用滑动窗口分析德彪西音乐中的局部音高与时长变化，发现跨维度对齐能更好识别结构边界。
From local kernels to global form: modeling the emergence of musical content
- 用重叠滑窗从单个乐谱推导局部转移核，无需预设分段。
- 在L=6时，音高和时长的熵值均达最大，但音高平台更宽，体现结构敏感性。
- 适合关注音乐形式分析与生成模型的学者，尤其对非均匀马尔可夫建模感兴趣者。
马尔可夫模型是符号音乐的常用工具，包括非齐次形式。本文聚焦一种基于观测数据的估计机制：通过重叠滑动窗口从单一符号序列中提取局部转移核，而非依赖外部划分。我们在德彪西《西林克斯》（1913）的273个逻辑音符上测试该方法，以常被提出的A-B-A'结构为参考而非真实标签。对绝对音高与记谱时长核分别进行验证。当窗口长度L=6时，两个维度的参考边界均达到詹森-申肖尔熵最大值；时长平台仅覆盖267次比较中的64次，远窄于音高的210次。理论上，连续滑窗比较的最大值由窗口几何决定，为1/√(L−1)，故音高在L=6时的宽平台本身不足以构成强证据。但跨维度对齐现象与结构敏感性一致，而宽平台也表明任一维度单独无法作为唯一自动分段依据。500次重合成实验量化了与源序列的偏离程度，并揭示在L=2时存在精确复制退化现象。
原文摘要 · Abstract (English)
Markov models are established tools for symbolic music, including non-homogeneous formulations. The narrower contribution examined here is an observation-driven estimation mechanism: overlapping sliding windows derive a trajectory of local transition kernels from one symbolic sequence rather than from an exogenous formal partition. We test this mechanism on 273 logical note events from Debussy's Syrinx (1913), using the often-proposed A-B-A' reading as a reference rather than ground truth. We apply the same validation to absolute-pitch and notated-duration kernels. At $L=6$, both reference boundaries attain the Jensen--Shannon maximum in both dimensions; the duration plateau is substantially narrower (64 of 267 comparisons) than the pitch plateau (210 of 267). Because the theoretical maximum for consecutive sliding-window comparisons is set by window geometry and equals $1/\sqrt{L-1}$ for maximal turnover of the entering/leaving transition, the pitch value at $L=6$ and its broad plateau are not, by themselves, strong evidence. Their cross-dimensional alignment is consistent with boundary sensitivity, while the broad plateaus preclude treating either curve alone as a unique automatic segmenter. Five-hundred-draw re-synthesis experiments quantify departure from the source in both dimensions and expose an exact-copy degeneracy at $L=2$.
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