A Multidimensional Model for Quantifying Tonal Strength: A Continuous Framework of Analyzing Tonal Evolution Beyond Tonal-Atonal Binary Classification
Tonality is a fundamental organizing principle of Western music. However, the gradual transition from common-practice tonality to atonality around the turn of the twentieth century cannot be captured by binary labels. To characterize intermediate tonal states and trace this evolution, we propose a multidimensional framework for quantifying tonal strength, grounded in tonal theory and mechanisms underlying tonal dissolution. This framework operationalizes the global statistical regularity, temporal coherence, and local perceptual alignment of tonal organization through three complementary features: pitch-class distribution uniformity, temporal stability of tonal centers, and local tonal clarity, respectively. To validate the model, we introduce two new datasets: a binary dataset comprising 196 tonal and atonal pieces, and a historical MIDI corpus of 1,561 compositions by 21 composers spanning the Baroque era to the early twentieth century. The proposed model achieves high discriminative performance on the binary classification task (F_1=0.985), and quantitatively reveals a continuous historical trajectory from established tonality through progressive weakening to eventual dissolution. Computational analysis of representative composers further confirms significant declines in tonal strength throughout the careers of late-Romantic and modernist figures. Additionally, analysis of EMOPIA dataset reveals a weak but statistically significant positive correlation between higher tonal strength values and positive emotional valence. This work establishes a unified quantitative model for analyzing tonal evolution and provides a continuous measure for future behavioral and neurophysiological investigations of the relationships among tonal organization, musical emotion, and cognition.