学习到的和弦嵌入中涌现的调性结构及其与调性张力的关系
Emergent Tonal Structure in Learned Chord Embeddings and Its Relation to Tonal Tension
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中文总结 AI 辅助
本研究探讨skip-gram和弦嵌入如何反映调性结构，发现基于移调的增强嵌入能恢复五度圈结构，并有效捕捉调性张力的结构方面。
中文摘要 AI 辅助
为分析西方调性音乐中的调性结构，已有多种调性音高空间和计算模型被提出，其中许多基于音乐理论原理，并用于支持对调性张力具有重要意义的调性分析。与此同时，诸如skip-gram之类的数据驱动方法已被用于从符号语料库中学习和弦嵌入，但它们在恢复调性结构及其与调性张力关系方面的能力仍未得到充分探索。在本研究中，我们探讨了skip-gram和弦嵌入如何反映调性结构，以及它们是否为分析调性张力的结构方面提供了有用的基础。使用带有和不带基于移调的增强的和弦序列，我们从几何、功能和张力相关视角评估了学习到的空间。我们表明，增强后的嵌入表现出强烈的移调等变性，恢复了清晰的五度圈结构，并支持学习到的空间中与调性相关区域之间的可解释移动。然后，我们从和弦到调性的距离和上下文和弦距离关系中推导出基于嵌入的度量，并表明它们通过与匹配的调性度量相对应以及与人类张力曲线适度对齐，捕捉了调性张力结构的有意义方面。在所有分析中，基于移调的增强通常提高了学习到的空间的稳定性、调性连贯性和可解释性。
英文摘要
Several tonal pitch spaces and computational models have been proposed to analyze tonal structure in Western tonal music, many of them grounded in principles from music theory and used to support tonal analysis with important implications for tonal tension. In parallel, data-driven methods such as skip-gram have been used to learn chord embeddings from symbolic corpora, but their ability to recover tonal structure and its relation to tonal tension remains underexplored. In this work, we investigate how skip-gram chord embeddings reflect tonal structure and whether they provide a useful basis for analyzing structural aspects of tonal tension. Using chord sequences with and without transposition-based augmentation, we evaluate the learned spaces from geometric, functional, and tension-related perspectives. We show that augmented embeddings exhibit strong transposition equivariance, recover a clear circle-of-fifths structure, and support interpretable shifts between key-related regions of the learned space. We then derive embedding-based measures from chord-to-key distance and contextual chord-distance relations, and show that they capture meaningful aspects of tonal tension structure through correspondence with matched tonal measures and moderate alignment with human tension profiles. Across analyses, transposition-based augmentation generally improves the stability, tonal coherence, and interpretability of the learned space.
