`OK," says Ronan Guilfoyle. We're talking about improvisation: the "imp" word. He says it can be taught. The Irish Times scoffs. How? "OK," he says. "I'm going to clap something, and as soon as you know what the answer is, you're going to respond." He claps. DUM; DUM; dum-dum-DUM; dumdum-dum DUM . . . "DUMDUM!" goes The Irish Times, without even thinking about it.

"Now that's improvisation," says Guilfoyle. But it's a football chant, The Irish Times objects. Everybody knows that. "Yes, but still, I didn't tell you to clap what you did," says Guilfoyle. "Your ear went, `do this - this is right'. That's improvisation."

Improvisation of a rather more sophisticated sort will be on offer when Guilfoyle, jazz musician and composer, gets together with the Canadian violist Tanya Kalmanovitch in the National Concert Hall's John Field Room on Sunday. Together they will be performing a concert in the Composers' Choice series, blending pieces by Guilfoyle with pieces of his choice by Bach and Bartok; the two are also giving a workshop on improvisation in music on Monday at 11 a.m.

Collaboration of this kind is unusual, to say the least. A working jazz musician composing pieces for the concert hall is one thing. Composing pieces to be partly improvised on the night is something else entirely - especially when some of the improvisation will be done by a classically-trained viola player. Does anyone hear the merry sound of boundaries crashing? Boundaries. Jazz. Classical. These are complex questions.

Guilfoyle and Kalmanovitch met at the Banff Centre for the Arts in Canada in the late 1980s; he was studying on a jazz programme, she on a classical one, but there seems to have been a good deal of musical fraternisation - in both directions. "I had just turned 17," says Kalmanovitch. "When I thought about my musical future I thought I'd become a classical musician, simply because no other options were available. It was like being a woman a couple of generations ago, and wondering what you were gonna do when you grew up. You didn't sit there thinking you were going to be a fighter pilot."

But, she says, at Banff she was exposed to jazz in a way that she wouldn't otherwise have been. And since taking a Bachelor of Music degree at the Juilliard School, she has played with a punk band, recorded with John Cage and Martin Hayes, and is currently studying for a PhD in ethnomusicology. She also has a degree in psychology, not to mention an anarchic train of thought. A classical musician? "See, what am I? Most people classify me as a classical musician if I say I play the violin or the viola, because jazz musicians don't usually play those instruments. Unless they see me in the pub with a violin in my hand, in which case I'm `a fiddler'.

"But I haven't played a classical concert in nine years; until this one, that is. Am I a jazz musician? People have no way of talking about being an improvising musician that doesn't involve jazz. I am - a creative contemporary musician. I am - what?"

Guilfoyle, for his part, grew up listening to both classical and jazz. His track record in jazz speaks for itself - he has gigged and recorded with a host of top artists - but his CV features a lengthening list of concertos, sonatas and quartets, and he insists that the piece he has written for Kalmanovitch is steeped in classical tradition. So are the boundaries between different types of music - especially between classical and jazz - more imagined than real? And if they are real, who draws them up? Kalmanovitch sighs.

This is her hobby-horse, she says. "I'll use up all your tape, but anyway, here goes. It's to do with the way that power is used in musical institutions - the way that classical music has been institutionalised in Western culture and preserved as a sort of cultural bastion which has to be defended against, God forbid, the surrounding culture.

"As a student of classical music, you're just not allowed to do other things. It's not as if they can stop you - but they have their ways. When I was at Juilliard I played in a ragtime orchestra. We played original tunes and dressed in historical costumes; and that was OK because the music was written out.

I got six months' leave of absence to do that. But when I played with a contemporary alternative band in 1989, a folk-punk all-girl acoustic trio, I couldn't get any leave of absence even though we played at some very prestigious venues and the band had two albums that were produced by John Peel. I don't really understand why it is that having string players improvise is going to cause mad havoc in the streets. I've - shh! - I've done it. The sky didn't fall in."

The ostracisation of improvisatory music is even more complete on this side of the pond, says Guilfoyle who, as founder of the jazz department at Newpark Music Centre in Dublin, has had plenty of close encounters with the educational establishment.

"You can't study improvisation at third level in this country at all - to get on one of my hobby horses. As far as the Department of Education is concerned, a musical education is a classical music education. My daughter plays electric bass - a fantastic instrument, very expressive, highly virtuosic - and she's probably going to get a very good result in Leaving Cert music, but she won't be able to get into a third-level college because it's not recognised as an instrument by the system." "On the other hand, for the Leaving Cert she's studying Gerald Barry, Tchaikovsky, and Queen." Sorry - did you say Queen? "Yup.

Bohemian Rhapsody. That's so typical of the attitude. It has a beginning, a middle and an end, and so it's supposed to be like classical music. They know nothing about popular musics, so they pick a piece of schlock."

Unlikely bedfellows though they are, rock and classical music have, according to Guilfoyle, joined forces to squeeze improvised music to the margins. "They are the two major kinds of music which people play, and both of them actively discourage improvisation," he says. "What goes on at a rock concert is very tightly controlled, because if somebody goes to see U2, they don't want to see a totally different version of one of their songs - they want to hear what's on the album, only louder. And obviously you can't play Beethoven's second piano concerto and make half the stuff up."

The marginalisation of improvised music has, in turn, given it a kind of unhelpful mystique. Musicians who have never been trained to improvise regard it as a kind of black art - on the contrary, says Guilfoyle, it is a language which, like any other, uses an agreed vocabulary and syntax. "Just as I'm speaking now: after all, I'm making it up as I go along.

If we spoke on the same subject tomorrow I would say exactly the same things, because my opinions on the subject wouldn't have changed - but I wouldn't say them in the same order. Improvisation is not about coming up with brand-new stuff. That's one of the biggest fallacies. I would say at least 90 per cent of what even the great improvisers play is stuff they've played a million times before - but never, of course, in the same order."

The works which will be performed at the NCH are partly pre-composed, partly improvised and according to Guilfoyle, he'll be the only person in the audience who will be able to tell which is which. But is it classical - or is it jazz? Both: neither. "The word `jazz' is as problematic for many jazz musicians as the word `classical' is for many classical musicians," says Guilfoyle. Kalmanovitch has, not an answer, but another question. "I think complete musicianship includes a basic competence with improvisation; I think it includes a grounding in the harmonic experience of jazz; I think it involves at least basic familiarity with advanced rhythmic concepts. For me that's musicianship."

"And I think the question we should be asking is, what does it mean to be a complete musician in the 21st century?"

This year's Composers' Choice series also features the work of Rhona Clarke, John Kinsella, Kevin O'Connell and Roger Doyle. It runs at the NCH from Sunday until Wednesday