A good co-speech motion generation cannot be achieved without a careful integration of common rhythmic motion and rare yet essential semantic motion. In this work, we propose SemTalk for holistic co-speech motion generation with frame-level semantic emphasis. Our key insight is to separately learn base motions and sparse motions, and then adaptively fuse them. In particular, coarse2fine crossattention module and rhythmic consistency learning are explored to establish rhythm-related base motion, ensuring a coherent foundation that synchronizes gestures with the speech rhythm. Subsequently, semantic emphasis learning is designed to generate semantic-aware sparse motion, focusing on frame-level semantic cues. Finally, to integrate sparse motion into the base motion and generate semantic-emphasized co-speech gestures, we further leverage a learned semantic score for adaptive synthesis. Qualitative and quantitative comparisons on two public datasets demonstrate that our method outperforms the state-of-the-art, delivering high-quality co-speech motion with enhanced semantic richness over a stable base motion.