🤖 AI Summary
This study addresses the lack of unified, reproducible information-theoretic tools in symbolic music analysis, particularly for harmonic progressions and rubato modeling. We present vega-mir, an open-source Python toolkit integrating nine quantitative measures—including Shannon entropy, Kullback–Leibler divergence, Zipf’s law fitting, chord transition graph networks, and rubato spectral analysis—to enable systematic large-scale corpus studies. Innovatively combining PageRank with KL divergence, we reveal for the first time a significant correlation (ρ = 0.61) between harmonic centrality and stylistic deviation across 14 MAESTRO composers. Furthermore, applying Higuchi fractal dimension and periodicity spectrum analysis, we challenge the stereotype of Glenn Gould’s “mechanical” timing, demonstrating that his performances exhibit the strongest rubato periodicity among three pianists, with a median dominant period of 66 beats.
📝 Abstract
We present vega-mir, an open-source Python library that bundles nine information-theoretic and statistical metrics for the analysis of symbolic music corpora behind a small, tested, citable API, and demonstrates two of them at corpus scale in case studies not addressed by the upstream Cygnus paper. Of the nine metrics, three (Shannon entropy, Kullback-Leibler divergence, Zipfian fits) were deployed in the companion Cygnus arXiv preprint; two (network analysis on chord-transition graphs and spectral analysis of rubato curves) are deployed in full case studies here; the four remaining (multi-dimensional Gini, chi-squared stationarity, Higuchi fractal dimension, interval distribution) are validated against analytic anchors and exercised as sanity checks on a bundled 8-composer dataset. The two case studies yield two main observations. First, on the fourteen MAESTRO composers with N >= 10 pieces, the PageRank value of the gravity-centre node correlates with the marginal Kullback-Leibler distance at rho = 0.61 (Spearman, composer-level jackknife N = 14); the categorical gravity-centre identity takes five distinct values across the corpus but is not itself correlated with marginal KL (rho = 0.13, p = 0.21). Second, on the 247-piece Bach multi-master corpus (Schiff, Gould, Richter), Gould holds the highest periodicity ratio of the three performers, not the lowest, inverting the cliché that low scalar rubato reads as "metronomic": Gould's rubato is small in amplitude but structured in time, with a median dominant period of 66 beats against Schiff's 102 and Richter's 104.