Abstract
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We propose a new model drawing on the concept of the Tonnetz -- we define two partially independent measures: \emph{tonal focus}, the concentration of pitch content near a tonal center; and \emph{tonal connection}, the degree to which pitch content reflects structured intervallic pathways back to that center. Analyzing over 2,800 pieces from Western classical and popular traditions, we find that these traditions occupy overlapping yet distinguishable regions of the two-dimensional space. Popular music shows higher tonal focus, while classical music exhibits higher tonal connection. Our complementary measures ground the differences between different tonal styles in quantitative evidence, and offer interpretable dimensions for computational music analysis and controllable generation.
Abstract (translated)
不同的音乐传统如何实现调性统一？迄今为止大多数计算方法仅从单一维度分析调性统一，而多维度分析尚未得到充分探索。我们借鉴音网（Tonnetz）概念提出新模型，定义两个部分独立的度量指标：**调性聚焦**（tonal focus），指音高内容在调性中心附近的集中程度；**调性关联**（tonal connection），指音高内容反映回归该中心的规则化音程路径的程度。通过分析2800余首西方古典与流行音乐作品，我们发现这些传统在二维空间中占据重叠但可区分的区域。流行音乐表现出更高的调性聚焦，而古典音乐呈现更高的调性关联。这些互补性度量指标为不同调性风格的差异提供了量化依据，并为计算音乐分析与可控生成提供了可解释的维度。
URL
https://arxiv.org/abs/2603.27035
