This paper describes a system developed to create computer based jazz improvisation solos. The generation of the improvisation material uses interactive evolution, based on a dual genetic representation: a basic melody line representation, with energy constraints (“rubber band”) and a hierarchic structure of operators that processes the various parts of this basic melody. To be able to listen to and evaluate the result in a fair way, the computer generated solos have been imported into a musical environment to form a complete jazz composition. The focus of this paper is on the data representations developed for this specific type of music. This is the first published part of an ongoing research project in generative jazz, based on probabilistic and evolutionary strategies.