Bach's Musical Offering, a set of 13 instrumental variations, is a piece of baroque polyphony with a formal rigour that leaves mathematicians dizzy with delight. It has what Brown calls "a preponderance of exquisite structure", yet typically of Bach it's also immediately accessible as ravishing music. Other fine choreographers have foundered on Bach. Trisha Brown responds with a playful intelligence that pays profound homage to the score yet also allows her to joke with it, work around and through it, and even to claim her piece could be danced without it.
It comes as no surprise to learn that her initial preparation for MO was to learn to compose baroque counterpoint. She knows how it works. Yet she avoids dogma by using a different tactic for each of the Offering's parts. Sometimes she goes for a strict visualisation of the notes. The dancers become voices in the canon, each cueing in with the same movement phrase and spiralling off as the theme elaborates, bunching into running pairs and threes and fours as the instruments divide and rejoin in working out the fugue. In Bach's contrary-motion number, two male dancers converge from opposite corners, then retrace their intricate steps in a perfect palindrome. A fast fugue has a string of dancers repeatedly careering across the stage in a frenziedly comic follow- my-leader.
The dancing itself is superb. Almost casual in its basis of loose-limbed, natural human motion (standing, leaning, falling, running), it has a fluid elegance that belies its compositional rigour and a dazzling precision that puts other companies in the shade. Brown claims that she reinvents her vocabulary for each new work, but the same crystalline qualities appear in Set and Reset, a groovy celebration of life on the sidewalk, and in a solo performed by Brown herself. Eloquent, challenging, uplifting and gloriously life-enhancing, the Trisha Brown Company offers the best contemporary dance I've seen this year.
Siobhan Davies is another mature dance-maker not content to sit on her laurels. On Tuesday I caught her latest piece, Trespass, twinned with the hit of 1995, The Art of Touch, in Colchester on a brief tour. Whereas in Touch, Davies's starting point was the music - Scarlatti's harpsichord sonatas - the new work starts from a blank page. She asked her composer and designers of costume, stage and lighting to come up with dynamically contrasting elements which might alter the other components in the work - trespassing on the others' domain.
It was a tall order. For a start, it's hard to see how Gerald Barry's score - tender, brooding monody alternating with fierce hammerings from a piano trio - did anything more than music normally does for dance. Nor is it obvious how Sacha Keir's grey outfits could have any influence unless by their very drabness. Stage designer David Buckland, however, came up with a striking, neon-edged gauze screen, which effectively splices the action in two whenever it descends, and an illuminated parchment globe which, rolled slowly about the stage, becomes an eerily beautiful partner in a dance. A gangling, 12ft praying-mantis puppet, devised by Buckland and Keir, glowers over the opening of the piece to no apparent purpose.
Davies's dancers are, as ever, infinitely watchable in their myriad permutations of swivelling, stretching, gliding and striding steps. Yet Trespass, for all its interest, remains an experiment - one that, like its components, fails to bring much to bear on anything else.
Trisha Brown Company: Newcastle Theatre Royal (0191 232 2061), Tues & Wed; Blackpool Grand (01253 28372), 3 & 4 Jun. Siobhan Davies: Newcastle Theatre Royal (0191 232 2061), Fri & Sat; Sheffield Crucible (0114 276 9922), 4 & 5 Jun.