用于降低乐谱中和声复杂性的托内兹驱动图楔块
Tonnetz-Driven Graph Wedgelet for Harmonic Complexity Reduction in Music Scores
- University of Palermo（巴勒莫大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
研究如何降低乐谱和声复杂性，提出基于二元楔块划分树的压缩方案，通过完全自适应贪婪算法在六维托内兹嵌入中生成楔块，经实验验证该方法能有效简化乐谱并保留关键信息。
中文摘要 AI 辅助
基于音符、歌词音节和伴奏事件构建的异构图是符号乐谱的自然表示，为文献分析和计算任务提供了基础。音乐特征因此能被图几何及其属性很好地捕捉。这种表示已被证明对诸如节奏检测、声部分离和风格分类等分析任务有效。在本工作中，研究了通过保留任务相关信息、音符间关系和图结构来降低图上乐谱的和声复杂性。提出了一种基于二元楔块划分树的声乐钢琴乐谱钢琴子图压缩方案。楔块通过完全自适应贪婪算法生成，该算法在音符的六维托内兹嵌入中递归最小化\(L^2\)误差。划分过程采用基于和声距离的分裂准则，得到能准确反映音符间内在和声关系的区域。通过分段常数函数和每个楔块内音符的平均值得到的重构乐谱用作新的简化且可读可演奏的乐谱。对三位不同作曲家的符号音乐乐谱语料库进行了一些实验以评估该方法。
英文摘要
Heterogeneous graph built on notes, lyric syllables, and accompaniment events is a natural representation of symbolic music score, providing a substrate for both philological analysis and computational tasks. Music features are therefore well-captured by graph geometry and its properties. This representation has proved effective for analytical tasks as cadence detection, voice separation, and stylistic classification. In the present work, the reduction of harmonic complexity of a music score on graph, by preserving task-relevant information, relation between notes, and graph structure is investigated. A compression scheme for the piano subgraph of vocal-pianistic scores, built on binary wedge partitioning trees, is proposed. The wedges are generated through a fully adaptive greedy algorithm that recursively minimizes the $L^2$-error within a six-dimensional Tonnetz embedding of musical notes. The partitioning process employs a splitting criterion based on harmonic distance, resulting in regions that accurately reflect the intrinsic harmonic relationships among notes. The reconstructed music scores obtained through piecewise-constant functions and the mean values of the notes inside each wedge are used as a new simplified scores human-readable and playable. Some experiments on a corpus of symbolic music scores of three different composers are performed to assess the proposed approach.
