用信息论量化音高集合的调性模糊度，实现连续测量。
Uniqueness on a Continuum: Quantifying Tonal Ambiguity Using Information Theory
- 基于信息论构建连续调性模糊度量
- 可区分具相同唯一性的音高集合
- 适用于不同律制与时间演变分析
我们提出一种连续的调性模糊度量，扩展了传统唯一性概念。尽管唯一性被广泛认为是调性的必要条件，但它无法（i）区分具有该性质的音高集合，（ii）捕捉有限转位模式中的层级结构，或（iii）反映时间上的展开过程。为解决这些局限，我们引入一个基于信息论的互补度量，可在连续尺度上量化调性模糊度。该方法适用于各类音高集合与律制系统，拓展了调性关系的分析范围，并为理论与分析提供实用工具。
原文摘要 · Abstract (English)
We propose a continuous measure of tonal ambiguity that extends the established concept of uniqueness. While uniqueness is widely regarded as necessary for tonality, it cannot (i) discriminate among sets that possess it, (ii) capture hierarchical organization in modes of limited transposition, or (iii) account for temporal unfolding. To address these limitations, we introduce a companion measure, grounded in information theory, that quantifies tonal ambiguity on a continuous scale. The measure applies across pitch-class sets and tuning systems, expanding analytic coverage of tonal relationships and offering a practical tool for theory and analysis.
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