Sectional Structure and Emotional Dynamics in Chinese Pop Songs: An Empirical Analysis of Valence-Arousal Trajectories across 100 Songs

A common intuition holds that a region's music mirrors the temperament of its people, so that melancholic melodies mark melancholic populations. We test the measurable half of that intuition and reject the inferential half. Using the Essen Folksong Collection, a corpus of thousands of notated folk melodies, we extract real melodic and affect-related features from 2393 deduplicated melodies spanning 16 countries and 7 geographic regions, with the analysis performed on symbolic scores rather than audio. The mode of each melody is computed with a key-finding algorithm rather than read from the file, because the collection's own documentation warns its major and minor labels are unreliable. Cross-country differences in melodic structure are large and highly significant. All 8 tested features differ across countries at p<0.001, with the leap-related features reaching p<10^-90, and China carries a distinctive wide-leap, high-activity signature (arousal composite +1.24 standard deviations, mean absolute interval 2.77 semitones against Germany's 2.17). We then test the inferential half. We correlate the regional musical-affect measures with two published, validated national indices, the World Happiness Report ladder score and the Hofstede individualism index. None of the 6 correlations is significant (0 of 6). The geography of musical affect is real and measurable, but it does not predict how happy or how individualist a population is, and any claim that it does is an ecological fallacy. We release the full extraction and analysis pipeline, and a fail-closed checker re-derives every number in this paper from the data.

Music is often used as a medium for communicating emotion, with performers shaping perceived affect through interpretation. This study addresses the challenge of identifying and predicting subtle changes in perceived emotion that are exclusively due to differences in performance. We focus on classical solo piano music, using a set of 6 commercial recordings of Bach's Well-Tempered Clavier Book I, annotated in terms of valence and arousal. By encoding the recordings through performance-specific features only, we isolate performance information from aspects of the composition itself, which tend to dominate the overall perceived emotional category. A preliminary analysis validates that these features vary meaningfully across performers. We then propose a relative regression framework, Delta-VA, to predict deviations in valence-arousal relative to an ``average'' performance, thereby focusing on the changes in emotion brought about by a specific way of playing a piece. In addition to the standard $R^2$ regression score, we introduce geometric evaluation metrics to assess the preservation of pairwise differences between performances. Results indicate high directional consistency with the ground truth, but also a compression in prediction magnitude, indicating that the model tends to underestimate expressive performance effects.

Statistical modeling of popular music presents a unique challenge due to the complexity of song structures, which cannot be easily analyzed using conventional statistical tools. However, recent advances in data science have shown that converting non-standard data objects into real vector-valued embeddings enables meaningful statistical analysis. In this work, we demonstrate an approach based on logistic principal component analysis to construct embeddings from global song features, allowing for standard multivariate analysis. We apply this method to a corpus of Lennon and McCartney songs from 1962-1966, using embeddings derived from chords, melodic notes, chord and pitch transitions, and melodic contours. Our analysis explores how these song embeddings cluster by Beatles album, how songwriting styles evolved over time, and whether Lennon and McCartney's compositions exhibited convergence or divergence. This embedding-based approach offers a powerful framework for statistically examining musical structure and stylistic development in popular music.