In this paper, we propose a sound abstraction for an efficient static analysis of synchronous programs describing multi-clock embedded systems in Signal. This abstraction combines the Boolean theory and numeric interval approximation to adequately address clock relations defined as combinations of logical and numerical expressions. Through a few examples, we show how the proposed solution is used to determine absence of reaction captured by empty clocks; mutual exclusion captured by two or more clocks whose associated signals never occur at the same time; or hierarchical control of component activations via clock inclusion. We also show this analysis improves the quality of the code generated automatically by the Signal compiler, e.g., a code with smaller footprint, or a code executed more efficiently thanks to optimizations enabled by the new abstraction.