Their leader, David Harrington, is like a schoolboy who's realised that even were he to live forever, there'd still be things to discover. "I am a person who loves to have musical experiences and the world of music is this vast human mystery and none of us can know it that well... Some people pray, and when I listen to music I think of it as a way of praying."
Harrington's listening habits have been "answered" by Kronos's unrivalled position as the world's most distinctive and adventurous quartet. They are in London for a series of concerts to mark their 25th anniversary - and the fact that since 1973, they've been responsible for 400 new compositions for string quartet, specially commissioned from composers from six continents. Back in the Seventies, recalls Harrington, "composers weren't writing quartet music any more. It had lived its life as an art form and was going off quietly to die." Of course, some works have been more successful than others, but the Kronos legacy includes pieces commissioned from Terry Riley, Philip Glass, Steve Reich, Witold Lutoslawski and Henryk Gorecki.
Kronos's three forthcoming London concerts point up the range of their achievement. Steve Reich's Different Trains (1990) is one of the acknowledged new masterpieces of the quartet repertoire. Live and recorded sounds from the quartet are combined with recorded voices remembering train journeys in the 1940s, in America ("from Chicago to New York") and Europe: "and then we went through these strange sounding names. Polish names. Lots of cattle wagons there."
Pieces of Africa (Nonesuch 1992) was another Kronos landmark in which they collaborated with seven African composer-performers. It's the most commercially successful of their albums and it paved the way for other collaborations with non-western musicians. That list includes some distinctive names from the World Music scene: kora player Foday Muso Suso, the great nuevo-tango musician Astor Piazzola, Chinese lute virtuoso Wu Man and Tuvan throat singers, to name but a few. In London they're performing for the first time with the Taraf de Haidouks, the wildest of Romanian Gypsy bands.
You might expect Harrington to be a bit blase by now, given the quartet's illustrious collaborative history, but he's found something new in this music. "I feel like I've met another aspect of the soul of the violin! I don't usually talk like this, but it's true. It's another expression of the instrument - a very strong, bold expression. Very refreshing."
The violin is indeed the soul of the Tarafs' music. They play battered instruments, but through them convey exuberance and depth. And of course they do it in a way no classical musician was ever taught, and that's part of the fascination for Harrington. "The thing about those violinists is that they don't play in the way you're supposed to," he says. "They each play in an individual way. You look at the stage and you see four different approaches to the instrument. And you come away from the concert with a vivid impression of each player's character, as a person and as a musician."
Quite what form their collaboration will take is still to be negotiated - they only start working together next week - but Harrington recognises that there's no point in Kronos trying to be a Gypsy band. What they do have is a common interest in musical colours. One of the most extraordinary techniques the Taraf uses involves tying a horse-hair to the lower string of the violin and pulling it rhythmically with the resined fingers of the bowing hand. This creates clouds of resin-dust and a guttural rasping sound. Harrington is already full of plans to extend this technique to the cello and explore how they can develop it in the quartet.
Their opening concert is based on their most recent album, Early Music (Nonesuch 1997). Here Kronos take the radical step of performing music that is pre-20th century - something they've rarely done before - alongside new commissions and ethnic collaborations. There's 14th century music by Guillaume de Machaut, Perotin (13th century), John Dowland (1604), Purcell (1680) brilliantly juxtaposed with pieces by John Cage (1950), Arvo Part (1993), Alfred Schnittke (1985) and others.
"I'm looking for ways in which we can bring Kronos's musical world together," says Harrington. "Early Music is an attempt to do that. The idea is to create the feeling of an undefined style, place and time. Hopefully the listener won't know how, where or when he got into this experience."
Much of this music sounds both ancient and modern at the same time. The ethnic ingredient comes in traditional tunes from Sweden and Tuva, with guest musicians Olov Johansson on the Swedish nyckelharpa and Tuva's leading throat-singers, Huun-Huur Tu. It's an inspired recording. In Dowland's Lachrym Antiqu, a beautiful plangent tune, the quartet are joined by Chinese lutenist Wu Man, who plays an instrument with a deep, resonant tone that sounds entirely appropriate in the Tudor context.
In concert, most of the tracks with guest artists are filleted out, although the Tuvan throat singers appear on a playback tape. But in the second half, Kronos are joined by klezmer clarinettist David Krakauer for The Dreams and Prayers of Isaac the Blind by Osvaldo Golijov. This shares many of the ideas inherent in Early Music. As a sort of epic history of Judaism it is culturally specific, but it throws the historical net far wider. It seems to start at the dawn of time, evoking the intonations of three Jewish languages - Aramaic, Hebrew and Yiddish - and touch on exile, tragedy, celebration and prayer. It's a sort of meditation, oscillating in performance between the sacred and secular, composition and improvisation, ancient and post-modern. Just the sort of world Kronos like to inhabit.
Kronos Festival at the Royal Festival Hall (0171-960 4242). Sun 24th May: Early Music and The Dreams and Prayers of Isaac the Blind Wed; 27th May: Trains, including music by Harry Partch and Steve Reich's 'Different Trains'; Sat 30th May: The World of the Gypsies - Kronos and the Taraf de Haidouks. Kronos play the British premiere of Terry Riley's 'Cadenza on the Night Plain' on Fri 29 May at the Bath Spa Contemporary Music Weekend (01225 463362).