It’s about time someone recognized the timeless quality of King Crimson’s music and its relationship to cutting-edge jazz. The seminal progressive rock band of the late 1960s continues to record and perform under the leadership of founder-guitarist Robert Fripp (2003’s “The Power to Believe” is the latest studio release) and remains a viable contributor to mature, contemporary music. Of whom else can this be said?

With its recording debut, the Crimson Jazz Trio pays long-overdue tribute to the sophisticated sounds of the band that introduced “21^st Century Schizoid Man” in 1969! It is fitting that the trio opens the recording with its own jazzy rendition of this classic.

Pianist Jody Nardone, bassist Tim Landers and drummer Ian Wallace are more than equal to the task, reinventing all the tunes here in their own style, without sacrificing any of the urgency, audacity, astonishing technique and twisted wit of the originals. Nardone’s lushly harmonized chord progressions and straight-ahead bop lines set the standard for Landers’ fluid and thunderous fretless bass ruminations and Wallace’s stately, colorful and pungent percussion.

Landers’ playing is especially lyrical on “Three of a Perfect Pair,” from the 1984 release of the same name. The intensity grows as his booming lead statement is followed by a pounding piano excursion, aided and abetted by Wallace. “Catfood” is a quirky blues number from KC’s second release, 1970’s “In the Wake of Poseidon.” The canine vocalizing of “Hagi the dog” adds the appropriate comedic touch.

From 1974 comes “Starless,” a melodic gem that is given a gorgeous 10½-minute treatment here. “Ladies of the Road” is a swinging little number from the 1971 release “Islands.” Nardone and the others really work out on this one. The trio slows down again for the ballad “I Talk to the Wind,” also from “Poseidon” and perhaps the most beautiful melody in the entire KC songbook.

“Red” is an edgy, off-kilter 1974 tune that sends the trio into hyper-drive in a dazzling technical display. The closer is “Matte Kudasai,” a lovely Adrian Belew composition from KC’s 1981 release “Discipline.” Its exotic beauty is heightened by Landers in a soaring bass solo and by Nardone in a romantically lush piano solo, reminiscent of Keith Jarrett’s yearning sound. Wallace keeps impeccable time and adds powerful accents on the cymbals.

After listening to “King Crimson Songbook, Vol. 1,” King Crimson fans—and jazz fans—can only ask, “When can we expect volume two?”