The Bad Plus have released a new album. Ring the church bells in the square, sing it from on high, rejoice both rich and poor alike: The Bad Plus have released a new album. If you haven’t heard of The Bad Plus, then first of all, I wouldn’t tell too many people, and second of all, you have got to buy their latest album “Prog.” Having stirred up quite a tizzy among blue-haired jazz conservatives about whether a “jazz” piano trio should be playing songs originally spawned by devil worshippers like Nirvana and Black Sabbath, The Bad Plus have plowed forward, releasing three stellar albums on Columbia. “Prog” finds them over on the Heads Up label, with legendary AC/DC producer Tony Platt manning the mixing board. The Bad Plus occupy a somewhat odd musical space. As authentic and sincere as they sound to young audiences, some critics have accused them of selling out, using more accessible pop repertoire as a cheap and easy way to connect with audiences. However, in an illuminating interview with NPR, pianist Ethan Iverson talked about covering “Smells Like Teen Spirit”: “When we played it in the club, I felt the sort of interaction with the audience that probably Miles Davis felt when he played ‘My Funny Valentine’ in the ’50s. In other words, a theme in the air at the time. When you play the Rodgers and Hart songbook that interaction really isn’t there anymore.” These guys aren’t sellouts and they don’t pander. If they really wanted to pander to a pop audience they wouldn’t bother covering tunes like “This Guy’s in Love With You” by Burt Bacharach. I mean, seriously, are they trying to corner the market on weak-kneed, swooning 55-year-old empty nested mothers who also happen to have a taste for aggressive avant-garde jazz? Actually, come to think of it, that’s the kind of ironic demographic marketing that might tickle drummer Dave King to the point of a silly fit. So we find them on “Prog” covering four pop tunes. There’s the opening wistful deconstruction of Tears for Fears’ “Everybody Wants to Rule the World.” Then, two tracks later, a revelatory meditation on David Bowie’s exultant “Life on Mars.” Later, it’s Rush’s “Tom Sawyer,” a strong-armed melody that they chop to bits with interspersed frenetic chatter. The next track is the aforementioned Bacharach tune. They treat this one remarkably simply and delicately. It’s not like they are out for blood, they aren’t deconstructionists just for the sake of deconstruction. They’re in it for the artistic insight. And if they come across a melody that provides all the insight they need, they have no problem just setting the melody up and getting very pretty with things. This is how most of bassist Reid Anderson’s compositions work. Two of his three contributions to this album, “Giant” and “The World Is the Same,” are fundamentally simple and elegant, poignant and beautiful. But it’s Anderson’s third contribution, “Physical Cities,” that sits as the centerpiece of this album. I asked a friend what I should write about “Prog” and he responded, “Just say ‘Physical Cities, duh.’ And leave it at that.” It’s tempting. The track concludes with an asymmetrical thudding rhythm in which, after about two straight minutes, the tension builds up to the point where King’s explosion into a freewheeling freak-out hits an unbelievably cathartic note. “Prog” showcases The Bad Plus as an even more mature, coherent, fun and courageous band than on their previous excellent releases. Check them out.