The fireworks that erupted over Dalston early Friday evening, after a fanfare from Andy Sheppard and the 200 players of the Dalston Saxophone Massive, were a two-for-one special, launching both Ken Livingstone's Public Spaces programme and the 2006 London Jazz Festival. It seemed like a symbolic conjunction. If the festival's programmers had their way, jazz - a traditionally urban art form with a long history of openness, inclusivity and fast reactions to changing social dynamics - would have a presence in every public space and on every communicative medium in the land. For 10 days in November in London, it almost begins to feel that it does.

At the Barbican, British pianist Stan Tracey and former Miles Davis and Weather Report sax legend Wayne Shorter kept the heat up with firework displays of their own. Tracey's trio played originals, Thelonious Monk tunes and standards, driven by the leader's vivaciously hopping runs, bamboozling silences, crashing chords and moments of unexpected tenderness. Wayne Shorter's quartet - perhaps the most exhilaratingly creative and spontaneous small jazz group on the planet - then played a seamless set of improvisation. Shorter's famous Footprints, signalled by a brooding piano vamp and the whiplash of Brian Blade's drums, was developed by the 73-year-old saxophonist as a masterpiece of airy, skimming sounds, dry long notes and inquisitive trills.

The late-night live Jazz on 3 show from a packed Pizza Express Jazz Club in Soho brought foretastes of events to come. World-jazz pianist Randy Weston combined sumptuous lyricism and cliffhanging improv with his trio; the Westbrooks' Village Band deviously reworked the blues for a brass ensemble; pianist Gwilym Simcock shone all the way through an unaccompanied solo; and Evan Parker, former Albert Ayler bassist Henry Grimes and others played ruggedly contrapuntal free-jazz.

· The festival continues until Sunday. Details: Londonjazzfestival.org.uk