Guitarist Jeff Parker is both a key contributor to Tortoise’s shape-shifting, coloristic avant-rock and a thoughtful jazz improviser, most notably in the Chicago Underground collective. The Relatives (Thrill Jockey), his second solo album, marks the first time he’s truly merged those two approaches. For his 2003 solo debut, Like-Coping, Parker led a trio, but here he’s added New York keyboardist Sam Barsheshet, whose Fender Rhodes and Wurlitzer electric piano give the music some springy depth and more harmonic refractions. The group now veers more often from its usual eloquent swing, and operates more like a rock band than a jazz outfit: it embraces overdubs, trance-inducing repetition, and texture-making as a collective endeavor. Like-Coping was filled with extensive solos, but here the players–who include bassist Chris Lopes and drummer Chad Taylor–step out more judiciously. On Taylor’s gorgeous ballad “Istanbul,” Parker plays calm, fluid sixteenth-note flourishes; elsewhere on the track the other members tinker with the groove, drop in and out, and overdub subtle layers like Lopes’s spare acoustic guitar lines. Parker continues to fuss with compositional structures: the opening line of “Mannerisms,” which sounds remarkably similar to that of “Day Tripper,” sets up a slinky groove that Parker embellishes, but the real emphasis is on the shifts in key, and on “The Relative” the band ever so slightly alters the tempo of its fixed grooves to, in Parker’s words, “aurally capture” how movement alters our perception of space. Despite the technical complexity of its music, the album makes for deeply pleasurable listening. This is one of only two U.S. gigs with the album’s lineup. Wed 2/9, 9:30 PM, Empty Bottle, 1035 N. Western, 773-276-3600 or 800-594-8499, $8.