The initial impulse to write the Concerto came when Pierre Boulez wrote to Barraqué asking for a new work for the Domaine musical's 1962–63 season.
Barraqué wrote back, suggesting the Concerto, and he began composing it on Easter Monday, 23 April 1962.
It was premiered on 20 November 1968 at the Royal Festival Hall in London, by Hubert Rostaing (clarinet), Tristan Fry (vibraphone), and the BBC Symphony Orchestra conducted by Gilbert Amy.
Au delà du hasard (1958–59): "the many currents cross / ... towards one convergent point / united among themselves they are the mirrors".
Boulez also projects a regular series of twelve alternations between his soloist and each instrumental group, whereas Barraqué's work is continuous.