It's day five of the EFG London Jazz Festival, and Snarky Puppy's show at the Roundhouse has sold out weeks in advance. And, as the crowd sings the gorgeous main theme of “Thing of Gold” in perfect unison, one of the reasons for the band's huge success becomes apparent. Yes, there's brilliant musicianship, spirited improv, blazing energy and the kind of impressively vast textures that only a band this size can achieve. But there's something else, which trumps all of these things. There's melody.

Now in its eighteenth year, the Scottish National Jazz Orchestra (SNJO) demonstrated last night why it's considered one of Europe’s finest big bands. Brilliantly directed by tenor sax player Tommy Smith and featuring the great Brian Kellock on piano, the band performed music from their acclaimed In The Spirit of Duke released earlier this year. The recording not only features some of the greatest music written in the last century but also captures the Ellington Orchestra sound down to the tiniest detail.

Distinguished jazz guitarists Philip Catherine and John Etheridge made (a little bit of) history at The Vortex last night, playing together for the first time. In a perfect balance of youth and experience, the evening also saw the launch of a debut album, Road Story, by the Igor Gehenot Trio (like Catherine, recorded by Brussels-based Igloo Records), with original compositions by the precocious 23 year-old pianist Gehenot. The evening was masterminded by Igloo and The Vortex; both deserve credit for an enterprising and worthwhile venture. 

Even Joni Mitchell wasn’t spared an affectionate ribbing, as jazz singer Ian Shaw continued his Joni at 70 Tour with a combination of sincerity and satire, both red-raw, in the Elgar Room last night. Stripping pretensions compulsively, Shaw gave an engrossingly witty performance of the work of the great singer once known, we learnt, as “Moany Mitchell” in the young Shaw’s household.

For someone who has built a reputation for limpid, introspective piano playing, last night was a new adventure both for Brad Mehldau and his (mainly) supportive audience. He has covered fellow introvert Nick Drake’s songs, and he is a master of thoughtful, expressive piano. So when we hear he's doing a show that references drum ’n’ bass and 1970s funk in a duo with a drummer with synths and Fender Rhodes, a certain apprehension is in order. It could have been like all those opera singers who suddenly discover jazz and usually make a complete hash of it.

With the bell of his Dizzy Gillespie-style “bent” trumpet pointing skywards like a rocket launcher, Scott dominated the stage at Ronnie Scott’s last night, every bit the iconic jazz trumpeter. Instead of the clearly-articulated, pure-toned pulse of a Louis or a Dizzy, Scott’s trumpet voice is smudgy, occasionally even grimy, with chromatic bursts of notes, played so fast you can’t always hear the join.

What does a stuffed penguin have in common with the religious concept of transcendence?  Even less than you might think, it emerged last night, during one of the London Jazz Festival’s less well matched programmes, featuring one trio named after each item. Gogo Penguin, an amiable and talented group, were outgunned by the intellectually and spiritually sensational vision of New York drummer Jaimeo Brown’s improvised setting of sampled spirituals from Gee’s Bend, Alabama, the Manchester band’s light-heartedness in danger of seeming simply lightweight.  

Last night’s Konitz and Wheeler concert was the sort of event at which the audience’s jaw has dropped before the music starts. Lee Konitz and Kenny Wheeler already have substantial legacies: Konitz’s cool sax style was a landmark sound, for decades the only serious alternative to Parker’s bop; his huge discography, varied in style but pretty uniform in quality, is a testament to his enduring commitment to experiment.

Wayne Shorter’s Quartet were introduced as “the greatest jazz band on the planet”. It’s an unexceptional thing, like the Rolling Stones being introduced as “the greatest rock’n’roll band in the world”. But unlike the Stones, who really haven’t done anything new or vital since the 1970s, Wayne Shorter and his cohorts, pianist Damielo Perez, bassist John Patitucci and drummer Brian Blade, who have been with him for a decade or so, have relentlessly magicked wonderful new music out of the air. Now 80, he doesn’t seem to be running out of steam just yet.

Five minutes into this concert, at that stage a polite cello and piano duo, there was a raucous bellowing from the rear, so loud that the front stalls leapt. The delicate cello spiccato continued, despite the persistent bellowing. Gradually, the musicians adapted to the new sound, and to widespread astonishment, Senegalese singer Mola Sylla, chanting in Wolof, descended through the stalls onto the stage.