As a saxophonist, keyboard player, composer, arranger, bandleader, producer, engineer and entrepreneur, Oliver Sain has worked with, influenced and mentored literally hundreds of musicians over the years. The Mississippi native who came to St. Louis in the 1950s has written and produced hit records for others, had his own work sampled by the hip-hop generation and recorded genres from gospel to avant-garde jazz to punk rock as well as tons of blues, R&B and soul artists at his Archway Studios. The broad outline of Sain's career suggests that he's perhaps a sort of St. Louis equivalent of Memphis' Willie Mitchell, who cut instrumental albums as a leader and produced hits for Al Green and others. But perhaps the most remarkable thing about Oliver Sain, now in his 70s, is that St. Louis listeners can hear him perform pretty much every week of the year (recent health problems notwithstanding) for a modest cover charge and the price of a couple of drinks. Sain appears Thursdays at BB's Jazz, Blues & Soups (700 S. Broadway in St. Louis; 314-436-5222). With a capable rhythm section, Sain's distinctive sax and organ playing, and guest vocalists such as Marsha Evans and Renée Smith, his regular weekly gigs offer music fans a living history lesson and a big bang for the buck.