You don't get false modesty with Toumani Diabate. When he welcomes me into his Seville suite the Malian kora player casually refers to his forthcoming album, The Mande Variations, as his “new masterpiece”. The awkward thing is that in an age of spin and hyperbole, it is difficult to disagree with him. Recorded in two hours, it consists of eight one-take, no-overdub instrumentals of such dazzling virtuosity that Europe's world-music critics have been summoned en masse to Andalusia to watch him perform. There is a scrum as we clamour to get a seat near the stage in the tapestry room of the old royal palace, the Alcazar. We all want to see how he does it.

“Any time I play a kora what results could be a CD,” he says before the concert. “That's why I invited you here to see this show. I cannot explain what is happening when I play. It's like I'm fighting something. But you don't need to be African to understand the message. Just sit down and listen carefully. It will touch you.” The kora is West Africa's harp. A lute made by sticking a thick pole through the side of a large gourd covered in a cow skin and then attaching 21 strings (traditionally fishing line) in two rows to both the pole and a bridge on the gourd. “But there is more to the kora,” Diabate adds. “You have to understand that it is unique, you have to know the significance of each part and the way it is built, then you have to learn the techniques, the spirit of the kora, what the music is talking about.” Such as?

“Ah,” he laughs. “There is a tradition you have to follow if you want to learn these things. And the first thing is that you must pay your teacher ten cola nuts, the old money of Mali, before the lesson starts. Do you have any cola nuts?” Sitting on a stool with the kora between his legs, Diabate plays bass with his left thumb and rhythm with his right thumb, leaving his fingers either to solo or support the instrument. When he concludes with Kaounding Cissoko, an old tune renamed in tribute to a fellow musician who died young, the magic is complete: countless notes tumble from his instrument, as if he is playing every part of an orchestra. The solo performance holds us spellbound. In recent years he has lent his powers to jazz and blues musicians, pop stars and fellow Africans as his musical reputation grew. He hit a golden streak three years ago with the release of In the Heart of the Moon (a series of improvised duets with fellow Malian Ali Farka Toure) and Boulevard de l'Independance, by his own big band, the Symmetric Orchestra.

With The Mande Variations, he has come full circle, recording a solo album that picks up where his earliest recordings left off. In one regard, it's not that great a jump: many of the basic tunes are shared by the new album and the first one he recorded, Kaira, which involved another two-hour burst of creativity in a studio. But now Diabate has far more power as a musician, and the tunes are just starting points for his improvisations. “Well, that was 20 years ago. It was time to make another album like that, but I wanted to take the kora to another level. I think people expect that of me, of the Diabates. As hereditary musicians, our knowledge has been passed from father to son for 700 years, each one playing a little differently, moving the music on. My grandfather played differently from my father and he introduced the idea of playing solos. I have grown up in a different time, with rock music. I have a different groove.”

Diabaté happily lists some musicians who have taken him away from the traditional path his father travelled, giving him the swing his ancestors lacked: the flamenco guitarists Ketama, the first Europeans he played with; Damon Albarn gets a mention for a number of joint projects; Bjork is a recent acquaintance, after she came to Mali to record a track for her recent album; Jimi Hendrix is hailed for virtuosity; and, right at the top, the German metal band the Scorpions, the group responsible for the first album he bought.

Now his 15-year-old son, Sidiki, is studying music at the Bamako conservatory, the first Diabate to learn how to read and write music, and playing kora in a hip-hop band. Expectations fall on young shoulders if your family name is Diabate. The Radio 3 presenter Lucy Duran recalls meeting a group of the most revered Malian kora players in the mid-1970s. All agreed there was one musician she had to hear, a young man called Toumani who could play incredible things. He was 11 at the time. A decade later, Diabate came to Britain for a handful of concerts. His tour manager recalls a young man whose behaviour resulted in a series of misadventures that could only be explained by him being guided by uncontrollable urges. Through the 1990s, when he was responsible for a series of groundbreaking albums, he also developed a reputation for being unreliable, contrary and capricious. Yet this is a trait Africans expect of their musician caste, the griots, who they believe to be possessed by spirits (djinns).

Today, that Diabate has matured. I ask him about the djinns and the control they have on an artist, partly because I wonder if such a worldly man still believes in sprites. There is a brief pause. “All I can say is I have God. I didn't learn the kora from anyone, I taught myself, so it is a present from God and the inspiration that comes to me when I'm playing must come from him. This is spiritual music. African music is not all dance music, but also for meditation or religious ceremonies. My tune Ali Farka Toure is typical of the music we play to pay tribute to somebody who has died.”

If anybody deserves the credit for nurturing the mature Toumani, Toure, who died in 2006, probably did more than most: encouraging him back to recording, sharing a Grammy with him. And the improvised melody bearing his name is a highlight of the new record. “I played it exactly as it was in my heart. I could play it a thousand times but I'll never be able to play it like that again.” In the Alcazar he shows that improvisation was no fluke by playing a new, still nameless tune that again takes a simple melody, adding new ideas every time he returns to the theme. It would be easy to label this intuitive brilliance as “genius”, but that ignores Diabate's guiding hands - the djinns and God - and how he has, in effect, been practising for 700 years. Somebody else got there first, but perhaps a better title for this music would have been The Enigma Variations.

The Mande Variations (World Circuit) is out on Feb 25

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