Coming to the stage are three young men in T-shirts and jeans, no different from nearly any other band in nearly any other venue. Crushed up against the stage are a packed crowd of artfully dishevelled teens and 20-somethings, with a smattering of aging hipsters sprinkled in. But on stage are the tools not of a DJ performance or a punk band, but the bass, drums and keyboards many would associate with a performance in a hotel lounge.

Wordlessly, the trio begin playing — groovy, lyric-less, swinging but not necessarily "jazzy" in a traditional sense. Instead, tunes like a piano-led cover of Waka Flocka Flame's "Hard in Da Paint" are presented in a fluid blend of post-rock, hip-hop and dance music. Four-bar loops are extended by improvisation, but this is no paint-by-chord-changes cocktail jazz take on a rap song — instead, the performance takes off, fuelled by the crowd's voracious enthusiasm, lighting the room on fire. The pogoing, shoving, dancing, heaving crowd only intensifies its reaction as keyboardist Matt Tavares, bassist Chester Hansen and drummer Alex Sowinski piledrive through frenzied takes on material that ranges from post-dubstep producer James Blake to shoegaze pioneers My Bloody Valentine. When they get to one of their signature covers, a take on Kanye West's "Flashing Lights" that owes more to progressive rock than it does to Hot 97, the crowd explodes.

This is likely the first time in a half-dozen decades that a jazz trio has inspired this kind of reaction. This is BADBADNOTGOOD.

To get here requires attitude and gumption. This moment — this seemingly instant burst of success into the world of hip-hop production — was prompted by an utter rejection of jazz education by a trio of keeners who'd pursued that very field, and in whose rejection one finds the spirit of jazz anew.

Jazz, since its early 20th century heyday, has codified the contributions of its pioneers, mostly from 1940s to the late 1960s, from Charlie Parker through John Coltrane and Miles Davis. Those innovators would take popular songs of the time — "My Favorite Things," for example, from the Rodgers and Hammerstein's The Sound of Music or the work of pop craftsman Cole Porter — and improvise around their foundational chords and melody. These interpretations were popular at the time because they supplied a new take on familiar hits of the day. But in the years since the 1960s, as this period of jazz has been entrenched in the minds of music historians, so too have these songs solidified into a canon of jazz itself.

When Tavares, Hansen and Sowinski enrolled in Toronto's Humber College jazz program, they quickly found themselves back in Charlie Parker's time, learning charts for the nuggets of his era, like "Stella By Starlight." However, in their spare time, they weren't poring over whose take on "Autumn Leaves" was most interesting — the trio instead bonded over a mutual love of Odd Future and MF Doom, the "standards" of today in their minds.

"The spirit of jazz should be creative and trying to push the boundaries and express yourself," Hansen offers. "Taking hip-hop seriously as a genre is something that a lot of musicians don't actually do." As part of a jazz performance assignment for school, the trio offered up a medley of Odd Future covers. Their educators found little to nothing of musical value in it.

Undeterred, they recorded a video of themselves performing that same jazz-influenced Odd Future medley, including drummer Sowinski hidden behind a David Lynchian pig mask. Calling themselves the Odd Trio, they posted it to YouTube and hits started to pile up in the thousands. That is, until chief Odd Future spokesman Tyler, the Creator took notice a few months later and tweeted a link to the video, dubbing it "sick." With the weight of his millions of followers behind them, the Odd Trio became BADBADNOTGOOD. They played their first show ever at a small bar in downtown Toronto in September 2011; it was jam-packed.

It's difficult to imagine the speed with which everything started moving. Within a few weeks of that first show, Tyler, the Creator was in the basement of Alex Sowinski's dad's house — these old princes still lived at home — laying down three songs with the trio as his backing band. The resulting videos quickly passed the million-views mark. Odd Future associate Frank Ocean hired the trio to perform as his backing band at Coachella 2012. Their live performances — which quickly started to include other hip-hop covers as well as songs by groove-oriented producers like Flying Lotus and TNGHT (Hudson Mohawke and Lunice) — started to resemble those of punk rock pioneers more than staid, chin-stroking jazzers.

With new success came new headaches, as the group had to find a new practice space after colourful noise complaints from Sowinski's dad's neighbours. BADBADNOTGOOD ended up sharing a studio space with III producer Frank Dukes, who co-produces many of the band's beats as well.

Keen to expand their sound via studio recordings, BBNG eschewed label offers for their first two full-length recordings, dubbed BBNG and BBNG2, instead posting them on their Bandcamp page. Content on the two full-lengths was split between covers of hip-hop (Slum Village, Nas), electronic (Flying Lotus, James Blake) and a handful of originals.

It was initially difficult to transition into their own compositions, Chester Hansen confesses. "It's always hard, because people are always going to be like 'play "Flashing Lights"!' because that's the stuff they know and they've heard us do most often."

Alex Sowinski offers a secret that has unlocked BADBADNOTGOOD's creative process moving forward. To make the originals go over well is, he says, "playing them with the same intensity, flavour and confidence that we would play a cover."

It's spring 2014, and on the eve of releasing their first proper, commercially released album, III, the members of BADBADNOTGOOD are being model hosts, offering beer and udon as well as memories of recent excursions. "It was insane," Matt Tavares offers, about a recent show at Los Angeles EDM hotspot Low End Theory — ground zero to beat music trendsetters like Flying Lotus. "It was so much fun." According to Sowinksi, esteemed DJ Gaslamp Killer screamed through their entire set.

Heroes in the audience have become a little old hat — they met De La Soul in L.A. too, after the legendary hip-hop trio recently caught BBNG's set at South By Southwest. Blur's Damon Albarn was also at their L.A. album preview, just one of the "cool ass people" Sowinski says were gathered.

Since giving away their first two albums — because, as Hansen says, "it gets out to the most people" — BBNG have become in-demand producers in their own right, crafting beats for Odd Future's Earl Sweatshirt as well as Danny Brown and the Wu-Tang Clan. Yet it's in full-length albums and original compositions that their hearts currently lie.

BADBADNOTGOOD have spent the past year and a half between tour dates, laying down III in Revolution Recording (where BBNG2 was recorded) and the band's own studio. Their first few releases were recorded piecemeal between shows and on the road on digital workstations, but this is the first time they've dedicated time to recording. Given that BADBADNOTGOOD's success started online, their choice to record III to tape is especially intriguing. However, it's not as surprising as it initially appears. "We've always wanted to get fucking old drum sounds, reference drum breaks and [think], 'How do you get that ill bass tone?'," says Sowinski. "Let's make this all analog and sound like an old record, but it's not going to feel like an old record because it'll have that young, new mentality."

Tavares chimes in, suggesting they chose analog "not because it sounds old, but it just sounds better to us."

The group have always been inspired by old recordings, including jazz and psychedelia. But for the first time, they wanted to make the breadth of their influences more explicit, beyond their choices of covers — a pre-album SoundCloud mix detailing III's inspirations runs from prog rock, John Coltrane and Serge Gainsbourg to 2 Chainz. They were trying to decide on the right musical direction. "We don't really have a cohesive sound in terms of what we do. [Our] first thing was these smooth '90s covers," Sowinski says, laughing. "It was about what was fresh to us and incorporating some cool influences between synth tones and drum sounds and performances."

The songwriting process posed a challenge for an act known for its covers. Hansen admits that it "takes a long time to form songs." III didn't start out completely original when they began writing the first song. Hansen adds that as the group "just kept jamming more, writing more and more ideas and getting stuff together. It just ended up as all original. The songs definitely evolved a lot over time. [We] went through a million different versions and demos." Tavares suggests the process took upwards of 300 iPhone demos to get the right takes.

Out May 6, III finds the band melding the cocoa butter-smooth grooves of their previous records to more experimental electronic textures. They dig more into psychedelic, prog and Krautrock sounds, experimenting with 808s and vintage synths while retaining the hip-hop influences that marked their first two albums. Though BADBADNOTGOOD have always shown chemistry, here they demonstrate an almost telepathic interplay. Where prior songs approximated the structure of instrumental hip-hop with jazz flourishes, III showcases more nuanced arrangements and a greater diversity of sounds.

BADBADNOTGOOD have occasionally been misrepresented in the press as new-jacks wilfully flipping the bird at jazz institutions. However, the band members are reverent when extolling the virtues of Coltrane or Bill Evans. III's "Differently, Still" is essentially a jazz ballad in post-bop mode, which Sowinski explains as a tribute to "the trio-style playing of [Evans'] era. Those recordings, those musicians of that era together is to us some of the most interactive, cohesive, vibed-out, amazing, beautiful lines and connectivity between people playing. We wanted to emulate something similar. We're not on that level by any means, but that was kind of the idea with that song."

Even given that respect, and the success they've achieved, Tavares remains sceptical that their former Humber College professors would be impressed, but doesn't see it as a problem. "I don't think this record will convince anyone from the jazz establishment who was hesitant, because it really isn't jazzy at all. It doesn't have the aspects that people who are into jazz like," he says.

And while Hansen, Sowinski and Tavares don't see the trio's music becoming standards like the songs they were forced to learn at Humber, Hansen says BADBADNOTGOOD sheet music is definitely in the works.

It's not that they feel their material is so great. Sowinski elaborates: "It's more just to help people who aspire to learn songs. Sometimes it's nice to have some fresh chord changes to read, something to practice on. It's just not available yet."