It can sometimes be hard to remember, in the barrage of what David Bowie called "teenage wildlife", what is truly remarkable and what is just flash and dazzle, shoved under our noses by men in suits. This is just one of the things that come to mind when Paul the Girl sings "Is that the emperor's bare arse I see before me, as he ticks towards me on his wide, high heels?" over the sparse electric guitar of Gods and Goddesses.

Paul the Girl is a girl called Paul and her band are possibly the most gifted group of musicians I have ever seen at what is ostensibly a rock gig. This is where the trouble starts, and from where the hope springs: it's impossible to say exactly what Paul the Girl does.

In their freedom and wit, these songs owe much to jazz. The band (an unorthodox line-up: drums, double bass, trombone, saxophone and Paul herself playing electric and acoustic guitars) spin lengthy, intoxicating codas, with sensual blasts of bass saxophone.

Yet another song begins with Paul spilling delicate, silvery peals of electric guitar over an insistent bass, developing into the kind of molten, bluesy playing that most (male) guitarists would sell their strings for. The ornery skronk of Captain Beefheart is here too. Just when you begin to pin her down, there's the vaudeville stomp that rises out of Thinking Song, or the macabre cabaret (macaberet perhaps?) of The Phony on the Jury.

Paul's voice, which could be described as kittenish only if the kitten had very big teeth, soars, screeches and gargles, capable of lulling sweetness and alarming swoops, hiccups and shrieks. That's not to say that this is difficult music: enormously sophisticated, yes, but the propulsive clatter of Don't You Know Yet Who I Am and the gorgeous drawl of Electro-Magnetic Blues (the title track of her new album) prove she can write addictive choruses, too.

Without management and on her own tiny label, Paul is making the most original music of any British artist, of either gender. An extraordinary, ravishing evening.