Ethiopiques, Barbican, London

It seems unreal that the musicians on the magical Ethiopiques records are about to step onstage. Brought to the mainstream by the soundtrack of Jim Jarmusch's Broken Flowers, and a compilation that was last year's best album, Francis Falceto's ongoing archive series unveiled a lost world: the swinging Addis Ababa that bloomed in Emperor Haile Selassie's last years, before the 1974 Mengistu dictatorship snuffed it out. Products of a nation too proud to absorb much outside African influence, yet peculiarly open to Western sounds throughout the 20th century, this was sensual, sophisticated jazz and soul from a parallel dimension. Thirty years and more later, we await its makers.

The crowd first have to swallow disappointment that Boston's Either/Orchestra are tonight's band, no Ethiopian ensemble left intact to play this music. But Mulatu Astatqe developed the sinuous "Ethio-jazz" riffs that snake through Broken Flowers in similar company in 1950s New York. A short, round-bellied old man now, he walks on to a hero's welcome. His seminal Ethiopian noir arrangements thrill where his vibraphone solos don't. He stays to modestly support diverse compatriots who have never shared a stage.

Alemayehu Eshete has been a star at home since 1960, and looks it, with his James Brown pomade and high kicks. A besuited showman who flirts with ridicule, he has a hiccuping strut matched by his voice, swallowing and sighing, then low and chatty. On "Ambassel", he quavers intimately; on "Qotchegn Messassate", he croons and groans, cruises through notes, then cries and clutches at them. He is at once earthily sexual and avant-garde, an Ethiopian ghost of Elvis. On "Mekeyershin Salawq", he is a soul shouter, leading the band in fast, sharp dance music that could have conquered the world 40 years ago if a note had been heard outside Addis's hotel bars. He leaves slowly, milking the applause.

Getatchew Mekurya blows his sax at the crowd he walks through, raising wild cheers. He is portly in a white shirt, robe with a Lion of Judah on its back and white-tufted crown representing a lion's mane, one part sophisticated jazzer to one of African tradition, and one of pure showbiz. His sultry shellela sax style, which he experimented with in 1952, parallels free jazz. He also recalls the Harlem jazz showmen that music lost to respectability.

Mahmoud Ahmed is the one Ethiopian star who did not need Ethiopiques. Since his 1975 album Ere Mela Mela's 1986 European release, he has built a following crowned here by a 2005 Womad performance and a subsequent BBC World Music Award. Grey-haired in a red-sashed white robe, he is more serious than the others. His husky voice seems the weakest, at first. But then "Ere Mela Mela" starts to build, varied verse lines answered by a title phrase that swells with each repeated plea. It is a quietly majestic invocation. Having captured us by stealth, he then sweeps us on to our feet. The full house, sedate until now, are dancing right up to the balcony. By "Kulun Mankwalesh", he is hurling out reverberating notes with unleashed force. Bouncing on his feet, he brings us as close as he can to the heady atmosphere that gave birth to this music.

Everyone returns for the encore, an ensemble never seen even in Ethiopia. As Eshete and Ahmed sing at each other, they are grinning. Astatqe looks on, his dreams of Ethio-jazz triumph at last coming true. The years these men have waited since their brutally crushed musical pomp, so long ago, must seem almost worth it. A historic night.