Pianist Enrico Pieranunzi keeps his improvisation within boundaries, he explains to Ray Comiskey

Talking to Enrico Pieranunzi reminds me of John Keats's line about wine; he's like "a beaker full of the warm south". This marvellous Italian pianist has such a palpable warmth and ease about him, with a ready sense of humour, that you can't help liking him. And though you can stretch the Keats analogy too far, as a jazz pianist he's definitely a classic vintage.

Cork will get a taste of that sunny south when he brings the gorgeous music from his Racconti mediterranei album (for the Italian EGEA label) to the Guinness Jazz Festival this week. Reinforcing the Mediterranean connection will be the superb clarinettist from the same album, Gabriele Mirabassi, with Marc Johnson's bass role from the original filled by Ronan Guilfoyle.

By birth and culture Pieranunzi is Roman; musically he's a blend of classical, jazz and folk. "My father was a very good guitar player," he explains, "both a jazz player and folk player, so I was influenced by that. I have, of course, a European heart and a Mediterranean heart."

The word "racconti" also means "stories", does it not? "That's right. When I'm playing, the choruses are not just an exhibition of ability, of 'chops'," he laughs. "It's much more the opportunity to tell a story. And composing is the same, so I composed these racconti as a kind of stories. This is important, because the music was very much written and the important thing there is not the improvisation. It's part of the story, but it's not the main thing. The main thing is the melodies and the structure of the compositions."

What inspired them? Public or personal things? "There is a tune called The Kingdom (where nobody dies). The expression comes from a great American poet, Edna St Vincent Millay. This inspiration comes from a wonderful poem she wrote in which the first words are: 'childhood is the kingdom where nobody dies'. And you know, we all keep our child in ourselves. It's something very emotional, very strong, a part of life we shouldn't forget."

Another piece is called Canto nascosto. "That means 'the hidden song'. It's a kind of melody that is very much to do with the folk tradition in my town. Probably people never imagine that Rome has a folk tradition, but there is a strong one here and it's a bit hidden."

There are other sources for these musical stories. Canzone di Nausicaa was inspired by an episode in Ulysses, while others have titles such as Les Amants and O toi dèsir. Were any of these inspired by a particular person? "Yes," he answers, laughing, "but you get into very private things, man."

He has also revisited some of this music for another EGEA album, Les Amants. For that he used a string quartet, saxophone, bass and piano. Again, improvisation was part of the plan, but kept within certain boundaries. "For me the importance is that the stories have to have a coherent development. Like in literature; when you read a novel the story has to have a logical development to it."

And, in fact, so coherent are these performances that there are times in Les Amants when it's difficult to tell whether someone is improvising or playing a written part.

There is another jazz side to his creativity, captured brilliantly on, for example, a series of consistently outstanding albums made for another Italian label, CamJazz. One, Fellinijazz, using variations on a quintet format, is a beautiful, delicate response to the music of Fellini's films. Two more delve into the music of Ennio Morricone, using a trio that came together by chance in the early 1980s, when Marc Johnson and drummer Joey Baron found themselves in Rome with a planned tour cancelled. He got a call to go to a club to meet them.

"They were very depressed and I said 'OK, my name is Rico. Why don't we play?' And from the first moment something unbelievable happened. Music in its highest degree of emotion, of warmth."

Part of the explanation originally may be that Pieranunzi was then in thrall to the late, great pianist, Bill Evans, with whom Johnson had played. But now, umpteen albums later, with Pieranunzi very much his own man, the chemistry still works.

Over the years, too, happy accidents have brought him in contact with several other players, who, like Johnson, played with Evans, including drummers Paul Motian and Eliot Zsigmund. And, within the past year, he became only the third pianist, after George Shearing and Evans, to record duets with guitarist Jim Hall, who made the celebrated duo albums, Undercurrent and Intermodulation, with Evans back in the 1960s. Just released as Duologues, it makes clear that Pieranunzi's debt to Evans is a thing of the past.

Enrico Pieranunzi, Gabriele Mirabassi and Ronan Guilfoyle will play at the Triskel in Cork on Saturday