about. "You go very high with the musical experience," says Martin, the fiddle maestro from east Clare. "I'm sure it's no different from drink or drugs, and sometimes it's a big let-down without it."
The Donegal sojourn - three intimate shows and a couple of radio interviews over two days - has been designed by their agent Amy as a rest cure in the middle of a longer tour to promote their first joint album The Lonesome Touch. They may be "fried" by the time they get to Donegal, but in a way it's the very pressures of life that fuel the fragile magic they create with only three devices: guitar, fiddle and the instrument of silence itself. But however much one strives for solemnity and soul, one has to deal with the mundane and the frivolous. And at this, the first gig was a triumph. A lunchtime recital at the visitor centre of Glenveigh Castle, with an audience roughly equal in terms of die-hards and tourists with small children. There'll be a lot of small children on this trip - they like Martin Hayes, he's funny, he's gentle and for all the Biblical fervour of his international press notices, he has a mischievous grin.
"I've had a request," says Martin, "from a bunch of five-year-olds (grin widens, ripples of mirth all round) for a slow air..." Of course, this is relative - everything Martin plays is slow. No fiddler or guitarist in Irish music play fewer notes than Martin and Dennis, and absolutely no one - past or present - comes remotely close to the sheer spiritual sensation they can create, when the moment is right. That evening, at the main concert of the day in Dunlewy, the "mystical thing" happens.
For perhaps 25 minutes in the middle of the show where the music has built continuously, in soaring, soul-penetrating tenacity, it feels like a trance. It's not something he can conjure up at will, but it's no accident either.
"There is a kind of soulful experience that is better than prayer or meditation," he suggests. "It's a space you can work yourself into musically, so you'd want to get yourself into that space. I'd spent a number of years playing in quiet corners for myself. Somehow in my mid-20s, the experience flipped about and I found that the only time I was getting the same experience was when I was reaching out to someone else - like the giving is the receiving."
The crowd, like all three Donegal shows packed to the rafters, is explosive in appreciation. Almost anything Martin says in-between sets will get a laugh simply because it punctures the tension, resolves the silence. "I remember reading in the back of one of Arvo Part's recordings that music was the space that silence had chosen to abandon. I liked that. I think that silent moment is the moment in which the audience subjectively create for themselves, in which they're actively participating. You make people aware of the silence. It's a challenge every time."
Just as Part, the Estonian ascetic, has created his own "tintinabulli" style of composition from deconstructing renaissance music, so Hayes has effectively created a stripped-down, purer form of Irish music - one that reaches back, he believes, to a time before the ancient airs and marches were grafted on to the imported structures of jigs and reels. He's pragmatic about it, and he's loath to be held aloft as a champion of anyone's cultural agenda. His music, traditional Irish "by accident of birth, I suppose", is possibly a vehicle in the search for the soul. "It is like a missionary thing," he says. Like the Blues Brothers, perhaps, on a mission from God?
"Yeah, that's it!" he grins, ambiguously. "I've actually played in that theatre, with my dad's band - the one in the last scene..." His dad's band, The Tulla Ceili Band, 50 years old this year, is the most venerable in Ireland. But seriously...
"Look at it like this - the evangelists today speak to more people than Jesus ever did and they'll have a minimal effect by comparison. I was reading this interview with someone who was saying `I'll always be known as the bass player from Kajagoogoo
Playing hundred-seaters and really communicating to those people, and paying his way through life, is all he wants. Both he and Dennis have been through the rock'n'roll mill and now they've found where, for them, it's at - soul music. Without trying, Martin Hayes has been compared to Bach, Hendrix, Miles Davis and God. He draws influence from classical minimalists such as Part and fusion pioneers such as The Mahavishnu Orchestra; he is constantly re-evaluating himself. He's also very funny. "The muse has no interest in press cuttings," he notes.
The next day, at a radio interview for a Gaelic station (he barely speaks a word), the presenter chirpily inquires what they do for a living. "Hey, it's all we can do," says Dennis, with a facial expression that says he's heard this a million times before. Then they play a tune. It's staggering, and entirely new. Sort of. "Something I heard my dad play when I was six, I think. It just came to me..." says Martin. On the way out, the radio presenter says to me: "So, are you all here on holiday?" Martin chuckles silently, which seems appropriate. "No," I say. "Martin is one of the world's leading traditional musicians in the commercial arena, Dennis is his accompanist and I'm writing about them for a national newspaper. We're all in pursuit of wealth."
That night in Glencolmcille, birthplace of St Columba, there are no lights, no amplification and the show is unbelievable. We repair to the best of three pubs in the village. We discuss what he's going to play on Later With Jools (an appearance is imminent), the processes of music and the state of our souls. Perhaps, he feels, he's done all he needs to do - he's touched a few people, said what he had to say. He doesn't need to be a star "but everybody wants to be loved, to be acknowledged for what they do." He is unquestionably the best in the world at what he does. And he makes a living at it. He's a lucky man. And he likes me. "You know," he says, "I've only met two guys from Northern Ireland who don't have a problem, and you're one of 'em"n
25 July Stamford Arts Centre (01780 763203); 26 July Cambridge Folk Festival (01223 357851); 27 July Preseigne Irish Music Day, Powys