Extensive studies have been conducted on both musical scores and audio tracks of western classical music with the finality of learning and detecting the key in which a particular piece of music was played. Both the Bayesian Approach and modern unsupervised learning via latent Dirichlet allocation have been used for such learning tasks. In this research work, we venture out of the western classical genre and embrace and explore jazz music. We consider the musical score sheets and audio tracks of some of the giants of jazz like Duke Ellington, Miles Davis, John Coltrane, Dizzy Gillespie, Wes Montgomery, Charlie Parker, Sonny Rollins, Louis Armstrong, Gil Evans, Bill Evans, Dave Brubeck, Thelonious Monk. We specifically employ Bayesian techniques and modern topic modeling methods and a combination of both to explore tasks such as: automatic improvisation detection, genre identification, key learning (how many keys do the giants of jazz tended to play in, and what are those keys) and even elements of the mood of the piece.