It’s strange to think that music recorded 45 years ago in what was once an old Yiddish theatre turned rock 'n' roll palace on the Lower East Side in the summer of 1970 – a few months before Jimi Hendrix’s death, as war raged in Vietnam and riots in the US – still sounds way ahead of our time, let alone the time in which it was made.

Zara McFarlane’s rise to jazz eminence has taken the scenic route, especially in these days of the super-educated jazz prodigy. From a Jamaican home where reggae was always in the air, via a love of musical theatre, and a degree in pop performance, McFarlane studied jazz and improvisation at the Guildhall. With the support of Gilles Peterson, who signed her to his Brownswood label, she released a debut album, Until Tomorrow, in 2011.

Seb Rochford’s five-piece Polar Bear is now ten years old, and the band's post-jazz amalgam of lugubrious saxophone phrases and scratchy riffs, scarified electronic soundscapes, and mesmeric, crackling drum and bass rhythms has matured. The giddy thrills of nearly winning the Mercury Prize (with Held on the Tips of Fingers in 2005) are long past, and they seem content with the trappings of the alternative scene, releasing limited edition vinyl and selling inscrutable T-shirts.

Julian Siegel’s urbane, generically layered voice has, as both reeds player and composer, forged a unique and revered position in the jazz world. He leads a quartet of pioneering drive and technique, featuring pianist Liam Noble, bass player Oli Hayhurst and drummer Gene Calderazzo. Their 2011 album Urban Theme Park was widely praised for its improvising ambition, diverse sound worlds and smouldering virtuosity.

Trumpeter and composer Rory Simmons is one of the most innovative and diversely talented musicians on the contemporary jazz scene, genre-hopping with startling agility across its many cutting edges. Fringe Magnetic, Simmons’ acclaimed 11-piece band, has been blending the compositional rigour of classical music with the freer playing style of jazz for nearly five years now. He’s a core member of the LOOP Collective, and has collaborated across Europe with jazz stars including Barak Schmool, John Etheridge and Byron Wallen.

Revelling in the acoustic precision of the recently opened Milton Court concert hall last night, Norwegian pianist Tord Gustavsen showed once more why his quartet’s combination of tersely lyrical melodies and syncopated rhythms is so appealing. For his new album, some of which was played here, his typically European, restrained sound was, to a greater extent than previously, augmented by some distinctly funky passages, which were drawn out with immense skill and sensitivity from what had gone before.

The Barbican brought two of the great originals of contemporary music together last night. Ralph Towner and Egberto Gismonti are temperamentally very different, but complement one another wonderfully, in an inspired piece of programming. Both are stylistically polyglot, straddling contemporary classical technique as well as jazz and, in Gismonti’s case especially, a range of folk idioms.

Bach, Duke Ellington and free jazz improvisation met at Cafe OTO last night, and joyously warped some minds. Composer Alexander Hawkins’ BBC Radio 3 commission, the nonet piece "One Tree Found", was part of last year’s Baroque Spring season. It takes the three-part structures of Bach’s trio sonatas for organ, adds echoes of Duke Ellington’s (known, Hawkins notes, as "The Hot Bach" at the height of his fame) numerous three-way orchestrations, and completes the creation with improvisations both contemporary and baroque in style.

A woman tramps the streets of Paris looking for a man. It’s night. It’s raining. She pops into bars asking for him. Everyone knows who he is. He’s been seen, but not recently. Earlier, early in the evening, she was supposed to meet him but he hadn’t turned up. She doesn’t know it, but he’s stuck in the lift of an office block. He thought he’d be in and out of the building in moments. While trapped, the car he’d parked across the street has been taken by a leather-jacketed young tough who brings his girlfriend from a florist’s along for the joyride.

Finland’s Jaakko Eino Kalevi, who played his debut British show last November, heads up theartsdesk’s latest regular round-up of what’s come down from the north. A spellbinding display of individualistic pop, the London outing coincided with the arrival of his first non-Finnish release, the Dreamzone EP.