Ethan Iverson (piano), Reid Anderson (bass) and Dave King (drums), aka The Bad Plus, appear in Seattle with Joshua Redman June 18-21.

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The Bad Plus — pictured from left, Dave King (drums), Ethan Iverson (piano) and Reid Anderson (bass) — has always done things its own way, mixing jazz, rock and classical music into unusual swirls, both intimate and grand. So it shouldn’t come as a surprise that an invitation to saxophonist Joshua Redman (right) to join the popular, 15-year-old trio on record and on tour hasn’t produced the stock scenario of a virtuoso tenor sax cracking the whip over a swinging piano trio.

To the contrary, on the new album, “The Bad Plus Joshua Redman,” two-time Grammy nominee Redman slides into the trio’s odd milieu as if he’d been just waiting for a chance to blend in. Redman’s especially effective on King’s slow, secret-sounding “Beauty Has It Hard,” as his sax glides down an unexpected scale into a pool of piano, or waxing free with an explosive King on Iverson’s speedy “County Seat.”

The quartet’s vibe ranges from controlled and arranged minimalist loops with hitches in the rhythm to expansive declamations out of 19th-century piano repertoire (which today feels more like movie music).

Redman and The Bad Plus perform at 7:30 p.m. Thursday-Sunday, June 18-21, with a 9:30 p.m. set Friday and Saturday, June 19-20, at Dimitriou’s Jazz Alley, 2033 Sixth Ave., Seattle; $34.50 (206-441-9729 or jazzalley.com).