Sonny Rollins opened his headlining London Jazz Festival concert at the Barbican by sketching the melody of “Cabin in the Sky”; his body language as rococo as the devious logic of the improvisations that were about to unfold. It was the second night of the 10-day festival, and he had been greeted with a standing ovation. His response was perfect; his tenor sax radiating warmth, his playing hovering above ballad tempo.

Rollins spins grandiose structures from the simplest materials. At this gig, two standards and the inevitable calypso were joined by a breezy original and Noel Coward’s “Someday I’ll Find You”. The finale was a perfunctory blues over a rock-solid shuffle. Each became a central motif sustaining a network of subsidiary themes, subtexts and blind alleys. Slashes of melody, flurries of notes, low-down honks and robust riffs were strung together with Newtonian logic.