Saturday commuters sprinting for the 17.33 to Ardrossan find themselves dodging an obstacle course of swing-dancing young couples, soundtracked by a pensionable trad jazz band. A shifting crowd of about 100 pause in their journeys at Glasgow Central station to enjoy Penman’s Jazzmen, skilful Scottish veterans comfortable with each other and the demands of this century-old New Orleans music.

It’s statement of intent to open your first British headlining show with a 15-minute version of an album track which lasts a minute and three-quarters – from an album which itself lasts barely more than 30 minutes. And then to riff on it, incorporating elements from a debut album which barely anyone beyond your native country has heard. In taking her current album No Deal’s “I Feel You” and merging it with A Stomach Is Burning’s “A Stomach”, Belgium’s Melanie De Biasio could have alienated an audience who had never seen her before.

New Orleans. New York. Kansas City. Chicago. These are the places where the soul of jazz breathes free. In London, you’d head to Soho. Dalston, or Camden; none of these places have a blade of grass to share between them. Jazz must be one of the most determinedly urban genres of music. Even rap these days has flirted with country music. (Look up Spearhead’s entertaining “Wayfaring Stranger” if you don’t believe me.)

Denmark’s Broken Twin take the lead in the latest of theartsdesk’s regular round-ups of the new music coming in from Scandinavia. Debut album May is melancholy. Minimally arranged, with lyrics addressing the pain brought by the passing of time, bleakness in the form of metaphorical references to weather and what happens after death, this is an affecting album.

The veteran South African jazzers Adam Glasser and Pinise Saul transformed the gleamingly elegant Crazy Coqs cabaret den into a throbbing township jazz club last night, with an exhilarating programme of original South African jazz, seasoned with standards and township folk. Joining forces with the percussionist Marcina Arnold, a relative newcomer to their ensembles, they roughed up this venue’s urbanity with unfamiliar fires of passion and yearning.

Jazz pianist Chick Corea put a bomb under his reverential “rare solo concert” billing at the Barbican last night, with an outrageously showmanlike variety performance that seemed to take in everyone from Keith Jarrett to Gareth Malone. Corea’s two ECM albums, Piano Improvisations (1971 and 1972), blazed a trail for similar work, music that was cerebral, even austere, from Paul Bley and the arguably even more distinguished Jarrett.

Zara McFarlane’s exquisite synthesis of jazz and nu-soul, an intoxicating proposition on CD, breathes more freely live, we discovered, in last night’s Brighton Festival performance. A recent appearance on Later... with Jools Holland was mentioned discreetly, and has clearly buoyed her confidence, as she gave an utterly engrossing demonstration of why Holland, and before him, Brownswood Recordings’ Gilles Peterson are supporting her.

Crazed magnificence, off the cuff improv, pinpoint timing. And that was just MC and trombonist Ashley Slater's on-stage banter. In one of the most hotly anticipated jazz gigs of 2014, the return to the Ronnie Scott's stage for the seminal and utterly singular big band Loose Tubes – almost a quarter of a century after their valedictory residency in September 1990 – surpassed all expectations.

Who knew the human spirit needed such bureaucratic care? The celebration of International Jazz Day, founded by UNESCO in 2011, at King’s Place last night was nothing if not well cared-for. Sponsored SGI-UK, an arm of the global Buddhist movement, who were raising funds for UNICEF, proceedings are guided globally by legendary pianist Herbie Hancock, a UNESCO Ambassador for Intercultural Dialogue and Chairman of the Thelonious Monk Institute of Jazz.

My preconceived and somewhat misguided idea of the Cabo Verde islands (the official name for Cape Verde these days) was that they were basically a hotter version of the Canaries, with a spare and volcanic landscape that, being a Creole culture in the middle of nowhere, produced a few remarkably wistful singers, most famously the great Cesaria Evora. The islands seem to be a hothouse of tremendous female singers - other purveyors of nostalgic music being the likes of Sara Tavares, Lura and the more cosmopolitan Paris-based Mayra Andrade.