A previously implemented realtime algorithmic composition system with live coding interface had rhythm functions which produced stylistically limited output and lacked flexibility. Through a cleaner separation between the generation of base rhythmic figures and the generation of variations at various rhythmic densities, flexibility was gained. These functions were generalized to make a greater variety of output possible. As examples, L-systems were implemented, as well as the use of ratios for generating variations at different rhythmic densities. This increased flexibility should enable the use of various standard algorithimic composition techniques and the development of new ones.