Every August when London dims, Edinburgh calls, promising nothing less than ‘the greats of the arts’ at the International Festival. As if this beautiful, haunting city wasn’t enough enticement, I always pack high expectations for the EdFest, which in the past has delivered some staggeringly good international dance events that commercially biased London could not entertain. Though in recent years things have gone off a bit, this year the ‘great’ box was ticked several times.

Israel Galván’s mesmerisingly extraterrestrial flamenco dancing has been seen in London before. But this 110-minute fantasy on the fate of gipsies under Hitler, Lo Real (The Real), built the explosive bebop of his dancing into a much larger landscape using folk memory to unlock a feast of musical and dancing exploration.

Galván is very strangely wired — skinny and beaky, he moves with the suddenness of electrical circuits shorting, with totally unpredictable jags and stabs of legs and hands. His sense of rhythm seems beamed in from another galaxy, but is well understood by the adventurous performers around him. An old piano got punishingly kicked, pebbles stood in for castanets, a saxophone swooped and fluttered about as if trying to find a note somewhere, and a huge old lady performed a funny flamenco parody of an American TV commercial. Railway girders, Leni Riefenstahl film and metal walls became the percussive arsenal of anger, surtitles showed us the distilled power of the lyrics as a voice wailed: ‘Huge tiredness came over me and I felt a great desire to cry.’

Galván’s female counterpart was Belén Maya, a revelatory dancer of dark, defiant sadness, dressed like a Roma woman in headscarf, clogs and leggings, sledgehammering in the big wooden shoes, then kicking them off and repeating the zapateado in bare, unprotected feet. There were absurd clashes — her sombre gipsy girl countered by a cabaret-Carmen episode starring the skinny, witty Isabel Bayón. But then Galván’s theme is the fascination of itinerant culture to outsiders, so why not? And the paradox is that his dance explorations are only possible with a profound mastery of flamenco techniques. Requiring deep individuality and highest physical rigour, driven by musicality and pride in roots — flamenco could tell classical ballet a thing or too.

A century ago Galván’s mindset might have got him incarcerated alongside Nijinsky, the subject of Company Chordelia’s impressive Fringe show Nijinsky’s Last Jump. This focused on the presumed schizophrenia that took this catalystic figure off the stage at 29, and mostly avoided the cliché of equating madness with creativity.

A concise, 65-minute script fused elements of Nijinsky’s diaries of 1919 with later knowledge. Old Nijinsky (James Bryce) catalogued his treatment, a 30-year parade of experimental medicine, including ‘228 insulin-induced comas’. Bryce movingly suggested the permanently blunted wits trying to reconnect with his younger, rawly sensitised self (Darren Brownlie, also commendable). Nijinsky’s celebrated jump was apparently born in his desperate attempt to save himself, aged five, when his father threw him into St Petersburg’s deep swimming pool. Bouquets to director Kally Lloyd-Jones for turning such tricky material into a concise, precise emotional experience.

Not entirely great, but worth seeing was Seven, Martin Schläpfer’s ambitious choreographic setting for Düsseldorf’s Ballett am Rhein of Mahler’s Seventh Symphony. With ballerinas in pointe shoes one moment, black boots the next, it had its contemporary clichés but also definite choreographic originality, in ensemble and pair work. It was sabotaged by the 105-minute symphony itself (they call it a ‘problem work’, and no wonder) and wooden conducting by Wen-Pin Chien of the valiant Royal Scottish National Orchestra, who shouldn’t be blamed.

Even so, Seven was not brutish or cynical, unlike the St Petersburg Ballet Theatre which turned up at the London Coliseum last week in Swan Lake emitting foghorn blasts of PR from dubious quarters. Production values were Soviet Fifties, with a famished orchestra coarsely conducted, a joyless and sometimes incompetent company of dancers, headed by a maladroit leading lady, Irina Kolesnikova, who gives us Russian mannerisms and blurs of steps instead of the proper care this endlessly traduced masterpiece asks for. The one redeeming feature was Denis Rodkin, a Bolshoi Ballet guest of grace and pedigree, who maintained an on-stage air of total detachment from this sorry travesty, though presumably pocketed the cheque happily enough.