Genetic algorithms (GAs) have successfully been employed in a wide range of artificial intelligence problems. This paper reviews the use of GAs in the area of art creativity and focuses on the connection between the human creativity procedure and the operators of selection-mutation-crossover in a simple GA trying to outline a new algorithmic analogue. It presents "Jazz Sebastian Bach", a novel GA-based computational music system that performs a style modification of a J. S. Bach theme to a Jazz melody. The system's sources of innovation are addressed and exemplified, as is an evaluation of its outputs. The paper concludes with a summary of the main findings and discusses the potential application of the system in the areas of computer-assisted composition and music education.