To be fair, her albums - which include The Singer (1992) and Malediction and Prayer (1998) - are astonishing, but at the same time the most challenging and uncomfortable I have ever heard. And there's a fair amount of screaming. It's not easy to describe what she does with those octaves at her command, but this perhaps sums it up best, at least in relation to the recorded work: "A performance-art banshee of shrieks, warbles, growls and guttural moans - the sound of a Hieronymus Bosch painting."

After her brother, the poet and playwright Philip Dimitri Galas, died of AIDS in 1984 she wrote her Plague Mass, which she performed in the Cathedral of St John the Divine in New York, stripped to the waist and covered in blood. Captured on the 1991 Mute album of the same name this has been described as "lyrically and musically one of the most uncompromising albums ever made", and rages against the hypocrisy and homophobia shown on the emergence of the disease.

Even the photographs of Diamanda Galas are disturbing - in some she appears beautiful (though distinctly gothic) with her long white face, cheek bones you could cut yourself on, long black hair and a gash of a mouth painted dark purple). In others she looks like a drag queen, which is perhaps not surprising when you learn that she spent time with Oakland's transvestite prostitutes and masqueraded as 'Miss Zina', "a woman dressed as a man dressing as a woman."

With a background like that a live performance was to be anticipated with a certain amount of foreboding. In fact it was astonishing in the very best sense of the word - thrilling, intense, passionate, uplifting. Diamanda Galas stalked imperiously on to an almost empty stage in a stunning, skintight black gown that trailed after her but left arms and shoulders bare. Sitting at the piano the first thunderous chords paved the way for the voice, so much richer in life than on recordings, somehow warmer and more human while at the same time even more searing. She also allows the sheer beauty of her voice to be heard, something that is difficult to assess from the extreme distortion she favours in the recorded works.

The programme was La Serpenta Canta - the serpent sings - and has been described as an evening of her greatest hits. She sang in English, French, Spanish and Italian, and some other languages I couldn't recognise (quite possibly Armenian and Greek - she was born in San Diego of Greek Orthodox parents). She sang blues, boogie-woogie, jazz - or rather, she took the conventions of such musical forms and turned them into something altogether her own, transfixing the whole audience with her virtuosity and commitment. How she can play about three different rhythms at once I don't know, but she can, and it's amazing. She uses delay effects to make a live duet with her own voice and sometimes with the piano (mostly very effective though it did make lyrics hard to hear); this is a Galas speciality and a technique she has spent time studying. She is a stunning pianist as well as singer, and using all of these skills combined she performed one song that resembled a diabolic fairground - towards the end it was as if a carousel started to increase in speed, the pitch constantly changing as it spun out of control into something quite extraordinary and wildly exhilarating. In her hands I Put A Spell On You by Screaming Jay Hawkins becomes serious voodoo.

Some haunting songs drew from the Greek tradition of women dirge-singers, a tradition preached against by orthodox priests but never totally suppressed. Women who were not otherwise allowed to be seen or heard were transformed when someone died: it was apparently an alarming performance. During the Second World War the women sang savage anti-Nazi tirades, mourning becoming incitement. "It incited people to be so angry they would fight. It was never mourning in the pacific sense", says Galas. Her own work is very much in this tradition: "In the transition from funeral singing to something that is also very political and antagonistic." A previous song cycle Defixiones is inspired by the troubled history of Turkey, including massacres of Armenians and Greeks earlier this century.

At the Royal Festival Hall Galas was in a slightly lighter mood and only directed her anger towards journalists who use the forbidden description and who misquote her. So if I have, Ms Galas, I apologise in advance. The fact remains that this was one of the musical and performance highlights of the year. The audience, not surprisingly, was deliriously appreciative and managed to extract two encores, and when a vast bouquet was presented we were finally granted a glorious smile. Yes, she is beautiful, though I expect she thinks that's totally irrelevant anyway. And I will now go back to the albums and listen to them in a completely new light.

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Mercury Prize 2009 nominees