James Allen in [All2] formulated a calculus of convex time intervals, which is being applied to commonsense reasoning by Allen, Pat Hayes, Henry Kautz and others [AllKau, AllHay]. For many purposes in AI, we need more general time intervals. We present a taxonomy of important binary relations between intervals which are unions of convex intervals, and we provide examples of these relations applied to the description of tasks and events. These relations appear to be necessary for such description. Finally, we provide logical definitions of a taxonomy of general binary relations between non-convex intervals.