Tinariwen: iTunes Festival, The Roundhouse, London

There's a moment in the DVD documentary accompanying Tinariwen's new album, Imidiwan: Companions, in which a few of their Touareg friends are lounging in garden furniture against a desert vista, sharing a smoke and glasses of the dark tea drunk in the Sahara. "The world is a ball, half covered in land, half in water," explains one. "Tinariwen have played everywhere there is land. They have played in Australia, America, Europe, Asia and Africa – they have played in all the continents of the world. This proves that their music is universal."

His grasp of geography may be a touch basic, but his argument is well made, all the same. For there is certainly something universal about the appeal of the cyclical, droning guitar lines, the steady, insistent rhythms, and the warm but rousing chants which constitute their distinctive musical style. The last time I saw them play was out in the desert near their base of Kidal, in northern Mali. Powered by portable generators, they were performing for a few hundred Touareg who seemed to materialise out of nowhere, arriving on foot, camel and 4x4, in order to sway gently to the hypnotic rhythms and draw succour from the songs' sentiments of revolutionary fellowship. Tonight, in the Roundhouse, the only people who understand the Tamashek lyrics are probably the seven performers on stage, but the effect of the drones and chants is much the same, particularly when the audience reacts to the encouragement of the clapping, dancing Alhassane Ag Touhami and Abdallah Ag Alhousseyni, swaddled in robes and heads half-hidden behind their cheche turbans. It's as if the thousands of miles separating the cultures are simply an elastic notion, suddenly snapping together through a shared sense of rhythm and mood.

A similar metaphor begins tonight's show, when the band's main songwriter and charismatic leader, Ibrahim Ag Alhabib starts their set with "Tenalle Chegret" (The Long Thread), the opening lines of which claim, "The revolution is a long thread/easily twisted, hard to stretch". It's not an obvious set-opener, being the slowest, quietest, most introverted song in their repertoire. But as soon as Ibrahim swaps his acoustic guitar for a Gibson SG and the band launch into a more typically trancey piece, the audience is locked into the groove. "Cler Achel", the popular opening track from their Aman Iman album, is greeted with an exultant wave of recognition, the crowd surging into movement when Eyadou Ag Leche's propulsive bassline drops in.

After a couple of songs, Ibrahim leaves the stage for a three-song burst from Abdallah, who picks up his acoustic guitar for "Tenhert" (The Doe), an adaptation of a poem praising the bravery of fighters on "the day of the confrontation", delivering the lines as rap-style fusillades of words culminating periodically in long, drawn-out moaning harmonies from all the band. The offbeat chords and stuttering bass of "Intitlayaghen" follow, and then bass, hand-drum and handclaps establish the rhythm of "Kel Tamashek" (The Tamashek People), before Abdallah's plangent, piquant chords ring out triumphantly. The kids packed up tightly against the stage barrier go nuts for it, bouncing up and down on the spot as the song reaches its climax. "'S'okay?" asks Abdallah for perhaps the fifth or sixth time of the evening. It seems to be, judging by the response, though the absence of the keening female backing singers from Tinariwen's floating line-up does deprive their sound of one of its more exciting elements.

Ibrahim returns for the rest of the set, starting with "Imidiwan", its haunting melody casting a magical spell over the room, before the old favourite "Amassakoul'n'Ténéré" (Traveller in the Desert) has everybody swaying along. By the time the set closes, with Alhassane's curious little sidestep dance reaching its most animated pitch while the band vamps mesmerically, it's impossible not to feel that one has experienced some form of shamanic ritual: the very root, perhaps, of the rock'n'roll communion.