Continuing our series on some of the best music of 2015, here is our critic’s pick of the year’s best jazz tracks – from a new sax star to a hip-hop interpreter

Polar Bear – Don’t Let the Feeling Go

Some albums seem steered by a hidden jazz hand, even if few signs of jazz presence are audible – almost everything the resourceful Polar Bear do sounds like that, hence their latest prize nomination of the year, the Mobos’ best jazz act award. The British group’s 2015 album The Same As You was outwardly their least jazzy yet, but the spirit of the genry could be found in the quiet improv, sublime drumming (by producer Seb Rochford) and hooky minimalism of tracks like this one.

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Robert Glasper – Stella By Starlight

Piano star Robert Glasper, the canniest negotiator of the territory between jazz and hip-hop in contemporary music, went back to the classic unplugged piano trio jazz format this year with his Blue Note album Covered. Pieces by Musiq Soulchild and Radiohead signalled a very different repertoire to jazz standards. There was one classic-jazz vehicle, however: the evergreen Stella By Starlight. Glasper’s version showed just how inventively he joins the tradition to 21st-century rhythmic sensibilities.

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Loose Tubes – Arriving

Loose Tubes, the much-loved and conceptually revolutionary British big band of the 1980s, re-formed in 2014 and then released a new album this year, showing they can still generate unpredictable new music as well as reprise past hits. Co-founder Django Bates (whose score for the new Around the World in 80 Days musical is currently being aired) takes the tenor horn solo on Chris Batchelor’s bluesy title track.

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Kamasi Washington – Change of the Guard

Kamasi Washington, the Los Angeles-based saxophonist and Kendrick Lamar’s sometime hip-hop collaborator, delivered the hottest jazz story of 2015 with his idiom-spanning, orchestral multi-album The Epic – hot, because it brought elements of the soulful free jazz of giants such as John Coltrane and Albert Ayler to a new, younger audience. Washington’s work feels retro, but he gives all kinds of traditional music a contemporary edge, and he’s a saxophone heavyweight of charismatic force.

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Joshua Redman and the Bad Plus – As This Moment Slips Away

The postbop master saxophonist Joshua Redman came to the UK in 2015 as both a sax front-man for idiosyncratic genre-benders The Bad Plus, and as co-leader of the catchily lyrical James Farm. Both bands were terrific, but the former produced plenty to reinforce hopes that Redman will keep playing games with the Bad Plus.