A new Swan Lake at the Royal Ballet is a once-in-a-generation event.

Everyone knows that Elizabeth I was a monarch of deep intelligence and sharp wit. Fewer know how good she was at the galliard. This was a virile, proud, demandingly athletic dance, usually performed by the men at courtly gatherings, and the fact that the Queen of England so enthusiastically flouted convention in this way says a lot about her.

You have to hand it to the Americans: they think big. Where the Royal Ballet or ENB might put on three or four new works in the course of a season – because commissions are wildly expensive and a box office risk – San Francisco Ballet has just presented a dozen in the space of two weeks. What’s more, the 12 invited choreographers – four of them Brits or British trained – were given virtually carte blanche to create whatever they liked.

Whatever you do in the next couple of days, be sure to grab a ticket for this wonderfully atmospheric production. A glorious fusion of athletic dance, creative visuals and intoxicating sound, the piece pays tribute to the island of Taiwan, named Formosa ("beautiful") by Portuguese sailors in the 16th century, and home to Cloud Gate Dance Theatre.

Brighton Festival is the UK’s leading annual celebration of the arts, with events taking place in venues both familiar and unusual across Brighton & Hove for three weeks every May. This year, the Festival boasts an eclectic line-up spanning music, theatre, dance, visual art, film, comedy, debate and spoken word, with visual artist David Shrigley as Guest Director.

There is a sense of loyalty from the Brighton audience awaiting Hofesh Shechter’s new work.

If you came to this programme knowing nothing about the choreographer Kenneth MacMillan, you may have learned a few things. That he died, tragically and rather dramatically, of a massive heart attack during a first night performance of one his own ballets. That he was "interested" in sex and death, and frequently choreographed violent forms of both in his ballets. That in later life he had a wife and daughter whom he loved.

One day someone will come up with an algorithm for the perfectly balanced triple bill. Until then ballet directors will have to make do with hit or miss. The Royal Ballet’s latest three-part offering would appear to tick the boxes: something old, something new-ish, and something just for fun. Yet while the evening can’t be faulted on the quality of performance, the effect is less than the sum of its parts.

A new William Forsythe ballet is quite a coup for English National Ballet; the choreographer hasn't made a piece in Britain in 20 years.