Melody skeleton extraction aims to derive a shorter melody that preserves structural notes while removing ornaments. Prior methods rely on hand-crafted reduction rules or note-wise salience classifiers trained with heuristically or procedurally generated pseudo-labels. Such supervision can inherit generator bias and does not explicitly optimize a coherent reduced melody. We introduce MeloBottleneck, a self-supervised framework that represents a skeleton as a length-controlled, order-preserving latent subsequence. A hard-bottleneck extractor selects note events, a rhythmic-closure operator produces a self-consistent skeleton, and a re-ornamentation decoder reconstructs the input melody. Training combines reconstruction, a frozen autoregressive melody prior, ornament-invariant consistency across procedurally ornamented views, and ornament exclusion. We evaluate three regimes: synthetic out-of-distribution ornament-to-skeleton, TAVERN variation-to-theme, and Jiugong ornamented-to-gongche. A matched pseudo-label classifier excels on the synthetic benchmark, while MeloBottleneck transfers better, achieving competitive selection quality on TAVERN and Jiugong. Skeletonized melodies also improve BM25-based fragment retrieval, boosting Recall@K and MRR while reducing query time. Overall, the results suggest that learning skeletons as latent subsequences yields more robust transfer than pseudo-label imitation.

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