Most music-generation systems are still framed and evaluated primarily as producers of complete outputs, whereas composition often proceeds through successive revisions to a shared musical artifact. This paper studies a different use of a general-purpose instruction-following large language model: not as a one-shot music generator, but as a reusable operator over an evolving symbolic score. We formulate incremental composition as a sequence of operation-aware state transitions over persistent ABC notation, with explicit requirements on what each operation may change and what it must preserve. The interaction includes two artifact-initialization variants and three editing operations -- chord addition, inpainting, and transposition. We instantiate the formulation by adapting Llama 3.1 8B Instruct with Low-Rank Adaptation (LoRA) on 496,038 operation-aware dialogue records derived from Irish traditional music. The comparison with the unadapted model is used to test the feasibility of learning this interaction contract, not to claim novelty for fine-tuning itself. Across 500 dialogues per model (1,750 attempted output states), checker admission rises from 29.37% to 99.37%, while compliance conditional on admission rises from 0.7205 to 0.9798. Strict eligibility for reference-relative musical-feature analysis increases from 14 to 1,548 outputs, and Longest Common Subsequence analysis does not show a systematic increase in high-overlap sequences relative to held-out baselines under the specified protocol. The results support the technical feasibility of persistent, operation-aware symbolic editing with a general-purpose instruction LLM. They do not establish superior musical quality or human-AI co-creativity, which remain questions for musician-centered evaluation.

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