‘I remember playing quartets when I was about 14,’ says David Harrington from the Kronos rehearsal space in San Francisco. ‘And looking at the globe and realising that all the quartet music I knew was written by four guys who lived in the same city. Even back then, I thought there must be other possibilities.’

It’s true that Vienna was the crucible for the creation of the string quartet (and the symphony) by Haydn, around 1750, and then taken up by Mozart, Beethoven and Schubert until his death in 1828. The homogeneous sound quality of the four instruments made the quartet celebrated as pure music, ideally with some rigorous musical development. But it shows how much the quartet world has changed in the 50 years since Harrington was a teenager, that although these composers are still central to quartet music in its classical form, there is a whole world of other quartet music now. Probably more than anyone, that’s thanks to the Kronos Quartet.

Right from the beginning David Harrington knew that he wanted Kronos to stick to the contemporary end of the repertoire. Their first concert in November 1973 featured a new piece from his composition teacher, Ken Benshoof, plus Bartók, Webern and Hindemith. They’ve gone on to record 60 albums, including many specially commissioned pieces from composers like Terry Riley, Steve Reich and Henryk Górecki. At least a dozen of those albums, including Astor Piazzolla’s Five Tango Sensations (1991) and Pieces of Africa (1992) feature composers and music from outside the western classical tradition. Their latest recording, Ladilikan, with the Trio da Kali from Mali, features music by Lassana Diabaté, the trio’s balafon (xylophone) player.

When David Harrington looked at the globe, aged 14, was it his intention to expand the quartet repertoire? ‘At that stage I don’t think I had an ambition to change anything, just to hear other things,’ he says. ‘I was in Seattle, Washington so I knew there were other cities and other cultures.’

Once established, the classical form of the string quartet was remarkably durable. In the early 20th century, Bartók was a hugely original voice with six quartets from 1909 to 1939. He was influenced by traditional peasant music which brought in new colours with snapping pizzicato and unconventional playing techniques. But the underlying techniques of motivic development and variation still came from Beethoven and the classical models. Similarly with Shostakovich -15 string quartets from 1938 to 1974 - who followed classical antecedents even more closely, with occasional exceptions like his last quartet made up of six interlinked slow movements!

It was arguably the American minimalists - Terry Riley, Steve Reich and Philip Glass - who in the 1970s decisively broke away from the ‘classical’ models that composers like Benjamin Britten (three quartets) and Elliott Carter (five quartets) were still following. It was specifically Black Angels, George Crumb’s piece for electric string quartet that inspired Harrington to start Kronos.

Last summer, Kronos played for the first time at the Esterházy Place in Eisenstadt, Austria. Their concert included, amongst others, music by Terry Riley (US), Aleksandra Vrebalov (Serbia), Franghiz Ali-Zadeh (Azerbaijan), N Rajam (India) and Lassana Diabaté (Mali). ‘I was so proud to be able to play there,’ says Harrington. ‘To play Haydn’s great great great great grandchildren. And we were saying thanks to Haydn not by playing his music, but by playing things that absolutely could not have existed without his music. I imagined we were pole vaulting our medium into the future.’

The music on their new album Ladilikan is by Malian balafon player Lassana Diabaté, from one of the ancestral musical families and one of the best players of the instrument. He’s a member of Trio da Kali with singer Hawa Kassé Mady Diabaté and bass ngoni (desert lute) player Mamadou Kouyaté - a kind of chamber trio created by the Aga Khan Music Initiative featuring some of the oldest instruments in Mali’s rich musical culture dating backing to the empire of Sunjata Keita in the 13th century.

The composer Lassana Diabaté doesn’t read or write Western notation and Ladilikan was created by Lassana sending recordings to Jacob Garchik, who’s been arranging music for Kronos for 10 years. ‘It sounded beautiful, but there was no indication of how the string quartet would fit into it,’ admits Gartchik. ‘I made arrangements so that Kronos could play along with Trio da Kali and after a few days of workshopping I fleshed them out.’ This involved specifying sections where Kronos would accompany, sections where Trio da Kali would play alone and vice versa. Sometimes Gartchik added extra interludes to fill out the structure. ‘Yes, you could say I composed them but within a very tight framework of the style the Trio da Kali created.’

So where’s the line between arranging and composing for a string quartet?

‘I try to keep myself as a background figure,’ says Garchik. ‘My goal is to let everybody else shine but facilitate things where possible. The nature of the music is somewhat improvised - with some landmarks that are composed and more or less set. So I transcribed some of Lassana’s improvisation patterns and presented them to Kronos as various choices in the piece. It keeps the spirit of the original which is not set in stone in the way a Western classical piece would be - and Kronos can participate in that too which is very important to the spirit of the music.’

After the Ladilikan experience Kronos asked Lassana to compose another piece for string quartet alone for their ‘Fifty for the Future’ initiative - 50 new compositions for students and young professionals from composers all over the world. Having met and worked with Kronos, Lassana came up with a five-movement piece called Sunjata’s Time in which he’d very much thought about the quartet and the ranges and characters of the individual instruments. The first four movements feature each of the instruments in a prominent solo role and the fifth features them all equally.

‘Lassana composed the piece on the balafon and I thought it was an amazing improvisation,’ explains Harrington. ‘And then he came to Abu Dhabi where we were rehearsing Sunjata’s Time together and he played it note for note with us - absolutely accurately. To think that it is not composed and each note is not important is incorrect.’

The traditions of Malian music are extremely rich and extremely old, but do these pieces relate at all the classical quartet tradition as established by Haydn, Mozart and Beethoven? ‘I think it definitely links back,’ says Jacob Garchik without hesitation. ‘Very often you get a melody presented, then improvisation in the middle and then the melody comes back at the end so it’s like a miniature sonata form. And they’re still using virtuosity, lyrical passages, excitement and dynamics and all things that are universal in music.’

If Bartók was the first to bring radical new sound worlds into the quartet repertoire, Kronos have expanded that hugely to imitate other instruments, electrify the quartet and use octave doublers and other effects. The first piece Jacob Garchik arranged was ‘Lullaby’, the original Iranian melody of which was played on an extremely plangent reed instrument with two pipes played (not quite) in unison with each other. For this they came up with a violin re-tuned with two pairs of strings in unison (D,D,A,A). ‘It works extremely well imitating a Middle Eastern instrument,’ says Garchik, ‘but it’s great to imitate a blues singer as well. David’s used it for many other projects and calls it the ‘Lullaby violin’.

On Ladilikan, Hawa Diabaté sings ‘God Shall Wipe All Tears Away’, a song by gospel singer Mahalia Jackson. David Harrington conceived the idea when he heard her sing a Malian praise song at their first meeting in 2012. ‘Hawa's incredible vocal power and the way she sings into the centre of each listener’s heart made this idea seem more and more inevitable,’ he says. The lyrics were translated into Bamana and the quartet, playing without vibrato and with a sub-octave divider on the cello, create something like the sound of a Wurlitzer organ!

Aside from making the quartet a global medium, Kronos are keen to rectify the gender imbalance amongst classical composers. Their Fifty for the Future compositions are written by 25 men and 25 women. This goes right back to their debut in 1973. ‘That was the first string quartet concert that my wife Regan ever heard,’ remembers Harrington. ‘When we got back she said, ‘where were the women composers?’. It was like a splash of cold water on my face. I didn’t know a single women composer at that time. From that moment, probably the most important project was to try and bring 50 per cent of the world’s population into the string quartet medium as composers.’

This might make it sound like Harrington has a well-planned strategy, which he quickly denies. ‘The one thing we’ve learned from the hundreds of composers we’ve worked with is that everybody who writes for the string quartet sounds different. It’s such a personal medium that everyone sounds like themselves. But the way it works for me, is something magnetises me in music and I don’t really have a choice. Whether it was Beethoven’s Op 127 when I was 12 or Black Angels when I was 23. I trust that instinct. That’s how I navigate through the world of music.’

And jumping from the music of Mali, to Iran, to India to Vietnam, couldn’t they be accused of being musical tourists? ‘It doesn’t seem like that to me – it keeps me on the edge of my seat. Isn’t it more musical tourism to be playing scherzos of Joseph Haydn?’

The fact that Kronos can fill a hall like the Barbican when they come to London suggests that their democratisation of the repertoire has also widened their audience - despite, or perhaps because of, the absence of familiar composer’s names. And the audience is clearly a pretty wide range of ages. But is there any hard evidence?

‘Fifty for the Future gives us evidence that there are groups playing Lassana’s music that may have never heard music from Africa,’ says Harrington. ‘The first group I heard playing Sunjata’s Time was a high school group of Canadian players of Chinese descent. And there was an audience listening to this session in Vancouver BC. There were a lot of people in this room that began to realise the string quartet as an art form can be much more than what they previously knew. And as the audiences get larger, they inevitably include people who didn’t grow up hearing Haydn, Mozart and Beethoven like I did.’

Gramophone's sister magazine Songlines was launched in 1999 and is the definitive magazine for world music – music that has its roots in all parts of the globe, from Mali to Mexico, India to Iraq. To find out more about Songlines, please visit: songlines.co.uk

The new album, Ladilikan, is out now on World Circuit Records. For further information: worldcircuit.co.uk