用图结构统一建模音乐层次，生成代表整个乐曲集的结构中心。
Synthesizing Composite Hierarchical Structure from Symbolic Music Corpora
- 构建结构时间图（STG），以图形式表达音乐从旋律到整体结构的多层级关系。
- 通过模拟退火与SMT求解器结合，找到乐曲集合的结构代表性中心图。
- 适用于音乐分析、自动作曲与跨作品结构比较，适合音乐信息检索研究者。
西方音乐是一种内在的多层级结构系统，涵盖从细微旋律到宏观形式的多个层次。为实现对音乐作品在多粒度下的整体分析，我们提出一种统一的分层元表示方法——结构时间图（STG）。STG 是单首作品的数据结构，定义了逐级细化的音乐特征及其时间关系。基于此，我们提出一种新的方法来生成音乐语料库的结构摘要，该问题被形式化为扩展的广义中位图问题，属于嵌套的NP难组合优化问题。方法首先使用模拟退火，基于图同构建立两首乐曲间的结构距离度量；随后结合SMT求解器的形式化保证与嵌套模拟退火，生成整个语料库中各作品STG的结构合理代表中心图。实验验证了结构距离能有效区分不同乐曲，且生成的中心图能准确刻画对应语料库的结构特征。
原文摘要 · Abstract (English)
Western music is an innately hierarchical system of interacting levels of structure, from fine-grained melody to high-level form. In order to analyze music compositions holistically and at multiple granularities, we propose a unified, hierarchical meta-representation of musical structure called the structural temporal graph (STG). For a single piece, the STG is a data structure that defines a hierarchy of progressively finer structural musical features and the temporal relationships between them. We use the STG to enable a novel approach for deriving a representative structural summary of a music corpus, which we formalize as a nested NP-hard combinatorial optimization problem extending the Generalized Median Graph problem. Our approach first applies simulated annealing to develop a measure of structural distance between two music pieces rooted in graph isomorphism. Our approach then combines the formal guarantees of SMT solvers with nested simulated annealing over structural distances to produce a structurally sound, representative centroid STG for an entire corpus of STGs from individual pieces. To evaluate our approach, we conduct experiments verifying that structural distance accurately differentiates between music pieces, and that derived centroids accurately structurally characterize their corpora.
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