Toumani Diabaté waves expansively. “Welcome to my palace!” Dressed in green robes and holding a pack of Marlboros, he is holding court in the sunshine on the roof terrace of a Seville hotel. He has a right to feel regal. At 42, Diabaté is the world’s foremost player of the kora, the signature instrument of the medieval Manding empire of west Africa, which he has helped to bring back to prominence. A 21-stringed harp with a resonator made from a calabash, the kora sounds like a cross between a guitar and a harpsichord. It is played with thumbs and forefingers, bassline and accompaniment and melody at once.

Diabaté has played with other musicians, both African (Youssou N’Dour, Baaba Maal, Ali Farka Touré) and western (most recently Björk). Two years ago, he released a CD of an ambitious project, the Symmetric Orchestra, a pan-west African big band. He is in Seville to launch a new CD, The Mandé Variations, eight pieces for solo kora that he hopes will redefine the way the world thinks of the instrument and of African music.

Diabaté is a griot, a hereditary musician. “In the 13th century, the Manding empire covered west Africa – Mali, Senegal, Guinea-Bissau, Guinea-Conakry. There were no writers writing books of African history. We are the archive, we are the memory of the west African people. Our instruments are to help us do that job. The griot is the ambassador of the community, the storyteller.”

His father, Sidiki Diabaté, was known as “the king of the kora”. “I didn’t get the chance to learn to play from my father,” says Toumani, who is essentially self-taught. In the early 1970s, Sidiki (along with Djelimadi Sissoko) made a record, Ancient Strings, that brought the instrument to western ears. Toumani (and Sissoko’s son, Ballake) recorded an assertive follow-up, New Ancient Strings, in 1999.

“My son, Sidiki, he’s 15½, and he’s learning the kora.” Diabaté junior is at the National Conservatoire in Bamako, where his father teaches, although he also has his own school. Might Sidiki eventually make Newer Ancient Strings? “One day. Inshallah. One day.”

Diabaté spent most of 1987 in London, living with the musicologist Lucy Duran in Camden Town and working as artist-in-residence for Womad.

“I tried to put together a band with young British musicians. We played at Glastonbury that year.” He looks back on his time in Britain with gratitude. “Danny Thompson [the ubiquitous double-bass player, with whom he played in the Songhai project] introduced me to folk music.” He claps out a clumping English folk-rock beat, and laughs. “My heart and mind started to change, to be more open to other music. London is a centre for Indian music, all other musics. And 1987 was the start of ‘world music’ as a concept, so I was there for that.”

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Tinariwen are Touareg nomads who met in a Libyan guerrilla training camp but turned from warfare to music. Aman Iman (Independiente) is desert blues refracted through 1970s rock’s surly, truculent guitar.

Bassekou Kouyate has mastered the ngoni, the harsh Malian lute, as Toumani Diabaté has the kora. On Segu Blue (Out Here) he and three other ngoni players play fast, intricate, recursive, tumbling grooves as long as the Niger.

This openness has led him into a number of collaborations. Most recently, he has guested on “Hope”, a moral koan about a pregnant suicide bomber that appears on Björk’s album Volta. Diabaté’s playing weaves confidently through Björk’s crowded, stuttering electronic beats. He speaks fondly of the Icelandic singer.

“She’s very nice. She listened to New Ancient Strings and decided to include kora in her music. She spent the week in Bamako, going to the market to go shopping. She was very cool, not playing the big superstar.”

We talk about other kora players who have taken the instrument in different directions: Mamadou Diabaté towards a jazzier instrumentation, Ba Cissokho using Hendrix-style wah-wah effects.

“I respect all those styles and I love these players. They are my cousins.” [This is true literally, as well as figuratively.] “We all have different ways of inspiration but we have the same source instrument. We are a family.”

Diabaté’s new CD, The Mandé Variations, is a solo kora album, his first since 1987. Produced by World Circuit’s Nick Gold and engineered by Jerry Boys, it is a startlingly recorded document, miked so close that every breath and every scrape of a string is audible. “We recorded it in Livingstone Studios [in Wood Green, north London] in two hours. Everything is a first take. But every time I take the kora to play solo, it could be a record.”

The return to solo recording marks a transition in Diabaté’s life. “It was my 40th birthday recently, and in Africa we have a saying that when you get to 40 you have to be sage dans la vie. The Prophet became a prophet at 40. So I feel that now I have got to change to be one of the great kora players in the world. I need always to be doing something different in the way of a gift.”

The tunes on the CD are named after Diabaté’s heroes, from the Malian public figures Ismael Drame and Moctar Ouane to musician friends who have recently died. “They are laments but they are also news. They are to give hope to the people who live on. When I play, it’s to say thanks. Thank you for what you did.”

One song commemorates the north Malian bluesman Ali Farka Touré, who died in 2006. Diabaté played with him on the Grammy-winning In the Heart of the Moon. “Ali Farka Touré was unique,” recalls Diabaté. “He did a great job all his life.”

Diabaté hopes that the new CD will help its listeners towards a spiritual reawakening. “In Europe, people have lost their spirituality. It’s very important in life – it’s why we were born. People have different spirituality – Christianity, Islam and so on. I’m a Muslim – if I have to say something I’d have to say, be like that. But all of us – let’s try to be more close to God. It’s not necessary to fight, to kill people.”

Later the same day, Diabaté plays a showcase at the Real Alcázar, Seville’s Royal Palace, a series of courtyards that unfold into myriad chambers and out into sumptuous gardens. Outside, the orange trees are gravid with winter fruit, and peacocks strut along the tiled terraces. The palace, half Moorish, half Gothic, is a perfect symbol of the meeting of Islamic and European cultures, but playing here also stakes the kora’s claim to being a classical instrument, at home in monuments to high culture.

“I wanted western people to know that African music is not only dance music. They know that the blues and jazz are from Africa, brought to America in the time of slavery. So people say African music is only for dancing. No – we have music for meditation and for other things. Mali is one of the poorest countries in the world, financially. But it is one of the richest in the world, in culture.

“I wanted the kora to be recognised as classical music. I’ve never heard a symphony with a kora, or a balafon, or an ngoni, as the lead. Perhaps this album can be that.”

A platform has been erected in the Salón de Tapices, which is hung with giant tapestries depicting the conquest of Tunis. On it stands the kora Diabaté inherited from his father, with its leather tuning rings. The silver studs that attach the goatskin to the calabash gleam like a royal treasury.

“The kora,” Diabaté told me earlier, “was always played at the royal court. But that doesn’t mean it’s not for the village as well. Poor people can have the same satisfaction, the same sensation. We can all share it.”

Diabaté wishes the audience a happy new year (it is the eve of Ashura, in the Islamic calendar), and launches into “Djourou Kara Nany”, one of his father’s songs, which honours Alexander the Great. He sets up a heavy bass downbeat with his thumbs, leaning into the rhythm, smiling, his eyes shut, head swaying from side to side and nodding emphatically. His kora is strung partly with fishing line and partly with harp strings, reinforcing the impression that the music must require more than one musician to play it.

Next is “Elyne Road”, derived from the reggae ballad “Kingston Town”, with a sweet singing, descending chorus. The music builds into abrupt hard flurries of high notes, Diabaté scraping his thumbnails pizzicato on the low strings, before sudden diminuendos. When he recalls playing this for the first time to Nick Gold’s parents, Gold and his wife, sitting in the second row, smile fondly.

“Cantelowes”, named for the London street where he lived with Lucy Duran in the 1980s, begins with a quote from The Good, the Bad and the Ugly that brings a ripple of recognition from the audience. Then it leads into a low, throbbing bass pulse with high notes occasionally bursting in like lighting flashes amid thunder. Some passages are impossibly fast; others as calm as moonlight reflecting in one of the ponds outside.

Diabaté plays a new improvisation in honour of the people of Seville (“it doesn’t have a name yet”). Off-microphone, he vocalises along with the pretty melody line, at the edge of hearing, so that only the first few rows can catch it; as if he were Glenn Gould and these not the Mandé Variations but the Goldberg.

“One more?” he asks. “One more?” And he plays a version of “Ala L’a Ke”, a traditional graduation piece for apprentice kora players, which appears on the album as a tribute to Baaba Maal’s kora player Kaounding Cissokho. His sharp stabs echo Wolof sabar drums, and he builds to a storm, before ending on a flamenco trill. There is a moment’s silence, and then he acknowledges the applause with the imperious hand of a sorcerer.

‘The Mandé Variations’ is released by World Circuit on February 25. Toumani Diabaté tours the UK in April