In 1972, the first man-made spacecraft left our Solar System. The Pioneer 10 probe could detect and record solar wind particles, magnetic fields, and UV light, but it also had a message to deliver. Mounted on the craft was a plaque, designed by NASA with help from Carl Sagan, with the graven image of a man, a woman, and symbols depicting planet Earth. It was the simplest of summaries: look, this is who we are.

If Sagan had added the Allman Brothers Band’s album Eat a Peach, which was released one month earlier, we probably would have heard back from some aliens by now. I doubt that a single jam band can encapsulate everything the human race is all about, but that’s album’s 34-minute centerpiece song, “Mountain Jam,” is as grand, spacey, strange, and brimming with humanity as anything our species has crafted so far.

The Allman Brothers Band and The Grateful Dead paved the way, of course, for future jam bands. Over the decades, mediocre acts have given us thousands of hours of less-than-catchy guitar noodling, which dissipates without leaving a trace. But TAUK is not one of those bands. In fact, the next time we send a probe into space, I propose we strap TAUK’s new live album Headroom to the front of the ship.

There’s nothing wimpy or ethereal about TAUK, a tirelessly touring group from Oyster Bay, New York, that describes itself as a “heavy instrumental rock-fusion onslaught,” playing genres “as diverse as gritty funk, fusion, hip-hop, progressive rock, ambient, classic rock, and jazz.”

That’s a tall order for four musicians. But Matt Jalbert (guitar), Charlie Dolan (bass), A.C. Carter (keyboards and organ), and Isaac Teel (drums) have spent years beefing up their sound and fine-tuning their stage presence. Their songs — many of them long; all of them without vocals — explode with melody, fit for dance-floor raves and bedroom headphone hangouts. Teel’s drumming is playful and intense, Jalbert’s great guitar solos are piercing and lush, and Dolan’s bass lines paint with a broad swatch of bright colors.

These days, fan followings for really, truly great jam bands like Consider the Source, Sound Tribe Sector 9, Lotus, and Papadosio speak for themselves. On the festival circuit, TAUK has built up a reputation for high-energy, captivating live shows, so it’s a bit of a surprise that their fourth LP Headroom is their first live album. Mixed by five-time Grammy winner Robert Carranza (The Mars Volta, Ozomatli, Jack Johnson, Taj Mahal), Headroom is a monster of a double-disc package: two hours long with 16 tracks, the shortest of which is five minutes long. Talk about making up for lost time.

Such a huge canvas gives this quartet plenty of room to wax experimental while returning, again and again, to catchy funk beats and joyous, head-banging grooves. And with no singing or lyrics, listeners can find their own free-wheeling stories and images in the wall of sound.

Dolan has said that the band listens to everything from Phish and Frank Zappa to Jimi Hendrix and Miles Davis. And they do seem to find great fun in slapping down the barriers between genres, letting labels bleed away until there’s just the beat, the tension build, and yet another moment to introduce something new into the mix.

TAUK plays Pearl Street in Northampton, with special guests Mammal Dap, on Friday, March 4. Headroom is available for digital download on the iTunes store and at•

— Hunter Styles,