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.

翻译：我们提出一种连续的调性模糊度度量方法，它扩展了已确立的"唯一性"概念。虽然唯一性被广泛视为调性存在的必要条件，但它无法：（一）区分具备该属性的不同集合；（二）捕捉有限移位模式中的层级组织；（三）解释时间性展开。为克服这些局限，我们引入一种基于信息论的配套度量，能够在连续尺度上量化调性模糊度。该度量方法适用于各类音高集合与调律体系，拓展了对调性关系的分析覆盖范围，为理论与分析实践提供了实用工具。