Uniqueness on a Continuum: Quantifying Tonal Ambiguity Using Information Theory

TL;DR

This paper introduces a continuous, information-theoretic measure of tonal ambiguity that overcomes limitations of traditional uniqueness, enabling nuanced analysis of tonal relationships across systems.

Contribution

It presents a novel, continuous measure of tonal ambiguity based on information theory, applicable across pitch-class sets and tuning systems.

Findings

The measure captures hierarchical organization in modes of limited transposition.

It applies across various tuning systems, broadening analytical scope.

Provides a practical tool for musical theory and analysis.

Abstract

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.