Language models now generate symbolic music from text, and research has focused on musicality. However, many applications require a score that meets explicit constraints, which models struggle to satisfy jointly: on MusicConstraintBench, our benchmark of 2,180 items over eight families of programmatically verifiable constraints, Llama-3.1-70B satisfies 0.630 of single-constraint items but only 0.044 of four-constraint ones. As a remedy, we introduce MusicRLVR, which trains a language model with group relative policy optimisation (GRPO) on verifier rewards alone, needing no human annotation, reward model or music-domain supervised fine-tuning. MusicRLVR incorporates (1) a hard validation gate that rejects malformed scores, (2) graded per-family credit that, unlike a binary reward, separates partially correct outputs, and (3) an all-satisfied bonus for meeting every constraint at once. Extensive experiments show that, in under four hours of training, MusicRLVR raises Qwen3-4B-Instruct-2507 from 0.160 to 0.797 on mixed constraints, outperforming Llama-3.1-70B, and generalises to unseen property combinations, out-of-range parameters and more constraints than any training prompt. The recipe transfers to Qwen3-8B, and neither trained model loses significant accuracy on general benchmarks.

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