People tend to forget about Nat Adderley, and they shouln’t. In this age of studious kid virtuosos, there are plenty of hornmen who can outrun Adderley in pure technique; few of them, though, can match the sturdy construct of his solos, or the happy mixture of his bright tone and musical ebullience–his shout. He played cornet alongside his late brother, the saxist Cannonball Adderley, for the better part of 20 years, during which time Cannonball’s white-hot brilliance often blinded listeners to his brother’s more modest (but stiff substantial) abilities. After Cannonball’s death in 1975, people tended to shelve their memories of both Adderleys, despite the fact that Nat continues to play well and write wonderful jazz tunes. (It was Nat who wrote two of the brothers’ most enduring hits, “Work Song” and “Jive Samba.”) You can expect to find several of those tunes–and the rest of the warm, potent Adderley ethos–this weekend, when Nat joins up with the Chicago quartet led by the superb altoist Mike Smith. Smith sports a voluptuous tone, imperturbable control, and silky glissandos, and he counts as his mentor and prime influence–you guessed it–Cannonball Adderley. (In fact, his 1990 Delmark album is a tribute to the Adderleys’ music.) Brother Nat will feel right at home. Tonight, 9 PM, and Saturday, 8 PM, Green Mill, 4802 N. Broadway; 878-5552.