Generating music that temporally aligns with video events is challenging for existing text-to-music models, which lack fine-grained temporal control. We introduce V2M-ZERO, a video-to-music generation approach that generates time-aligned music with disentangled time synchronization and semantic control (e.g., genre, mood) from video while requiring zero video-music pairs at training time. Our method is motivated by a key observation: temporal synchronization requires matching when and how much change occurs, not what changes. While musical and visual events differ semantically, they exhibit shared temporal structure that can be captured independently within each modality. We capture this structure through event curves computed from intra-modal similarity using pretrained music and video encoders. By measuring temporal change within each modality independently, these curves provide comparable representations across modalities. This enables a simple training strategy: fine-tune a text-to-music model on music-event curves, then substitute video-event curves at inference without cross-modal training or paired data. Across OES-Pub, MovieGenBench-Music, and AIST++, V2M-ZERO achieves state-of-the-art performance without any paired music-video data, surpassing the strongest prior baselines per metric with 5-9% higher audio quality, 13-15% better semantic alignment, 21-52% improved temporal synchronization, and 28% higher beat alignment on dance videos. We find similar results via a large crowd-source subjective listening test. Our results validate that temporal alignment through within-modality features is not only effective for video-to-music generation but also leads to better performance than paired cross-modal supervision. Furthermore, our approach enables independent controls for timing and music style (e.g., genre, mood) for more controllable generation.