Uniqueness on a Continuum: Quantifying Tonal Ambiguity Using Information Theory
This work provides a new analytic tool for music theorists and analysts to quantify tonal ambiguity across pitch-class sets and tuning systems.
The authors propose a continuous measure of tonal ambiguity based on information theory, extending the concept of uniqueness to address its limitations in discriminating among tonal sets, capturing hierarchical organization, and accounting for temporal unfolding.
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.