Brilliant Corners takes its name from pianist Thelonious Monk’s 1956 album of the same name – an original and exciting recording that has endured. It’s an appropriate name for the festival, which celebrates musical innovation in some of Belfast’s best venues. Fitting too, that the festival opens at that bastion of the arts, the Crescent Arts Centre – a brilliant corner of the community – with a double dose of jazz bearing a Made in Belfast stamp. The Jeremey Lyons Dectet’s original program draws from big-band tradition. Richly layered strands of brass steer a course between late night blues, cool impressionism and hard swing, with drummer Steve Davis a galvanizing presence. A little big band it may be, but on tunes like 'Bit by Bit' and 'Disquiet', the dectet’s limber grooves owe as much to the classic jazz quartet tradition. Saxophonist Meilana Gillard’s surging solos crackle with energy and invention. Hers is the outstanding individual voice, but Lyon’s success lies in harnessing the collective to such potent effect.

Trumpeter, broadcaster and educator Linley Hamilton’s new-look quintet is clearly in the zone on the occasion of the album launch of In Transition. Italian guitarist Julien Colarossi dovetails beautifully with the trumpeter on 'Our Tune', bringing greater dynamism to the core group that recorded Taylor Made in 2011. Hamilton’s quintet swings hard on 'The Kicker', adopts a Miles Davis-like balladry on the emotive 'Song for Pav', and treads lightly on Abdullah Ibrahim’s lyrical 'Joan-Capetown Flower'. There’s a nod to tradition on the standard 'Without a Song', crowned by Hamilton and pianist Johnny Taylor’s fine exchange. A gorgeous arrangement of Rufus Wainright’s 'Dinner at Eight' underlines that whilst the jazz idiom prevails here, an injection of new vocabulary is perhaps overdue. The grooving 'Happy People', meanwhile, is peppered with charged solos, and appropriately leaves everyone basking in the afterglow of an exhilarating performance. The Black Box hosts Brilliant Corners day two, with David Lyttle featuring Soweto Kinch and Duke Special. By any yardstick Lyttle is an outstanding drummer, and his finger is on the pulse of what moves an audience. Bookended by old school jazz of great swagger and soul, his set is an eclectic mix of hip-hop and reggae rhythms, improvised rap and sophisticated pop balladry, and everything gels beautifully. Kinch is in blistering form on the stonking 'City Life', unleashing a tumbling, soaring improvisation. Pianist Kaidi Tatham responds with a fluid, upbeat solo. Tatham’s feathery lyricism illuminates ‘After the Flood', easing into a reggae vamp that launches Kinch on another exuberant, wildly inventive flight. Lyttle seals this infectious slice of Jamaican jazz with a cracking solo display. Lyttle then embarks with hands in lieu of sticks on 'Happy Easter', progressing to stick-cum-shaker and finally two sticks as this soulful blues number swells. Dynamic yet unflashy, Lyttle’s rhythmic vocabulary charts the globe and is unerringly musical. Duke Special and Anne Lyttle bring vocal panache, combining on 'The Greatest Escape Artist in the World' – an infectious pop vamp. Duke Special is a poet of unique stamp: 'Jesus and his blood don’t mean so much anymore' is the striking opening line from a new song inspired by a new Belfast. Gil Scott-Heron’s spirit rises as Kinch raps over the tight jazz and hip-hop grooves of 'Raise Your Spirit', his vocal improvisations matching his firey alto work. The crowd proffer word prompts, which Kinch incorporates in his stride. Only in Belfast could Kinch get away with using the proffered 'terrorist' and get a laugh.

The captivating ballad 'Pure Imagination', featuring a fine bass solo by the quietly impressive Conor Chaplin, ends the set. The musicians oblige the vociferous crowd with a loose jam encore, which, like the entire performance, is all about having fun. Serious fun. Day three features Spanish guitarist Eduardo Niebla, who for 40 years has explored the confluence of influences that make up flamenco. On 'Rosie', 'Mirror of Life' and 'India', Niebla’s fleet, dazzling technique combines the flavors of the Middle East, Iberia and India in a dense, evocative stew. Rhythm guitarist Matthew Robinson’s subtle accompanying role frees Niebla to follow his melodic muse, yet despite the brilliance, the music has the feeling of recital as opposed to a descarga, with the crowd subdued. Niebla’s guitar doubles as percussion instrument on the tremendous rumba 'Calle de la Tina'. Dashing buleria rhythms ('Para James') and Django Reinhardt-esque romps ('H for Helen') outweigh more ruminative passages. 'I Can’t Wait Any Longer' concludes a breathless set with a flourish. The final day presents two strikingly different concerts. In The MAC, the Bourne Kane Davis Trio give the performance of the festival. In BKD’s world, minimalist gestures and frenzied flurries cohabitate, and pockets of dissonance and melody flirt with each other. The stealthy drama of 'Dark Days' – where Davis’ crinkling paper constitutes the percussion – is so hushed that the creaking of someone’s leather jacket seems intrusive. Pianissimo lyricism ('Light'), heady trio grooves ('Cold') and light-hearted vocal vamps ('Fa La La') round out the first set. The second half of BKD’s performance sees the world premiere of Piers Hellawell’s 'Sound Carvings, Strange Tryst'. The through-composed yet flexible undulating waves – bold in conception and endlessly dramatic in execution – represent a triumph for composer, performers and organisers Moving on Music alike. BKD’s merited encore, a delightfully woozy, Monk-esque blues, caps a truly memorable performance. A stone’s throw away at the Black Box, the pulsating Manchester trio GoGo Penguin offer an exciting alternative to a jazz scene awash with piano-led trios. Pianist Chris Illingworth’s strong melodic contours, bassist Nick Blacka’s fierce arco sheets of sound and drummer Rob Turner’s vibrant, shifting rhythms acknowledge the influence of e.s.t., while forging a personal and heady creative path. The short yet intense set provides the proverbial fireworks to four days of absorbing, eclectic music. In just two editions, Brilliant Corners has established itself as one of the most adventurous music festivals in Northern Ireland. The challenge now will be to raise the bar in 2015.