Music creation is fundamentally a process of revision. Yet symbolic music generation remains dominated by paradigms that produce complete sequences from scratch, with limited support for selective modification. Edit-based methods have proven effective for text transformation tasks, but remain largely unexplored for symbolic music. We trace this absence to the representational level: conventional event-based music encodings lack the structural properties required by explicit music editing. In contrast, the BEAT encoding, a beat-grid-anchored representation originally designed for autoregressive generation, possesses structural properties amenable to editing. We propose BeatEdit, the first framework for symbolic music generation based on explicit edit operations, recasting generation as producing new content by editing a draft rather than synthesizing from scratch. BeatEdit comprises three complementary mechanisms along an axis of increasing edit density: per-token sequence tagging for error correction, iterative refinement for accompaniment editing, and tag-then-fill for segment completion. All these mechanisms share a single encoding and pre-trained backbone, achieving higher precision and perceptual quality than autoregressive and diffusion methods across all three tasks, while remaining efficient, with single-pass inference completing in under 100 ms. Cross-encoding evaluation further reveals that encoding design substantially influences editing effectiveness, with notable encoding-method interaction effects. Code is available at https://github.com/Haoyu-Gu/BeatEdit-code

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