It’s fair to say that vocal jazz ranks modestly in British awareness of Danish culture, certainly below the instrumental music and the phenomenon of the moment, the cable-knit-sporting detective Sarah Lund. Which is a shame, because this second event in Pizza Express’ week-long festival illustrated the variety and strength of that country’s scene very effectively. Sinne Eeg is a multiple award-winning performer broadly in the American tradition, while Cathrine Legardh exemplifies a Scandinavian, folkloric style.

Madeleine Peyroux made her name channeling Billie Holiday. White stars have never ceased to model themselves on African-American genius – Mick Jagger on Don Covay, Rod Stewart on Sam Cooke and Joe Cocker on Ray Charles. The resemblance is often uncanny, and yet there is always something missing - call it authenticity, roughness or soul. Peyroux has grown away from Lady Day, and found her own voice, but the jazz and blues that characterize most of the covers she sings with great skill and feeling, don’t quite have the edge of the originals.

Pianist Morten Schantz has been a prominent and pioneering figure on first the Danish, then international jazz and fusion scene for more than a decade. With saxophonist Marius Neset and drummer Anton Eger, also members of his new trio, he founded ground-breaking quintet JazzKamikaze in 2005, playing an exhilarating fusion of jazz, rock, funk and hip hop. Since then he has composed and performed across the full range of jazz-related fields, with ensembles including Unicorn, playing North African music, and Segment.  

As I waited outside the entrance to the Royal Albert Hall, someone leaned over to me and said: “My cocaine is to your left.” I glanced in that direction and realised they’d actually said “Michael Caine is to your left”, and indeed he was, on his way inside to hear a prom devoted to music by his old friend Quincy Jones. It’s hard to know where to begin with Jones’s musical CV. He’s had a towering career in jazz, film music and pop, and any one of these genres could enough provide material from him to fill a series of proms.

Cinema has waited a long time for a film about Miles Davis. It hasn’t been for want of trying by Don Cheadle, who stars in, directs, produces and takes a co-writing credit on Miles Ahead. Despite the support of Davis’s son, daughter, nephew and first wife Frances Taylor, the film was trapped in a pipeline for aeons. While he waited, Cheadle had plenty of time to turn himself into a trumpeter good enough to perform onstage in the film’s coda with Davis collaborators Herbie Hancock and Wayne Shorter.

Some years ago broadcaster Andy Kershaw introduced on BBC World Service radio a piece of Brazilian music with this blunt dismissal: “When I hear a track by, say, Gilberto Gil, I tell myself: ‘Right, time to take the lift and go to bed’.” It wasn’t a terribly joined-up complaint, but (in Kershaw-speak at least) it made sense. He’d arguably chosen the wrong musician for his swipe – Gil remains relentlessly inventive and, at 74, fantastically dynamic – but it was clear what he was getting at.

"Jazz,” said Keith Jarrett once, “is there and gone. It happens. You have to be present for it. That simple." For an audience, it produces a never-to-be repeated event: yes, you were there, and you didn’t miss it. One of the pleasures of seeing a group at the peak of contemporary jazz like The Impossible Gentlemen is to witness that joyous, open-minded and defiant spirit. In six years of existence, and now presenting their third album, the trust between the members of the group has visibly deepened. There is also a sense they are evolving, that they can and will go still further.

The Montréal International Jazz Festival's 37th edition presented its accustomed surfeit of gigs, covering the complete range from concert hall spectaculars to small club sessions. A large part of this, the globe's biggest jazzfest, is the massive-scale freebie shows on various outdoor stages. The festival completely takes over Montréal's downtown centre, which just happens to be this French-speaking city’s cultural area.

Copenhagen-born bassist Jasper Høiby moved to London in 2000 to attend the Royal Academy of Music. In 2005 he created the trio Phronesis which has toured extensively in Europe and North America and won awards for Jazz Album of the Year in Jazzwise and MOJO for its 2010 album, Alive, as well as a London Jazz Award for its "Pitch Black" performance at Brecon Jazz festival in 2012.

Few new releases come with quite such a specific technical claim as this double release from British saxophonist John Martin. His album title refers to his incorporation of multiphonics, an established technique in free improvisation, within his 11 new tonal compositions, which are in other respects from a recognisable idiom of contemporary jazz, often flavoured with a country and Latin tinge.