The 23rd annual Flamenco Festival New York comes “direct from Andalucia,” boasts the brochure. But the dance headliners, at least, have arrived by way of Madrid, swapping the tiresome question of authenticity for a tantalizing challenge to self: What are you going to do with your tired old dance? The flamenco star Olga Pericet is going to mess with it—lovingly, absurdly, comically, outrageously, like the best of her bold and sophisticated cohort (Israel Galvàn, Rocio Molina). The Ballet Nacional de España’s task is trickier, given the hybrid look of traditional “Spanish dance”—rough-hewn, soft-shoe ballet accessorized with the relentless buzz of castanets. But under the company’s much-hailed new director, Rubén Olmo, and with a veritable army of handsomely costumed dancers, the idiom begins to make sense. It’s all about volume: the swirling dress and cape, and the conical shape the body takes, with arms held as if around an invisible partner, as the dancer turns and stands proud. —Apollinaire Scherr