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This is an uncommonly good week for jazz, especially over the weekend. In instances like these, where it’s especially difficult to choose between two or more conflicting gigs, Setlist makes use of an innovative policy: a coin toss. Here we go.

Thursday, February 26
February just wasn’t busy enough for Paul Carr. The reigning Best Tenor Saxophonist is the producer of the Mid Atlantic Jazz Festival and heads up the Jazz Academy of Music and leads its orchestra. But just to show you what a trooper he is, Carr went and booked himself a quartet gig at Thursday night’s Dukem Jazz festivities. The straightahead sax man par excellence has assembled a splendid band to do it with: bassist Michael Bowie, another incumbent Jazzies winner; guitarist Donato Soviero; and drummer Lenny Robinson, fresh off his month-long February residency at Bohemian Caverns. It’s a powerful combination, and they won’t be alone: By tradition, the second set at Dukem turns into a jam session, so you yourself might get a chance to join this crackerjack ensemble for a tune or two. They perform at 9 p.m. at Dukem, 1118 U Street NW. Free.

Saturday, February 28
What’s the best thing about Dix Out: the band’s name or its description, “an avant-trad band”? Avant and trad, together! George Lewis meets George Lewis! Roswell Rudd meets Roswell Rudd! Or perhaps, in this case, Jimmy Giuffre—-a multi-reedist with avant-garde leanings, and one of the major inspirations of Dix Out’s leader Brad Linde—-meets Fats Waller. Waller, one of the founding fathers of what we now call the jazz repertoire, is having himself a bit of a renaissance lately, thanks to a major project by pianist/Kennedy Center artistic director for jazz Jason Moran. Now it’s Dix Out’s turn, with Linde joined by banjoist and electronics man Aaron Quinn, tubist Liz Prince, drummer/percussionist Deric Dickens, and trombonist Nicole Connelly. Fittingly, it’s part of the Atlas Intersections Festival. It takes place at 9:30 p.m. at Atlas Performing Arts Center, 1333 H Street NE. $11-$16.

Sunday, March 1
Bethesda Blues & Jazz opened its doors to D.C. music lovers on March 1, 2013, and quickly settled in to become an important player in the local jazz community. It had already done so by the time of its grand opening gala that May, when a fellow named Branford Marsalis was on hand to headline (with his quartet) that ribbon-cutting. So it’s nice, and apropos, to see him back for the second anniversary of the venue’s de facto opening. And once again, Marsalis’ quartet is behind him: pianist Joey Calderazzo, bassist Eric Revis, and drummer Justin Faulkner. There are, perhaps, some who will be disappointed that it’s not a solo gig, in support of Marsalis’ most recent recording In My Solitude: Live at Grace Cathedral. But if you are among the disappointed—-well, look again at that quartet lineup. Besides, who’s to say that their presence prohibits Marsalis from doing a solo number or two? The quartet performs at 3 and 7:30 p.m. at Bethesda Blues & Jazz, 7719 Wisconsin Avenue in Bethesda. $36-$90.

Tuesday, March 3
He doesn’t even have to be leading the band to be its guiding factor. When Howard “Kingfish” Franklin is behind the drum kit, you can be certain of two things: first, that the very sound of the drums is going to pull your ears toward them all night long, and second, that the rhythms within them will do the same not just for you but for the other musicians. Fish is a drummer of precision, of technical facility, so when he pushes up to the front of the beat (as he frequently does) you know he means it. And the effect is immediate, turning the groove immediately up to 12 and recalibrating the other players’ relationship to it. But note that remark about the sound of the drums, as well; Franklin knows more than a little bit about the resonance built into his traps, so that even the tautness of the snare takes on a certain thickness, and his bombs and change-ups of syncopation have serious juice. So you can imagine how exciting it gets when Franklin is leading the band—-but you don’t have to imagine. He is the March artist in residence at the Caverns, and he starts it off with a quintet (trumpeter Donvonte McCoy, tenor saxophonist B.J. Simmons, pianist Todd Simon, bassist James King). They hit at 7:30 p.m. at Bohemian Caverns, 2001 Eleventh Street NW. $10.